Force of Destiny


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Logic Law


Dismantling Spin

Arguments and rebuttals.

Fallacies – Classical
Courtesy of Dr. Michael C. LaBossiere

Fallacies1 Classical
Courtesy of Stephen Downes

Contextual inferencing

Fallacies of Conduct

Critical thinking .. Venn Diagrams

Dave Straker's,
A-Z, huge List of Fallacies
More.... New sections coming, with the rise in semantic presuasions, especially through legal power structures with the help of 'think tank' advisors, these tools are vital in the argument forms that LIE ahead and against the innocent, and those who want these disciplines . Ignorance of the law is no excuse, is a worn out phrase from lawyers that suggests they can take unfair advantage of you, where their integrity is lacking and trusting them, no longer may be relied on. All these argument forms are taken from real live court / tribunal cases.
Unambiguous Contextual Inferencing
.
Class Immediate Inference




The elements of Logic, its uses and applications.

Hunt the proposition, and point out the fallacies”.

A thorough treatise and guide.

From and for practical use in everyday life.

New and modern fallacies. A new beginning.
New and modern fallacies. A new beginning.
Tony's Complex Fallacies. 
Tony's Irrelevant Thesis. (1) ( 'Ignoratio Elenchi.' )
Tony's Begging The Question.(2) ( 'Petitio Principii.' )
Two of the most common and widespread fallacies being thoroughly 

exposed in depth from British Judicial bodies. Wilful deception dismantled 
from real life tribunal examples. A disgrace to British Human Rights. 
Simply Human frights. How this is all done, with PR spin semantics
word order, prominence, negation, loaded generalised terms 
and amalgams of selection and ignoration 
Page 1
Page 2
NEW FALLACIES Here and Coming.
Complex. With thorough disambiguations.
False prominence, amphiboly, sentence modifying adverbs in negation, 
that are anti-logical and indeterminate truth on a truth table.
One Transport for London paragraph disambiguated.
Two Greater London Authority letters disambiguated.
Three The ONE LINE fallacious construction willfully pursued.
      

What is Logic

The three Laws of Thought

Matrix Truth Tables

Scientific Method

Legal Maxims

Caselaw .. Jokes

Main list of fallacies
Left Navigation Bar, see A-Z of fallacies


Questor © 1999. These pages are copyright and free for personal or academic use. Questor © 1999

They may not be used for profit, without express permission of the author, Tony Winter.

A very different Fallacy list by Questor ©

Fallacies of conduct. Click fallacy above or 13 below.


Get the primer free for your computer, a pdf file click here.....

Practical Logic, by Questor ©

A completely new set of 100 modern fallacies starting here.

A guide to formal clear reasoning, the laws of thought, practical usage & anecdotes


Chapters ready for reading have 1st letter in Pale red as Preamble.

  1. A General Introduction and Preamble on Sentences, Propositions & Fallacies with legal anecdotes.

  2. What is Logic? An easy quick primer at 'O', 'A', level and beyond.

  3. Aristotelian Logic and Syllogisms. Framing a question that gets closer to the truth.

  4. Formal Logic.

  5. The Three Laws of Thought.

  6. Minimal Truth tables.

  7. Disjunctive and Conjunctive Truth Tables, the Scientific Methodology.

  8. Essential tools of Integrity.

  9. Venn Diagrams and Boolean logic explained.

  10. Knowledge, Truth, Probability and Belief.

  11. A brief look at the nature of Knowledge and TRUTH as opposed to belief.

  12. A few unacceptable consequences of formal reasoning

  13. A look at the more complex calculus of logic.

  14. THE 'sui generis' Fallacy list by Questor © to augment the one on this site provided by Dr. La Bossiere.

  15. Instant recognition of fallacious forms in tone, fraudulent questions with purpose and the like.

  16. Affirmations are of some, but little advantage, resolving inconsistencies, and denials are the key.

  17. Glossary of Terms.

  18. Annex.

  19. Index



Introduction.

I have not restricted this treatise to the customary boundaries of theoretical disciplines, for two reasons.


  1. While they illuminate differences in specific areas, they tend to narrow the field of view from what otherwise is visible by non categorisation. Eg:

  2. Take for example Knowledge and Belief, Truth and Falsity. Too much focus on the categorisation leaves otherwise very interesting notions unexamined. In the two categories just mentioned, one would overlook a fascinating correlation between Knowledge and Truth that may fail to be seen by focussing on the separate concepts in the customary manner. Such that Knowledge cannot exist without its being the truth, otherwise it is no longer meaningful in its context, since what was formerly presumed to be knowledge turns out to be a belief, which is a vast and essential distinction bringing about the downfall of what is essential and at the heart of epistemology.

  3. Contrarieties and contradictions in speech acts and their corresponding real acts, the 'actus reus'. Also become sidelined. So that when a judiciary states it has a policy of NOT repealing major constitutional statutes, impliedly, but will follow the well trodden path of doing it expressly, and THEN fails to expressly repeal a prior constitutional act, when it is inconsistent with a later one, BUT introduces laws that have the precise implied repeal that is pariah, the government is seen clearly to have said in law, 'de jure' what is does NOT do in reality, 'de facto' which is a contrariety closest to the pure form of contradiction, indeed in some cases a pure contradiction and simple hypocrisy. Thus contradictions and contrarieties exist outside the realms of written and spoken acts, sentences, and propositions, they involve conduct, behaviour, integrity, hypocrisy, lies, and so on. The fallaciousness is not merely to be found in formal logic, it is everywhere there is communication with terms that have well established meanings, senses and references, that should correspond with reality. This has caused our once leading nation to fall from grace. Few people are strong enough in their assertions to state anymore they KNOW something, but have become constrained to speech acts of 'I believe', placing enormous strain on credibility. There are many things the average person who formerly said they know X, like I know I had egg and bacon for breakfast today, when put the proposition 'it all might have been fake food combined with hallucinatory perception', choose to say I believe I had egg and bacon, rather than 'ceteris paribus' ( all things being equal ), that IS what I ate, and I know it along with all the other things that make up life as we know it, essentially that the efficacy of building houses and motor cars, would all crumble to dust if they didn't work or stand up against the winds. These artifacts have to be the results of knowledge rather than belief, and reality rather than illusion. Knowledge exists in the same way that 'cogito ergo sum', I think therefore I am, Descartes leads us to KNOW that we exist, because NON-existence is not consistent with cerebration.

Go straight to the Fallacy list.



  1. A General Preamble on Sentences and Propositions with legal anecdotes.


  1. Unusual words are hyper linked to their definitions in an internal glossary ( OED primarily ) to save the reader's time and ensure fidelity with the precise

  2. meanings intended while avoiding ambiguity.

  3. Logic in sentences is to be found by examining their propositional forms. A proposition is the literal meaning of an indicative sentence, therefore rule out examining sentences whose forms might be exclamatory, allegorical, questions, commands, meaningless and the like, although at some level, many propositions may be found in these forms, the meanings may be obfuscated by a play on words, puns and emotive content.

  4. What is an indicative sentence? It is a sentence that denotes (or purports to denote) a fact. The discipline 'On denoting' is a department of philosophy, in its own right, just as questions like “What is a fact?” , What is Truth?” and “Is existence a predicate?”

  5. Find two propositions at different times in your opponents testimony, sworn evidence or affidavits, that are fallacious,

  6. and ask him how he resolves the inconsistency, OR

  7. ask him to show how he resolves them to be jointly true, or else admit to the contradiction and take responsibility for it, OR

  8. point out the fallacy of reasoning,and ask him to desist from such assertions that fail to conform to proper reasoning.

  9. You will find invariably that in casual daily conversation, the average person commits many fallacies of reasoning, in their pursuit of either an agenda, or some form of persuasion they are working on.

  10. It all began with abuse, invidious prejudice and derogation and a want of knowledge in Law, but a good working knowledge in Logic.

  11. HERE are several real life cases in law with fallacious logic, that show how the art of questionable advocacy can be defeated with sound reasoning.

  12. I was stopped by a policeman in central London; this is true, who said:

  1. the reason he stopped me was that my tax disk was not displayed on the windscreen”. Call it proposition P1.

  2. Subsequently in a sworn section 9 statement for truth, he said “the reason he stopped me was, I was driving without wearing my seatbelt correctly”; call it proposition P2.

  3. while the ticket he gave me for the offence stated I was driving without wearing a seatbelt, and in a subsequent PCA complaint investigation, he admitted the truth of P1, corroborating my own statement, and added that he then noticed the seatbelt was not worn correctly.

  4. It follows unequivocally from all this context, that I was stationary while he determined the status of my seatbelt; overlooking a vital sequence of events, and the ticket issued was perjured, and inferring erroneously, that I was driving in the same manner before he stopped me.

  5. The investigating member of the PCA ( Police complaints authority ), was no longer with them; after I pointed out the contradictions, and by the time I wrote to ask about the delay in responding, I was replied to by Sir. Alistair White, stating the investigation could not be continued for the absence of that member and the now too long time between. You should draw your own unequivocal conclusions from these attested depositions at this point, but this is to the purpose of a dissertation in logic rather than an exposes of a fallacious and statistically failed system of justice in unaccountable bodies. The fuller story is at http://logiclaw.co.uk/page6.html

  6. I had been closely monitored by up to 17 police in a carefully sequenced; filmed by myself, focus on my activities while having a video in my car.

  7. The magistrates hearing of course resulted in a withdrawal by the Crown Prosecution Services as my presence upheld costs of £625 for the deplorable affair.

  8. Many of the propositions drawn from the deposed sworn statement were not merely fallacious, but denoted a mind in want of formal education in grammar, reasoning and integrity of conduct under PACE 1984.

  1. After a successful injunction service, a defendant tried to avoid paying the £200 of the judges award, they succeeded, at a cost of about £3500,was that a price to pay, see for yourself?

  2. How logic overturned a defence by Amtrak Express Parcels Ltd, using the problematic Privity rule of 1861. They continue to plunder the unwary in their entitlement to refunds.

  3. How emotive issues and scoring points got in the way of sound reasoning at the Local Government Ombudsman in 2005 who got themselves into a contradiction and made fools of themselves at every level.

  4. Here is one fascinatingly ridiculous assertion by a person on a legal form, who averred he was lawyer,and a good one. I quote.”The law does indeed say that "and" can mean "or" and that "or" can mean "and". When questioned as to his authority for such an averment, he produced a URL { containing the terms opinions, lo morales [sic] } that related to a US attorney's argument, rather than a proper source of integrity, made by a Judge, in case law. All of that was propounded against my putting before him seven high authorities of unquestionable soundness & integrity in UK case law since 1891. He would not give up, convinced that and means or and vice versa, sounding like No means Yes in that we are referring to the YES side of NO, (as in the BBC Chambers comedy), so I revealed to him that if that was the rule, then where I owed a debt that could be settled by money 'and' interest, ( say £100 plus interest of £5 ), when it come to settlement date, I only have to say that 'AND' means 'OR', so I can settle the debt with the mere £5 ONLY. How convenient! He had no answer, this personal new trend in advocacy is hilarious, but beware it could be convincing to a non analyitic mind, to which it is aimed.

  5. The above examples will be used in varying forms to show how one should examine, and record where possible, these statements by persons in comparative authority, in attempts to derogate and abuse the advantageous asymmetry of information in their field of expertise,as opposed to yours.

  6. FASCINATED? I can assure you if you are interested, this preamble will not resolve things, but it should open them in such a manner that, henceforth, you are more likely to keep an open mind on all things SAID, for most of your time.




  1. What is logic?

  2. First the short, then longer definition. OED 1. a. The branch of philosophy that treats of the forms of thinking in general, and more especially of inference and of scientific method.

  3. The beginnings of some of this type of reasoning was earlier than Aristotle, but he and several others are a landmark in time, over two thousand years ago. Parmenides, (b 510 BCe) first considered the distinction between opinion and truth, Truth being what IS, and Opinion being errors in the first assumption.

  4. Aristotle (384 BC) defined Truth as:

    To say of what is that it is not, or of what is not that it is, is false,

    while to say of what is that it is, and of what is not that it is not, is true”,

  5. but this concern with Logic picks up the topic whose essence was in the deduction. A deduction follows necessarily from several things that are supposed, namely premisses, that are considered to conform with reality. How did we get at reality in those days? Simply by taking the blue highlighted proposition above that is more than entirely reasonable for that time. So we are primarily concerned with deductions that follow from premisses whose truth somehow follows the notion derived above. Once this became better defined, it was clear that the truth of the premises, while important, had no longer a central role, what was more important, was the process of reasoning, whatever the veracity of the premisses. The beginnings of a calculus of logic, much like mathematics, and algebra, where variables could be substituted by whatever propositions one wished, and the deduction that followed was necessary, but its truth or correspondence with reality was a separate and entirely new discipline,of the validity, or verifiability of percepts. This while opening a new methodology of scientific procedures also opened a new discipline of doubt, where language became a tool for treating the new found doubted percepts in a class of seeming, appearances. Lost was the former certitude of knowledge, and welcomed in was the new disciplines of persuasion, and brain washing of masses of people to fallacious conclusions, derived from perfectly sound reasoning principles. You need of course at this moment some examples. Simple two premisses and a conclusion types.

  6. All single men are bachelors, John is a single man, conclusion – John is a bachelor. The key term here is single. Single being part of the definition of a bachelor. NOW.

  7. A sleight of hand was used here, to contribute to the certainty of the conclusion, but it wasn't needed. This was achieved by using the middle and predicate terms that was a pure definition anyway. Take away that certain, and you will see the conclusion remains CERTAIN. The reason is that the certainty is embodied in the principle of the MIDDLE term being transitional between 1st and 2nd premisses.

  8. Begin again.....All men are mortal, John is a man, conclusion – John is mortal. The key MIDDLE term here is men, and the predicate is mortal. When the middle term term gets carried over, it compels of necessity the conclusion. Fallacies follow when one displaces the middle term and predicates, as you will see from this example of everyday common fallacies:

  9. All men are bipeds, All men are mammals, therefore, All mammals are bipeds. What? Or, all men are bipeds, some bipeds are female, therefore some men are women. What? Or else All bipeds are human, Sammy over there is a biped, therefore Sammy is human. What? I was pointing at a penguin called Sammy.

  10. All single male blue and green tigers are bachelors, Bigtooth is a single male tiger, conclusion – Bigtooth is a bachelor. The logic is the same, but the premisses are hopefully false, since there are no blue and green tigers, at least on this planet, and we don't normally regard single male tigers as bachelors, that is where the notion bachelor includes some notion of marriage.. Try another.

  11. All theatre tickets for last Saturday's performance of Hamlet, are no longer valid, this is a ticket for last Saturday's performance of Hamlet, therefore – conclusion, - this ticket is no longer valid. Clear? Because we normally understand the date to involve a date of expiry of validity.

  12. All theatre tickets for next Saturday's performance of Hamlet, are no longer valid, this is a ticket for next Saturday's performance of Hamlet, therefore – conclusion, - this ticket is no longer valid. Problem?..... We need an additional premiss answering the question why next weeks tickets are invalid, or at least our money back. The premiss is suppressed in the example, but on pressurising the speaker we may get........., the lead player is ill, or we cancelled the performance, or even we have a new rule, people that buy a week in advance are payers and losers. Truth and falsity of premiss's here depend on something different than ones own observations. Now the logic is fine,just as good as the perfect model in (i.) BUT the validity of the premiss's can't be so easily verified, by empirical means.

  13. NOW we move on to a similar example, where the conclusion is an outright lie, but the premmisses credible, for one simple reason, the speaker is assumed to be a person or body of authority, their label says so, and thus credibility resides in a false background premiss before we even begin. This is a relatively new and widespread phenomenon that is unequivocally and irrefutably a disgraceful abuse of logic and derogation on members of the public. A simple example; The local council spokesperson for a NOW relabelled Local Authority, using a computer statistical and seasonal model for extrapolating data concerning the number of wheel clamps they have applied to vehicles in relationship to their target number for the year says...... “We are concerned with the disproportionate nature of penalty to offence on immobilisation of vehicles, and are doing something about it”. (premiss 1). “We are happy to say that the rate of clamping is now under control and slowing down”. (premiss 2). No conclusion is provided, deliberately leaving that for the listener to instinctively use sound principles of logic, and work out the conclusion that feeds their hopes, but satisfies the councils? appetitive for more. The lie is suppressed, (suppressio veri), and relates to the time of year when the holiday season has commenced, and there is invariably a slump in clamping correlated with more people being abroad. The reasoning process leads one to feel better as the situation is gong to be more humane than at present. There's only one phrase for this,

{ Hamlet. Excellent, i' faith; of the chameleon's dish. I eat the air, promise-cramm'd.

You cannot feed capons so. }

  1. HOW on earth does one deal with this profusion of mental detritus coming at us, in the declining years of health for the planet, and peoples mental acuity. It is a major problem that is NOT solved by this kind of alarming derogation and subtraction of an electorate equally brainwashed into re-electing the same people time and again, when the ideology has little to do with the personal appetites for abuse of power. You have to look at the nature of each proposition, and its reliance on empirically verifiable reality. If the details are manufactured by the body delivering the speech act, then DOUBT it. If there is a discernible agenda like for example, the speakers wishing to aggrandise themselves, then Doubt it, and equally if there is revenue behind the whole operation, don't merely doubt it, you might as well take it that THE OPPOSITE is more likely to be true............


I hope this brief introduction to the basic logical principles has been enlightening. The conclusion you can reasonably draw from the main thrusts of my arguments above is:

  1. Sound logic, is absolutely required, most of us know it instinctively , but there are also many in power who don't even have the wit to use it in the manner I have shown, they don't even reason logically, and I have reliable evidence in my legal cases of exposure of authority, elsewhere on this site, to rely on to show that logic in authority is visibly and palpably on the verge of collapse, where simple contradictions are marinated against all convincing force of logic merely on the grounds that the deliverer of such ridiculous assertions has the label of authority that stamps their statements with 'credent bulk'. This adds to the decline of the planet and of mankind in general.

  2. It IS essential that in deriving any form of conclusion from assertions delivered, from a rostrum, that the paper that is being generally read from, or the teleprompter, is a paper that has formulated and manufactured the speech for a purpose and with profound consideration given to the way each word, act as touchstones to the mind, and its associative complexes to drive the will of independent minds towards a conclusion they probably already wish by merely being a listener of such or such a particular speaker. Its regarded as almost axiomatic that one can be convinced of the existence of God, when one wishes to be so convinced beforehand.

  3. The third consideration is an amalgam of all possible influencing factors that throw a hue, slant or nuance on plain utterances that are loqutionary,a s opposed to illocutionary or perlocutionary. Such factors are agendas of revenue, maintenance of a status quo, control of people's minds, achievement of objectives or goals decided behind closed doors, not stated on manifestos, and such like background factors.

  4. The next area of malfeasance is that residing in the manner of advertising and persuasion. If persuasion has to be involved, then there is an agenda behind it. People don't need persuading, we can all think reasonable well for ourselves thank you. Consider when one states “to tell you the truth”, and how such an assertion normally touches the mind. If one wishes to believe, then one shall. But to presage any statement with such self approving verification is to be very seriously doubted. The first sign of a lie is when someone tells you they are going to tell you the truth. Hence when a body such as the Local Government Ombudsman, advertises you can come to them for reporting maladministration, and councils also advise if you are remotely unhappy you can take your complaint to them, you need to consider to what degree that body is accountable, and its composition. When you discover it is NOT accountable, and its composition is from former Chief Executive Officers of local councils, I think a reasonable person would doubt it that's the place where maladministration can exposed, rather than simply reported... note the distinction. Indeed their byword is they can only investigate maladministration IF injustice has occurred, which should sway it ll. Forget about maladministration being investigated, its consequences are the only reason for investigation. Thus it can continue unfettered so long as the invisible injustices are side stepped.

  5. At this juncture I think my own agenda is showing clearly. Plainly stated it is, I don't mind games and semantic jokes, but I dislike semantics used to cloak abuse and conferment of detriments on the weak and vulnerable......intensely! For this reason, and little other, the extent and depth of this treatise on all the pages of these associated sites. The world of illusions we are increasingly surrounded with, is the worst possible tool of integrity for safeguarding our future. To perhaps think of a parallel, I suggest if any reader is familiar with the film matrix, then that portrays in modern terms such a world of illusions where the body public is farmed for its energies, to no particularly good purpose that could not otherwise be achieved by consent, co-operation, sincerity and truth. That is perhaps the legacy I should like to leave in these works.

  6. The primitive notations and their linguistic equivalents very quickly explained.

Essentially we are looking for sentences whose forms include formal concepts such as: 'not', 'and', 'or', and 'if ..... then ....' with the propositions referred to as 'P'. The standard notation for these functions are in red below, and shall be repeated where appropriate.

  1. 'not' = '~',

  2. 'and' = '·' ,

  3. 'or' = '' Ú', and

  4. 'if ... then = 'É' if P then Q, 'if ... then = '' if P then P or P is the same as P, where 'P' is a proposition

  5. 'P' is a propositional variable.


  1. These are primitives of the relational functions between elements of as well as propositions, examples like these are simple and plentiful in everyday speech.




  1. 3. The Three laws of Thought.

  • As Aristotle wrote them, they are as follows:

  • (1) Law of Identity: Each existence is identical with itself;

  • (2) Law of Non-contradiction: Each existence is not different from itself; and

  • (3) Law of Excluded Middle: No existence can be both itself and different from itself.

These have been re-arranged in order of interest and treatment. Note: the assertions assumes that existence IS a predicate of things, another complex question in philosophy. Compare them with the modern formulations below, (re-ordered in sequence of treatment), and then see HOW they can be tested in truth tables for certainty. No doubts, no ambiguities, no equivocations, sophistry, can, casuistry or other forms of mis or dis informational semantical delusions.

More formally these require brief explanation of the essential primitives of formal notation.

These are primitives of the relational functions between elements of as well as propositions, examples like these are simple and plentiful in everyday speech. Their formal notations you will see frequently in these sections are the following symbols...again in blue / red.

'not' = '~', 'and' = '·' , 'or' = '' Ú', and 'if ..... then = '' if P then P, or P is the same as P, where 'P' is a proposition.


  • 1. The law of NON-contradiction. ~ (P . ~P) { NOT the case that, P and not P are jointly true. }

  • 2. The law of excluded middle. P v ~ P { Either P is true OR not P is true. }

  • 3. The law of identity. P P { P is the same as P, itself. }



In modern language I suggest to make the sentences more common to everyday thought and speech the following may be easily understood. This order is also perhaps the commonest moving from easiest to more difficult., but hardly necessary.

All the following is considered under the notion “all things being equal”, ceteris paribus, and at the same time.

Don't confuse this with what appears to be an opposing notion embodied in Heraclitus's theory of flux “ One cannot step into the same stream twice”.


  • (1) Law of Identity: A thing is identical with itself;

  • (2) Law of Excluded Middle: A thing IS either identical with itself or NOT identical with itself.

  • (3) Law of Non-contradiction: It is not possible for a thing to be BOTH ( identical with itself AND NOT identical with itself).

Placing these forms in a truth table matrix it's easy to see at a glance they are true propositions without any reference to reality, hence the variables P may be substituted for any proposition.




Get the primer free for your computer, a pdf file click here.....


  1. 4. The Three laws of Thought.

  • The modern notations and formulations, they are as follows:


'not' = '~', 'and' = '.' , 'or' = ''v', and 'if ..... then' = '' if P then P, or P is the same as P, where 'P' is a proposition.

--------------

The short logical set of primitives.

'not' = '~',
'and' = '
.' ,
'or' = '
v',
'if ..... then' = '
>' , P > Q, BUT WHERE P ''P.

It must be noted that P > Q is a contingent proposition (on states of affairs in the world), and P '↔'P is a tautology, (true at the same time and in the same sense, for all truth values of any contingencies).

if P then P, or P is the same as P, where 'P' is a proposition.


  • 1. The law of NON-contradiction. ~ (P . ~P). P and not P cannot be true together.

  • 2. The law of excluded middle. P v ~ P. Either P is true or not p is true.

  • 3. The law of identity. P P. P is the same as P, itself.


--------------


  1. P is any proposition, and its substitution in the expression is immediately governed by the law.

    1. A Proposition is the 'literal meaning of an indicative sentence,' eg; “this is a fire,” “the horse is black.”

    2. If your sentence is not literally indicative; like Fire! that is essentially a 'sentence word', then translate it, or the indicative clause, literally as in; “this is a fire”. It could be also “there is a fire; take care and run away from it.” But you only want that part that is literal and indicative, not the part that is a command, suggestion or exhortation or other such grammatical moods. Note: the meaning of the word Fire! will depend on context, either written or circumstantial. If the circumstance is a firing squad or sport competition, then Fire! may mean either “shoot to kill” or “shoot to start the race.”

  2. Thus the proposition shall remain valid throughout its substitutions. Eradicate ambiguities.

  3. Look at 1. above; ~ (P . ~P).

    1. It is not possible for ( “this is a fire.”, AND NOT “this is a fire.” ) to be jointly TRUE.

      1. Similarly for “the horse is black.”

    2. Adversarial exchanges can be caught, and taken to court, using this method to take out semantic, Neuro Linguistic Programming, Semantic Priming, and Public Relation brainwashing with comparative ease. The methodology will be explained in another section, to be linked here soon. Two major fallacies in common use are explained already in depth from British court's o'flaw, where the packs o'flies are disambiguated with pinpoint accuracy. Begging the Question, and Irrelevant Thesis.

  4. In 2. above; P v ~ P.

    1. Either “this is a fire.”, OR NOT “this is a fire.”

    2. NOTE: there are no degrees, between P and ~P. If P is false, ie; “this is 100 apples” is false, then, where “this is 99 apples” is true, it follows incontrovertibly that IF the second expression '99' is true, then '100' is categorically false.

    3. In many cases where seemers, deemers, and purporters argue that '75' to '99' is substantially '100', a student pass mark at 45, is deemed a pass at 42, the 'moving the goalposts' is anti logical and irrational. It also discloses the bias inherent in bending truth, fact and reality. However this is the manner that fallacious 'authority' conducts decision towards itself, and disfavours others. Decisions that affect subordinates are handled in this way, completely overlooking the scales of equitable exchanges by false focus, and emphasis. Thus minor infractions that are punishable in law, are emphasized as 'contraventions' and punished; as seemingly serious, ( wrapped in grave countenance ) but are actually trivia, while major infractions by 'authority;' that is 'authority in the terms of power, force, or money; as opposed to intellect, are trivialized.

      Shakespeare had this in a nutshell some 400 years ago.

      1. Because authority, though it err like others, Hath yet a kind of medicine in itself
        That skins the vice o' th' top.

      2. That in the captain's but a choleric word Which in the soldier is flat blasphemy.

      3. Hence shall we see, If power change purpose, what our seemers be.

      4. Your sense pursues not mine; either you are ignorant
        Or seem so, craftily; and that's not good.

    4. Our Genius Bard, here captures precisely the moment when a thing IS NOT itself; the law of identity, and shows us how 'seeming' so, is the guise and trick of it all, making something else, the same, in chameleon style, unlawfully. The semblance is not the same as Heraclitean flux, that shall be treated elsewhere. Intent at deception being the inner 'mens rea.'

      1. Many variants of 2. b), c) can be constructed with this insight;

      2. either you are honest Or seem so, craftily; ”

      3. either this is relevant Or seems so, craftily; ” (often used in the fallacy of Ignoratio Elenchi.) where plausible arguments gain possession of truth, where irrelevant, but in close guise and resemblance.

      4. The true test in fact and reality, is any example from say mechanical engineering. A metal structure has a hole precision bored, and a similar metal rod has to be inserted with say a tolerance of 10,000th of an inch. IF the rod is made 100,000th of an inch too large it simply will never fit. There are NO degrees of oversize that ARE or deem to be, that will never be!

    5. Either a female is pregnant or not, there is no such thing as a little bit pregnant. Truth and falsity are mutually exclusive concepts.


The proposition can be as long as is reasonable to understand and without ambiguity.


--------------


Inconsistencies: The first Law of Thought, the Law of NON-Contradiction. belongs to the class of tautologies, and you may recall the contradictory function shown in the preamble during the legal case.

In the calculus of logic there truth tables like the ones shown below, that provide a wonderful opportunity to prove the irrefutable nature of these laws. The laws are innate to thought, that is their essence belongs to thinking, and thinking in any manner contrary to these laws is mind bending. Take the law of non-contradiction.

The formal expression of this function of contradiction is shown in the table below.

In all cases of P being either true or false, the conjunction of the two is always false and best expressed by

~ (P . ~P) which is a tautology. See what a tautology looks like in the truth table below, next section.





  1. 6. Essential tools of integrity. (work in progress)




  1. 5. Minimal Truth tables.

Inconsistencies:

The first obvious Law of Thought, the Law of NON-Contradiction, belongs to the class of tautologies, and you may recall the contradictory function shown in the preamble during the legal case.

In the calculus of logic there truth tables like the ones shown below, that provide a wonderful opportunity to prove the irrefutable nature of these laws. The laws are innate to thought, that is their essence belongs to thinking, and thinking in any manner contrary to these laws is mind bending. Take the law of non-contradiction.

The formal expression of this function of contradiction is shown in the table below.

In all cases of P being either true or false, the conjunction of the two is always false and best expressed by

~ (P . ~P) which is a tautology.

First the truth table for the contradiction ( the left magnolia coloured two columns ), that easily shows that when P is true then not P is false and vice versa.


It is Not the case that P and NOT P are true together, begins with the conjunction of P and not P; (P . ~P)

and concludes ( the right pale blue and yellow coloured three columns ), that it is not the case that P and not P are true together. ~(P . ~P).

They show every logical result for a valid propositional form, where P is either true or false.

The two columns to the right side below are actually the truth table for the contradictory function.
The full law of non contradiction, three column set, shows that for every values of truth or falsity for P, the result is always TRUE. The yellow column

P

~P

T

F

F

T

It follows that the matrix below is for the negation of the contradictory function above.

~

(P

~P)

T

T

F

T

F

T


This shows unconditionally the proposition ~(P . ~P) TRUE for ALL the truth-possibilities of its elementary propositions and by virtue of its logical form. A statement that is necessarily true. Hence for all worlds, space and time, where there is THOUGHT, these formulations are necessarily true. Isn't that fascinating? Unlike laws of nature, that can be defeated, or at least understood so well as to utilise in a way that looks like defeat.


For example; Sir Isaac Newton's: The Universal Law of Gravitation states that: every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Understanding of which enables us to construct

mechanisms that as it were defeat gravity so that machines can fly. The differences between the laws of thought and laws of nature are simply and essentially, that the former do NOT require empirical observation to validate, merely requiring thought itself, where the latter require empirical determinations, and consequently may be subject to manipulation as in this example of say aircraft.


To conclude then, these are special laws, not subject to manipulation, and not subject to that previously qualified term defeat. Defeat is inconceivable, to re-iterate for a thing to be both itself and its own negation at the same time IS inconceivable, despite the possibility of entertaining the notion in the mind. Such may be the ponderable nature of what I deliver to the reader, while pressing forward, having considered this already more than sufficiently. Time is of the essence in this rule, since the moment a thing has traversed a measurable instant of time, it has altered, in accordance with the Heraclitean theory of flux that states that everything in the universe is in a state of ceaseless flux, from which was derived the notion that 'one cannot step into the SAME river twice' that requires a little thought to see just how. This is worth bearing in mind when considering such necessary truths, since the temporal significance does not affect the laws, but of course in reality where thought exists, these laws are considered irrefragable. I for one have not found that person who can reconcile a contradiction, and shall not wait for such.


An important comment is required here. When looking for contradictions with any proposition that may be substituted for the variable P1.

Anything that is NOT P1, can be the rest of the entire universe in space, time and objects of any reference. So if P1 is the proposition “This tabletop is rectangular”. All other things from “This tabletop is oval” to round, hexagonal, to seats, pianos, animals, vegetables, minerals and so on to infinity, while they are ALL NOT the first proposition, P1, they do not fulfill the condition of being NOT P1 in the required sense. They all are simply propositions OTHER THAN P1, namely p2, p3, q, q1, r, r1, r2 and tn......

We are only focussing on propositions that are the NEGATION of the original propositions. While that is not to say that the alternatives are useless in comparison, it IS to say that alternatives are not specifically negations. Where alternatives can come close to formal contradictions in the full blown sense is the temporal element in assertions that one proposition is true or false. I shall give a fascinating example of this, in a section 9, sworn police statement for truth, that came to be shown as a contradiction because two very different propositions were asserted to be both true to but could not possibly stand together as true simultaneously. It was known in any case that one was falsely manufactured to commit the contravention to some category of the paperwork in issuing a penalty, but even had it not been manufactured, and had been true, the two propositions could have been true together as different propositions, because they were different in nature and time. This class of inconsistency is the class of contrarieties, and you can take a short digression from here to see its application to a real life perjury case with a policeman with noting better to do on a quiet weekend than make mischief, and put me in my place.


A necessary truth, is a truth that is referred to as A Priori. Considered with due seriousness, it is also a truth that can be maintained at any time, in any space. Truths like this while not being very informative, are exceedingly valuable from the point of view expressed in the preamble above. Reasoning which carefully follows the rules of logic will be infallible in argument, particularly in a court of law, but also many situations where illogical persuasion (fallacies) is being attempted and refutation required.



The second Law of Thought, the Law of Excluded Middle.

This states that only one of the disjuncts, (alternatives) needs to be true, for the whole proposition to be true, as shown in the middle cell columns.


P

Ú

~P

T

T

F

F

T

T


The third law of Thought, the law of identity.


T

P

P

T

~P

~P

This states that

where P is true, it is identical with itself; ....... P ( P is the same as P ) and

where Not P is True, it is identical with itself; ....... Not P ( Not P is the same as Not P )


Disjunction and Conjunction.


They underpin the concept of scientific methodology, in the determination of causes, simple and complex.

An example of a simple causal relationship might be the conditional:

IF oxygen is a simple cause of life, then the presence of oxygen is necessary for life, IF and ONLY IF

the absence of oxygen is sufficient for the absence of life.


An additional truth table matrix is useful for increased awareness of the world of alternatives, and the functions of disjunction and conjunction.

The function of disjunction ( P v Q v R v S v T ) that states either P or Q or R or S or T is true.

and conjunction ( P · Q · R · S · T ) which states that P and Q and R and S and T are true.


For a disjunction of propositional alternatives that are not so much laws of thought, but better align with scientific method, (necessary and sufficient conditions in causal or nomic relationships) it is sufficient for ONLY ONE of the disjuncts to be true for the whole proposition to be true, and necessary for ALL to be false for the whole proposition to be false.

whereas in a conjunction of propositional variables it is necessary for ALL of the conjuncts to be true for the whole proposition to be true, and sufficient for only ONE of the conjuncts to be false for the whole proposition to be false.


Here are the truth table matrices for these sequences.



Disjunctive proposition.



v P

v Q

v R

v S

v T

T

F

F

F

T

F

F

F

F

F

F

F


Conjunctive proposition



· P

· Q

· R

· S

· T

T

T

T

T

T

T

F

T

T

F

T

T


Note as we move to scientific method,

the concomitant absence of the tautologous, and hence certainty of determinations. The results do not rely on not innate thought, ie; a priori, they rely on empirical – a posteriori, observations that confirm or deny the truth value of the propositions as a whole. The principle involved here is that each and every confirming instance of the proposition increases the probability closer to 1, ie; certainty, and just one dis-confirming instance is sufficient to render the hypothesis and or theory probable to a lesser degree each time the dis confirming instance is repeated until it reaches 0, ie uncertainty or improbable.

From these principles the structures of civilisations are built.

For example, at each stage of the causal process, the nomic relationships are determined, such that a house built with bricks relies on the determination that specific ingredients are necessary, where some are sufficient, depending on the type of bricks used, to ensure a house stays built when constructed. In determining the cause of heart obesity, studies are made that show the presence of certain fats, are necessary to ensure obesity where the absence of those fats are sufficient to reduce or eliminate obesity. It's important to understand that these principles operate within a frame of reference, eg; water will boil at 100 degres centigrade, but when the pressure is constant, vary the pressure and the boiling point is varied.


To test the truth table matrix for a simple instance of scientific method as depicted in the above example of oxygen being a causal and important factor in the existence of life, one might add the next one being water, that in humans at least, constitute a large part of their make-up, without which their life would also be extinguished.


Let us say Oxygen AND Water are two causes of life in humans. ( O & W ) are necessary conditions for life in humans, if and only if their absence jointly is sufficient to extinguish life.


The alternative consideration is the disjunctive form, namely that ( O v W ) are necessary conditions for life in humans, if and only if their absence singly or jointly is sufficient to extinguish life.


Here are the respective truth tables, with a third element let us say a portion of vitamin C.


Closer focus on scientific methodology.


ONE the Presence of Oxygen OR Water, ( in the body ).

The necessary condition. 'T' represents the result of Life being TRUE.

This shows all conditions where ONE or both ingredients are present

is necessary for life to be sustained, and when both are absent, life is absent.

We only know that one is necessary from this table, not if BOTH are necessary.

This Truth table matrix is the LOGICAL truth conditions of the disjuncts.

The determination of cause has yet to be made in empirical observation under test conditions in TWO below.


v O

v W

T

T

F

T

F

T

T

T

T

F

F

F


TWO the Absence of Oxygen AND Water, ( in the body ).

The sufficient condition, is the more powerful in this table since

'T' represents the result of Life being TRUE.

This shows all conditions where both ingredients are present / absent JOINTLY,

when both are absent, life is absent. When either one is absent life is absent

We know that BOTH are a sufficient condition from this table,

since all other possibilities show life absent when one is absent. This shows both are

jointly part of a more complex cause.



( · O

· W )

F

T

F

F

F

T

T

T

T

F

F

F



THREEthe Absence of Vitamin D AND presence of Oxygen AND Water, ( in the body ).

We already know that water AND oxygen are necessary and sufficient conditions.

'T' represents the result of Life being TRUE.

This shows all conditions where both Vitamin D is present / absent with ( the other two JOINTLY ),

when Vitamin D is absent, or when it is present, then life is present.

( Vitamin D helps properly control calcium and phosphate levels in the body ).

This shows Vitamin D as jointly part of a more complex cause.

Long term absence of Vitamin D is likely to produce rickets in the bones,

so this is a factor for the quality of life, but not the presence or absence of life itself.

If tests show the presence / absence of rickets that correlates with the presence / absence

of Vitamin D then you have a probable cause of rickets.


( · O

· W )

· Vd )

T

T

T

T

T

T

T

F


This entire section is being overhauled and added to in depth, please revisit fairly frequently, though the unfamiliar traveller will require some time anyway to digest. I am making it more interesting with legal cases where questionable advocacy by lawyers failed against straightforward logic.




Down

Glossary of terms.

Acausal.................... not causal; not causally related.

Analytic.................... (of a statement etc.) such that its denial is self-contradictory; true by definition

A priori.................... (of concepts, knowledge, etc.) logically independent of experience; not derived from experience

A posteriori............. (of concepts, knowledge, etc.) logically dependent on experience; not a maxim.

Averment................. The action of positively declaring as true; assertion, affirmation. OED 3.


Balk.......................... To miss or omit intentionally. b. fig. To pass over, overlook, refrain from noticing (what comes in one's way); to shirk,

ignore. OED II. 2. trans.


Cognitive dissonance. As presented by Leon Festinger in 1957, dissonance theory began by postulating that pairs of cognitions (elements of knowledge) can be relevant or irrelevant to one another. If two cognitions are relevant to one another, they are either consonant or dissonant. Two cognitions are consonant if one follows from the other, and they are dissonant if the obverse (opposite) of one cognition follows from the other. The existence of dissonance, being psychologically uncomfortable, motivates the person to reduce the dissonance and leads to avoidance of information likely to increase the dissonance. The greater the magnitude of the dissonance, the greater is the pressure to reduce dissonance.

Contradiction.......... c. Logic. One of the four kinds of Opposition (contradiction, contrariety, sub-contrariety, sub-alternation): see quot. 1864. principle (or law) of contradiction: the axiom that _a thing cannot be and not be at the same time' or _that nothing can have at the same time and at the same place contradictory and inconsistent qualities'.

Contrariety............. 6. Logic (from sense 1). contrary propositions: those most opposed to each other as regards affirmation and negation, each denying every possible case of the other, as All A is B: No A is B; both propositions cannot be true, but both may be false. contrary terms: those which are extreme opposites within the same class, as black and white. contrary opposition: the opposition of contrary propositions and terms. OED.

Copula...................... a connecting word, esp. a part of the verb be connecting a subject and predicate.

Correspondence........ agreement, similarity, or harmony. (with reality)


Denotes.................... stand as a name for; signify.


Elocutionary..............The art of speaking in regard to delivery, pronunciation, tones, and gestures; manner or style of oral delivery

Empirical................... based or acting on observation or experiment, not on theory.

Epistemology............. the theory of knowledge, esp. with regard to its methods and validation.


Fact........................... truth, reality


Hypostasised........... OED To make into or regard as a self-existent substance or person; to embody, impersonate.


Illocutionary............. a speech act that amounts to stating, questioning, commanding, promising, and so on. It is an act performed in saying something, as contrasted with a locutionary act, the act of saying something, the locution. (wikipedia dictionary) J. L. Austin How to do Things with Words (1962). Additional comment; this speech act can be just as effective in the sense of being perlocutionary, if used selectively in the stating sense. Stating some things while omitting to state others, IS perlocutionary.

Indicative................. (of a mood) denoting simple statement of a fact. (that is subject to proof or disproof)

Intra Vires..............."within powers."conduct by a corporation or its officers that iswithin the powers granted by law.


Literal...................... taking words in their usual or primary sense without metaphor or allegory.

Locutionary..............Of or pertaining to an utterance by a speaker

Logic......................... not contravening the laws of thought, correctly reasoned.

Logic........................ The branch of philosophy that treats of the forms of thinking in general, and more especially of inference and of scientific method. (Prof. J. Cook Wilson.) Also, since the work of Gottlob Frege (1848_1925), a formal system using symbolic techniques and mathematical methods to establish truth-values in the physical sciences, in language, and in philosophical argument. The proper scope of this department of study has been and is much controverted, and books on _logic' differ widely in the range of subjects which they include. The definition formerly most commonly accepted is _the art of reasoning'; for various modern definitions see the later quots. At all times the vulgar notion of _logic' has been largely that it is a system of rules for convincing or confounding an opponent by argument. In the Middle Ages logic (or dialectic, q.v.) was one of the three sciences composing the _trivium', the former of the two divisions of the seven _liberal arts'. OED- 1. a.


Mens Mentis............ Mind – thoughts, of.

Mens rea...................The state of mind indicating culpability which is required by statute as an element of a crime


Noblesse oblige....... privilege entails responsibility; to honourable behaviour.


Ontology.................... the branch of metaphysics dealing with the nature of being. Anselm wrote in the Proslogium that “God is something than which nothing greater can be imagined.” (A definition of God where the nature of God is 'in the understanding') The conclusion that God exists, is derived from the absurdity that “If the nature of such a being can be understood” then his non existence cannot be consistent with this understanding.”


Perlocutionary.......... a speech act that amounts to persuading, convincing, scaring, enlightening, inspiring, or otherwise getting someone to do or realize something. When examining perlocutionary acts, the effect in the hearer or reader is emphasized. Unlike illocutionary acts, which stress some linguistic performance, a perlocutionary act's effect is in some sense external to the performance. (wikipedia dictionary) J. L. Austin How to do Things with Words (1962).

Predicate................... assert (something) about the subject of a proposition.

Premiss..................... a previous statement from which another is inferred.

Proposition................ the literal meaning of an indicative sentence that can be tested for truth or falsity. EG: take a slightly unusual sentence, simply the exclamation ... FIRE! The meaning being, this or there is a fire. This proposition can be verified for truth or falsity, but the sentence in its first utterance is hardly even a sentence for propositional purposes.


Spectre..................... a haunting presentiment or preoccupation

Speech act................ an action performed by means of language, such as describing something ("It is snowing."), asking a question ("Is it snowing?"), making a request or order ("Could you pass the salt?", "Drop your weapon or I'll shoot you!"), or making a promise ("I promise I'll give it back.") (wikipedia dictionary)

Subject...................... the part of a proposition about which a statement is made

Synthetic................... (of a proposition) having truth or falsity determinable by recourse to experience

Syllogism.................. a form of reasoning in which a conclusion is drawn from two given or assumed propositions ( premisses ): a common or middle term is present in the two premisses but not in the conclusion, which may be invalid (e.g. all trains are long; some buses are long; therefore some buses are trains: the common term is long).

Synchronicity.......... the simultaneous occurrence of events which appear significantly related but have no discernible connection.

Suppressio veri........ suppressio veri, suggestio falsi: The suppression of the truth and / is the suggestion of a falsehood.


Tautology................. Logic. A compound proposition which is unconditionally true for all the truth-possibilities of its elementary propositions and by virtue of its logical form. A statement that is necessarily true. See the truth table matrix for tautologies and similar truth functions. (to be added shortly).


Ultra Vires..............."beyond powers."conduct by a corporation or its officers that exceeds the powers granted by law.





Annex

Frege........................Sense and reference.” One of his primary examples therein involves the expressions "the morning star" and "the evening star". Both of these expressions refer to the planet Venus, yet they obviously denote Venus in virtue of different properties that it has. Thus, Frege claims that these two expressions have the same reference but different senses. The reference of an expression is the actual thing corresponding to it, in the case of "the morning star", the reference is the planet Venus itself. The sense of an expression, however, is the "mode of presentation" or cognitive content associated with the expression in virtue of which the reference is picked out.

Brain fingerprint.......Dr. Farwell, a method of reading the brain's involuntary electrical activity in response to a subject being shown certain images relating to a crime. Unlike the polygraph or lie detector to which it is often compared, the accuracy of this technology lies in its ability to pick up the electrical signal, known as a p300 wave, before the suspect has time to affect the output. "Brain fingerprinting doesn't have anything to do with the emotions, whether a person is sweating or not; it simply detects scientifically if that information is stored in the brain."

Seeing thoughts.........A team at University College London found with fMRI they could tell what a person was thinking deep down even when the individual was unaware themselves. By looking at the functional magnetic resonance imaging (fMRI) scan results, the scientists were able to predict what had been displayed on the computer screen better than volunteers themselves. When two images were flashed in quick succession, the volunteers only consciously saw the second one and were unable to make out the first. But the brain scans clearly distinguished the patterns of brain activity created by the "invisible" images.




Index






The entire section below is being re-arranged into sections, please peruse only, for time being if interested.

_____________

work in progress...............




Essentially we are looking for sentences whose forms include formal concepts such as:


'not', 'and', 'or', and 'if ..... then ....'


examples like these are simple and plentiful in everyday speech.


a) This is not blue. This is not the man that I saw yesterday.

b) This is an apple and this is an orange. Peter is a bachelor and Paul is a salesman.

c) Either this is a cat or it is a dog. Either he will return today or the moon will stop rotating around the earth.

d) If that costs less than £1000 then it is excellent value. If the rise in inflation exceeds ten percent then there will be a revolution.

e) If blue tigers mate in the Autumn, then Spring will come early.


It is important to note that propositional sentences contain three elements. A subject, predicate and copula. A short set of extended examples of word, sentences, and meaningful sounds follow where the propositions require more understanding of the meaning of what is said, where the propositions we are looking for have to be teased out.


f) Fire! This may be an exclamation generally ruled out of being a real proposition, but the meaning 'something is on fire' shows that it is possible to see the proposition contained in the single word. The context will be important, so that if exclaimed simply as a word without emotion, there would be no information transferred to the listener, as in stating the word 'blue' or simply the letter 'B'. When exclaimed in the context of raising an alarm, it is clearly relevant to a propositional analysis.

g) This is black, Ceci est noire, Dies ist schwartze, are all identical propositions but different sentences. I could achieve the same result as a dumb person, by pointing at the appropriate colour on a palette and writing the word 'black' on a piece of paper.

h) When my dog, Princess,used to come to me, gain my attention and whimper a little, lifting her paw, I would stop and try to understand what she wanted to communicate.

What is it Princess? Show me, let me see your paw. I would examine it and notice she had picked up a broken chink of glass between the soft parts of her pads. Gently opening her pads while re-assuring her, I would see the offending object and remove it. Up she would jump, happy and grateful. The information was passed, and understood. Equally one day we would return from a brief outing for supper, her normal excited greeting was coloured by a sense of shame. In to the kitchen we all would go and notice the very nice steak left out to thaw was missing. On looking at her, her head and ears went down, she knew she had been responsible, and in a sense owned up to the misdmeanour (as she knew it would be to us) Of course we all understood and loved her too much for chastisement. It's all right treasure, don't worry about it, we said. This information was transferred but the form of the proposition 'I am guilty' and reassurance, tinged with some measure of disapproval was the response.


So what is essential to a proposition is that the sentence should conform to the rule of having the above three components, expressed or else implicit.


  1. Note: In e) above, we are not concerned with the truth or falsity of sentences, their propositions or conclusions derived thereof. Their truth or falsity depends upon several disciplines that have puzzled philosophers for thousands of years.

  2. I shall discuss the two primary disciplines of reasoning that govern and influence the outcomes of truth and falsity, namely Logical truth, and Empirical truth. In logical truth we are concerned with propositions whose truth relies upon certain 'a priori' principles which unhappily do not yield much information. Empirical truths rely on logical reasoning and comparison of propositions, with reality; within some sound framework of Correspondence theory, and Epistemology.

  3. A simple logical example of truth can be drawn from the class of A priori truths. All triangles have three angles. One has only to understand the meaning of the proposition to understand that it requires no reference to empirical testing in order to establish its truth. The truth is implicit in the construction of the sentence. The predicate 'three angles' says nothing about the subject 'triangle' that is not already implied. The proposition this triangle is blue says something more about the triangle than was previously implicit. Kant, expresses this distinction as the former being analytic and the latter synthetic.

  4. For an empirical example, Descartes began with the extremely sceptical view that our knowledge about the world may be an illusion, we are all living in some kind of dream constructed by a very clever Devil, and all data derived from the senses had to be doubted. His conclusion drew a wonderful degree of certainty, as close as one might get with Empirical data, that 'Cogito ergo sum', 'I think therefore I am.' If all else fails, then at least one thing is reasonably certain, that if I can think, then I must exist. This appears conclusive, but the area is minefield, and just when you thought there were at last some things of which we can be certain, that is where probability is as close to 'one' as possible, then you might come across a short treatise by W.C. Kneale, “ Is existence a predicate?” and you are reaching for your dictionary to find out what it is to predicate something of something else, and why and where Anselm's Ontological argument for the existence of God has its flaws.

  5. Think there are conclusive answers to these questions that have been a puzzle for so long? Unlikely!

  6. What is perhaps important, is that with respect to thinking; to rely on certainties derived from empirical sources, will be as fallible as scientific methodology and probability theory. The axiom of causes is based in principle on the ' absence and presence of sufficient and necessary conditions.' So that 'if life has a single and simple cause then', 'if the presence of oxygen is necessary for life, then it is sufficient for the absence of oxygen to remove life'

  7. The principle that a sufficiently large sample will establish a hypothesis beyond a shadow of doubt, while compelling, is to be firmly doubted, it merely establishes that hypothesis beyond a reasonable doubt to be overthrown in the future. The essential caveat for such epistemic methodologies is that while every 'confirming instance' supports the hypothesis, only one 'disconfirming' instance is sufficient to destroy the theory absolutely or else to require additional qualifying conditions. You shall see immediately that for plants and trees, the above hypothesis is in need of qualification, because they require carbon-dioxide to sustain them, and discharge oxygen in the process.


Returning to logic, you can now see in the short digression above, how many propositions are embedded in the sentences I used. Propositions have been drawn out with their forms highlighted in red. Can you see other propositions in the sentences that I did not draw out and learn how easy it is to extract them so as to get closer to their meanings?

Take 5. for example, you can see the form of my argument by adding 'If you' before 'Think', and 'Then it is' before 'Unlikely.' I tried to persuade you. Now it is for you to be the sceptical and decide if the arguments put forward are doubtful, reasonable, or certainties.


The logical forms of the sentences above are:


Not P.

P and Q.

Either P or Q.

If P then Q.

P. (requires no special examination as the simplest of all the propositions.)


The letters P, Q, R, X, Y, Z etc are variables that are substituted for the propositions, and the truth values of such variables is dependent solely on the truth values of the propositions so substituted.


To better express the logical form we use a notation, so that it becomes clear that logical form makes no difference to the truth or falsity of conclusions provided there follow the rules on correct reasoning which also follows rules in the calculus of logic, the above sentences would be written:


Function of Negation ~ P

Function of Conjunction P . Q

Function of Disjunction P v Q

Function of Implication P > Q



Complex sentences will be more difficult to break down to propositions.


It is important to distinguish between the illocutionary and the perlocutionary types and forces of speech acts.


A) I love caviar, chopped onions and crumbled egg yolk on toast. OR

B) I always (customarily) eat my caviar with chopped onions and crumbled egg yolk on toast.


Which both contain a disguised implicative function, the 'if... then...' construction.

Thus breaking down the meaning of these sentences lead to possible ambiguities.

Either it is a simple statement of preference or more likely, it tries to exhort the listener.

The implication is:

If I like this, then you should too. OR If I always take this recipe then you should too.


These are misuses of several fallacies (of which there at least 70 well established) like the 'Appeal to Authority' where the person stating the proposition is suggesting he is the authority. OR 'Appeal to common practice' or 'Appeal to emotion.' which are self-explanatory.


Notwithstanding this, they are propositions in the form of arguments. They try to persuade.


The problem is that in certain peer groups, class structured situations, or rhetoric used by say, politicians, they all are capable of achieving the desired effects if the listener is not attentive, and at all times critical should the argument be derived from a fallacy or else from a fact established as true, either empirically or logically. Such forms may increase in complexity requiring some familiarity of procedures to break compound propositions to simpler ones, they also flow from the intonations of speech, and manners of expression.


Here is a short anecdotal piece of reasoning which attempted to defy the Laws of Thought, more specifically the Law of contradiction. The owner of the assertions was severely bruised just as if he had tried to defy the Law of Gravity, and jump off a cliff without a parachute. The use of Premisses permit a build up of sequences of arguments perhaps with substantial complexities amounting to conclusions that may be then used to defeat an adversary in court.


I had a particular fascination with forms of syllogisms and formal logic. Having taken 'O' and 'A' level logic in my very early twenties, and being a member of the then 'Royal Institute of Philosophy' at an earlier age, gave me a particularly useful tool; some fifteen to thirty years later in life when all had been digested. I was no longer intimidated by barristers, particularly one who informed me prior to entering the courtroom, that he was going off to get into his battle-dress. While he returned suitably be-gowned, his plaintiff tut-tutting me for being reckless enough to attend and defend myself.


I had sought an injunction against my Landlord, the chairman of the board of directors of the company that managed the leasehold property of which I was a leaseholder. We had not particularly formed any acquaintance beyond formal greetings when we passed each other. I was not particularly liked, and for some mild misdemeanour I had unwittingly performed, he had resolved to punish me by terminating the electricity to my offices in the same building (for an extensive period, beyond that declared in a circular; “no leaseholder shall have their electricity supply terminated for a period of more than two hours) ) where I lived, during a period when the entire block was being re-wired. I had called the electricity board in to investigate, and the switches were behind a box to which only he or his agents had the key. The next day I sought an injunction to get the electricity re-connected, and served it through his letter box, to no avail. Two days later I returned to the court and obtained a stronger injunction to serve on all five directors, that were the electricity not restored in 30 minutes from receipt of the injunction, then committal proceedings would begin to see all five in prison. I served this on three directors, and the electricity was back on so quickly even I was surprised. I had to return to the court to inform them of the result, and while asked if I wanted costs, I said “no, all I had wanted was the electricity back” and the lesson was worth its weight in gold. The very kind judge awarded me £200.


On the chairman's return from holiday, he challenged the ruling not wanting to pay the £200. We had a hearing set for 11 am on a Friday (not the best of court days with sessions ending early before 4pm where possible. I decided to bring my family for moral support. As we entered the building we were welcomed by a security officer who said respectfully “Good morning.” Then he invited us to enter, one by one this odd looking cubicle explaining that it was a metal detecter. I said “So we are getting a shower, that can't be bad can it?” He seemed hugely amused as he exclaimed to my wife “Yes ma'am we are very clean here” After we were okayed by the machine. My wife replied “That can't be bad, cleanliness is next to Godliness.”


Shortly after the opposing team of three followed us in, identified themselves and sat down opposite, under one of three lights above each section of seats. The light began slowly blinking. We had nothing to say to each other. The Plaintiff was constantly looking at me, tut-tutting quietly and justifiably confident with his legal team. Lunchtime approached and the court usher came to advise us we could all go over to the restaurant for lunch, as the trial had been postponed until afternoon, with the purpose of possibly allowing time to reach a settlement out of court. We lived five minutes away, I was in no mood to compromise, went home and returned at 2.30pm. On our return we took up the same seats as before, the light was permanently back on. After about ten minutes the light over the Plaintiff began slowly blinking again, a thing only my wife might notice, drew to my attention, (“Do you see his light is fading?”) and I might give a meaning to in accordance with Jung's theories of acausal synchronicity. The light eventually failed, shortly after we were all invited in to the courtroom. The nature of such meaningful coincidences is characterised by feeling (but not being in) the presence of some spectre, as the rational psyche struggles to give an alternative meaningful explanation outside the realms of ordinary causation, probability or coincidence. The experience is particularly enhanced when several such events occur serially in a short time frame. While Jung puts this phenomenon down to a special kind of coincidence, he also posits a fifth dimension to space-time, namely the psyche, which is responsible for giving such events a meaning. One might be drawn to the suggestion of psychic interaction. But while such an inference may be attractive, it might not be quite so fair to place this in the realm of acausal phenomena, rather causes we yet have to unravel.


The Plaintiff had engaged a solicitor and barrister at some considerable expense, I imagine some £3500 to £5000 at that time. The barrister easily overturned the previous costs ruling based on a precedent I was unaware of. The judges dismissed the costs awarded and then told me I should have to open another case whose costs would be expected at about £10,000 if lost. I consulted my wife and son, and decided against spoiling our Summer holidays together. I said I would let the Plaintiff go, but wished to ask one question, being that time when the prosecution had finished and it was my turn.


I said, “Your Honour, would you please have the Plaintiff answer one question, and that it be under oath?” The judge nodded his assent and I turned to the Plaintiff.


Bearing in mind your two sworn statements in exhibits 1 and 3, (below), and that you, are the Chairman of the board, would you please explain how; when served with the injunction on the Tuesday, and again served along with two other directors on the Friday following, your sworn statement 'The board of directors did not know about the plight of the Defendant.' can possibly be true?


The Plaintiff had separately presented as evidence


Premiss 1. The board of directors did not know about the plight of the Defendant.

Premiss 2. I knew about the plight of the Defendant.

Both sworn as true, at difference times in writing.


'The undisclosed premiss.'

Premiss 3. He was a member of the board of directors. (the chairman)


The Plaintiff's face reddened as his barrister turned to him for his explanation. And responded “Your Honour, I am instructed by my client” to say????” (which I cannot recall.) I did know however that in this circumstance the first part of the barrister's reply was a disaster for the Plaintiff since the semantics revealed, even his own barrister, by now could not believe him. The question having been all I had to ask meant the hearing was now at a close. The plaintiff's barrister , considerably humbled then asked in the meekest tone possible. “Your Honour, we would respectfully ask for costs?” Judge G's reply was to look at the ceiling, and laughingly say “I think the least you can do is to both carry your own costs, don't you? The Plaintiff left so fast (like a rat out of hell) all I knew of the event was the sound of the 'guilty' door behind me, swinging vigorously back and forth like a rocking chair. I will leave it to you to draw up the document and with that he stood and left while the final agreement was written out and signed. My son of nine years came to the front, sat beside me, and began drawing also. On his return the judge asked “what does this young man want to do when he grows up? My son replied “I want to be a judge sir”


The result insofar as justice is concerned, could be viewed as I did; partially then and, more competently now, that I had experienced a wonderful opportunity to argue personally my case, saving all the legal fees, as well as an intense short course in law, which alone was to me worth at that time about £1500. The letter of the law had been upheld, namely the precedent adduced was lawful, and my costs were dismissed. But the spirit of the law was not upheld (since I had been injured and not compensated) until the Judge dismissed costs on their side. This resolved the matter, since I was not seeking the proverbial pot of gold, from a legal case, more the experience and learning. The Plaintiff was seeking (God only knows) perhaps to teach me a lesson, and make some money or make me pay for their sport, which could not in all Justice be permitted. (On returning to Bedford Court, I saw the Plaintiff talking to the porter, and later asked the porter what was said, to be informed with mild incredulity “I fixed him.” After the bill had been covered; in every sense of the word, about eight month's later, the Chairman was removed, as expected.


Examine now the logic.


The plaintiff had constructed Premiss 1, as a 'suggestio falsi' (what he most likely had in mind, but did not wish to reveal was, 'the other members of the board did not know.') An important comment needs to be made here. The perennial liar actually tries (as do we all) to tell the truth. And Premiss 1 is true in the sense just mentioned. That is to say that what one has in mind and what one may say (if intentionally misleading) is invariably a particular sense or meaning of a sentence that lacks fuller qualification, and is undisclosed when truth is under stress. I refer to my sonnet on the two oaths sworn in court. (“Truth... the whole truth and nothing but is best, While truth and nothing but.., leaves out the rest.”) If one listens in a sceptical mood (questioning rather than disbelieving) , these 'holes' tend to show through. The plaintiff then feels quite comfortable with Premiss 2, he can hold both in his mind without undue cognitive dissonance. Holding two contradictory propositions in the mind is almost painful, so when confronted by this truth, the liar will apply a rheostat to the span of meanings that attaches to most words, and seek out that which sits more comfortably.


Premisses 1 and 2 will clearly be seen as a construction; the truth of which, is logically undetermined until premiss 3 is added. Whence it becomes false.

(and not requiring any empirical test to corroborate) since the board does not exist without its members, and it is sufficient that one member of the board, in particular its chairman (a class with members) knows, for it to be FALSE that the board does not know.


The first law of thought, 'the law of contradiction' brings any response to this argument to a crashing fall.

This law is expressed in the form “It cannot be the case that both (something and not something) may be true simultaneously.”


In our notation this is shown as:

NOT both (P and NOT P)


~ (P . ~ P)


Arguments that are susceptible to logical analysis, testing in a truth table and therefore likely to not require empirical testing (corroboration in the world of reality) are quite clearly the most effective, since once established as true or false, they are so, at any time, in any space and any world.


In a truth table, which shows all possible outcomes of a sequence of formal expressions. this contradiction shows up as:


P

~ P

T

F

F

T


When P is true, NOT P is false, and when P is false, NOT P is true. The classic form of contradiction.

The function of conjunction (the large dot · in our notation) standing for AND, binds the two propositions, unlike the disjunctive function Ú standing for OR, which permits the truth of either P or NOT P. Hence no matter what substitution of the variables P, Q, R, etc, it is axiomatic that any proposition cannot be true simultaneously with its own negation.


There are two forms of inconsistencies, Contradictions and Contrarieties.

The contradictory form has been briefly examined above, and it needs be added that such forms; as distinguished from Contrarieties, are mutually exclusive where the truth of one proposition entails the falsity of the other and vice versa, because they are jointly exhaustive. Contraries are slightly different insofar as; while they cannot be jointly true, they can be jointly false. This will be shown later in the section on formal logic.


If you like, matter and anti-matter (the negation of matter) cannot co-exist, where it is attempted there is mutual destruction.


An alternative method of examining the class concept expressed in the above propositions is with Venn diagrams which makes use of several intercepting geometrical forms, circles for example. They allow one to instinctively see the immediate inferences that follow. Slightly more advanced Venn is here.


A further truth table of the above will show how it belongs to the first law of thought, ~ (P . ~ P) in section (3) Formal Logic.


Glossary for this section.




End of this glossary section.....




Going back several thousand years may be a good way to begin. Without the formal notation used in modern logic, plain English (translated) may be easier for some to come to terms with, although personally I find the formal notation easier to hold in the mind (rather than long sentences) when treating abstract concepts.


I shall focus on a minute part of Aristotle's works, in the section Metaphysics that concerns itself with logical reasoning.


Just examine this proposition from Aristotle, Metaphysic book IV ch 7: 1011b 26-7:


(1) “To say of what is that it is not, or of what is not that it is, is false,


This looks very much like the modern logic (contradictions) in its simpler form of the preceding section and appears so perfectly acceptable as to be axiomatic.

What we have; in modern terminology, is two disjunctive propositions using the terms or (Above Either P OR Q.) which separate either a contradictory proposition that is denied, or else an identical proposition that is affirmed. This in my view appears to be the root of today's Formulation for the Law of Non-contradiction.


A few extracts from slightly earlier Metaphysics, 1005b 17-25


"The same attribute cannot at the same time belong and not belong to the same subject at the same time......” , "This, then, is the most certain of all principles.” , “ For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. (” in reference to his doctrine of flux and the unity of opposites.)


The close similitude of Aristotle's logic, with today's shows clearly how much his reasoning has impacted modern philosophy and logic.


Moving away from the principles above, and returning to the elements of “subject, predicate and copula,” we shall see how Aristotle treats the ideas of logical reasoning in the syllogisms, and also existence, (the essence of being,) which also remains a difficult topic.


(2) He states “the intermediate between the contradictories will be so either in the way in which grey is between black and white, or as that which is neither man nor horse is between man and horse.”


Critically, the is” in this last sentence (2), as a copula has an entirely different 'sense and reference' to the is” in (1) above. (see Frege)


The is in (1) uses the sense of identity as derived from Frege's works on mathematics namely the sense of “=”, whereas the sense used in (2) uses the that derived from the present indicative of the verb “be”, (that is a fact or quality of existence.) A vast difference, since the former has more the qualities of abstract logic, and the latter the attributes or qualities of things existing in the real world, that of empirical experiment and observation.


Here; in m view, is a very serious problem in using the terms contradictories with supposed opposites like black and white or man and horse, while black and white may be considered opposites, I fail to see how man and horse can be. You may recall how earlier I stated one of the particular difference between contradictions and contraries is that Contradictions are mutually exhaustive, having no middle ground, the truth of one contradictory proposition entails the falsity of the other.


Using the modern tools in formal notation it becomes clearer where the errors lie, and also that which invariably infuriates me, in the erroneous (deliberately so in many cases) framing of a question which permits a truthful answer where the respondent is permitted to hold in their mind some sense in which the answer is or may be true, and the listener gets the falsity because brain fingerprinting and seeing thoughts are as yet a new sciences? The technique is subtly related to the definition of “suppressio veri, “suggestio falsi.”


For many thousands of years we have relied on a number of factors in getting at the truth, and they all rely on a basic good instinct, use of all senses combined with a sound mind's eye for logic, and in most cases these are more than enough to make a reasonably sound determination. My dirft is to lead this passage towards a short study of other ways than contradictions, more inclined towards Aristotle's work in the area already touched upon, and will use the example, somewhat well known where a question was asked “Did you have sex with Miss X?” and how the answer “I did not have sex with that woman.” can be stated with a convincing appearance of truth, while being completely false.



The errors lie in the area of firstly an erroneous notion that opposites are in some way identical with contradictories, and that there is any intermediate between the elements of disjunction of contradictions. You have already seen the law of non-contradiction ~ (P . ~ P) and shall see (section 4) the law of the excluded middle P Ú ~ P which states that either P or NOT P is the case. Essentially there is NO middle way.








Glossary for this section.




End of this glossary section.....


Note: section below is simply a scrapbook section to be laid out more formally later.


Aristotle, Metaphysic G 7


But on the other hand there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate. This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false; but neither what is nor what is not is said to be or not to be.-Again, the intermediate between the contradictories will be so either in the way in which grey is between black and white, or as that which is neither man nor horse is between man and horse. (a) If it were of the latter kind, it could not change into the extremes (for change is from not-good to good, or from good to not-good), but as a matter of fact when there is an intermediate it is always observed to change into the extremes. For there is no change except to opposites and to their intermediates. (b) But if it is really intermediate, in this way too there would have to be a change to white, which was not from not-white; but as it is, this is never seen.-Again, every object of understanding or reason the understanding either affirms or denies-this is obvious from the definition-whenever it says what is true or false. When it connects in one way by assertion or negation, it says what is true, and when it does so in another way, what is false.-Again, there must be an intermediate between all contradictories, if one is not arguing merely for the sake of argument; so that it will be possible for a man to say what is neither true nor untrue, and there will be a middle between that which is and that which is not, so that there will also be a kind of change intermediate between generation and destruction.-Again, in all classes in which the negation of an attribute involves the assertion of its contrary, even in these there will be an intermediate; for instance, in the sphere of numbers there will be number which is neither odd nor not-odd. But this is impossible, as is obvious from the definition.-Again, the process will go on ad infinitum, and the number of realities will be not only half as great again, but even greater. For again it will be possible to deny this intermediate with reference both to its assertion and to its negation, and this new term will be some definite thing; for its essence is something different.-Again, when a man, on being asked whether a thing is white, says 'no', he has denied nothing except that it is; and its not being is a negation.





Inconsistencies: The first law of Thought, the law of NON-contradiction. belongs to the class of tautologies, and you may recall the contradictory function shown in the preamble during the legal case.


The formal expression of this function of contradiction is shown in the table below.


In all cases of P being either true or false, the conjunction of the two is always false and best expressed by ~ (P · ~ P) which is a tautology.

It is Not the case that P and NOT P are true together.


P

(P . ~ P)

T

F

F

F


P

~ (P . ~ P)

T

T

F

T


An important comment is required here. When looking for contradictions with any proposition that may be substituted for the variable P1.

Anything that is NOT P1, can be the rest of the entire universe in space, time and objects of any reference. So if P1 is the proposition “This tabletop is rectangular”. All other things from “This tabletop is oval” to round, hexagonal, to seats, pianos, animals, vegetables, minerals and so on to infinity, while they are ALL NOT the first proposition, P1, they do not fulfill the condition of being NOT P1 in the required sense. They all are simply propositions OTHER THAN P1, namely p2, p3, q, q1, r, r1, r2 and tn......

We are only focussing on propositions that are the NEGATION of the original propositions. While that is not to say that the alternatives are useless in comparison, it IS to say that alternatives are not specifically negations. Where alternatives can come close to formal contradictions in the full blown sense is the temporal element in assertions that one proposition is true or false. I shall give a fascinating example of this, in a section 9, sworn police statement for truth, that came to be shown as a contradiction because two very different propositions were asserted to be both true to but could not possibly stand together as true simultaneously. It was known in any case that one was falsely manufactured to commit the contravention to some category of the paperwork in issuing a penalty, but even had it not been manufactured, and had been true, the two propositions could have been true together as different propositions, because they were different in nature and time. This class of inconsistency is the class of contrarieties, and you can take a short digression from here to see its application to a real life perjury case with a policeman with noting better to do on a quiet weekend than make mischief, and put me in my place.



A necessary truth, is a truth that is referred to as A Priori. Considered with due seriousness, it is also a truth that can be maintained at any time, in any space. Truths like this while not being very informative, are exceedingly valuable from the point of view expressed in the preamble above. Reasoning which carefully follows the rules of logic will be infallible in argument, particularly in a court of law, but also many situations where illogical persuasion (fallacies) is being attempted and refutation required.


The second law of Thought, the law of excluded middle.



P

P ~ P

T

T

F

T



The third law of Thought, the law of identity.






Tautology................. (logic) a statement that is necessarily true a truth table for this will be shown soon, with comparison to similar truth functions and how they differ.




_____________________________________



Questor © - The author of this short treatise is qualified with a B.A. In Literature, B.A. (Honours) Philosophy, and additional studies in Law, Shakespeare, Music, Psychology and not a bad cook, as well. While without a formal degree in Law, the author has personally fought some twelve cases in law in as many years, having used only the principles of logic outlined above,

invariably proving the adversary to be either an abuser of authority, or else a self-contradictory liar, in some cases at their serious loss,or my personal gain.

The point being that use of slightly more than elementary logic does work in everyday life,





Might's not right, where argument's not treason,

Treason's his who's Might, denies good reason.


'Truth, the Whole truth and Nothing but..', is best,

While 'Truth and Nothing but..', leaves out the rest.



Short digression. Full story here......


I was taking my chorister son back to school and the approach road was Ludgate hill, to St. Paul' cathedral Choir School, London.

At the security cordon in vigour at that time, I was directed to stop by a policeman,who stated that I had no tax disk on display. I leaned over to the left of the windscreen and retrieved it from the top of the dashboard. On showing it to him, he was satisfied, but on looking at my seat belt, he than said I was not wearing it correctly. (it had fallen off the right shoulder in the previous movement). I held the belt upwards showing it was clipped in correctly to the centre block, and suggested that it was lawful because I WAS in fact wearing it. The situation grew out of proportion, and on setting my on off to school, I confronted the policeman, and his second, with the question, “Was the seat belt clipped in the holder?” Three times. Without reply, while he proceeded to issue a ticket for “driving without wearing a seat belt”. There is no category for not wearing it correctly or in a specific manner. I said I would see him in court.


His sworn section 9 statement stated, as aforesaid.......“driving without wearing a seat belt” But more particularly, he stated in the testimony that he stopped me for that reason. This had to be false on several counts. In fact he stopped me for the tax disk, and he could not possibly see from his standing position through the bulkhead of the car to say that I was wearing it incorrectly or not at all. Not to go into the finer detail here, there were now TWO propositions.

  1. P1. He stopped me for not displaying the tax disk, (at time T1) and

  2. P2. He stopped me for not wearing the seat belt (at time T2), correctly or otherwise.

Consequently the reasons for P1 and P2 are not merely different they cannot be true together, precisely because P2 was false. The wearing / not wearing was discovered AFTER I had moved my arm to the left of the vehicle, the belt slipping off my right shoulder. It had been in place correctly all the time,and when discovered, I was STATIONARY not driving. Even had both been true, they couldn't be true together, since the first thing to catch the eye is the tax disk, from a distance, and the belt would not be visible until much closer. The reason for stopping is the primary function of the contradiction, directing focus to the two laws of thought, Non contradiction and exclude middle. If reason P1 is true, then reason P2 has to be false and vice versa, hence the contradiction because under the law of excluded middle, the reason HAS to be either reason P1 or P2, EXCLUDING any middle alternative. The empirical test of truth was established when I subsequently measured the distance my left arm had to traverse to reach the tax disk, and the conclusion was it's impossibility to achieve without releasing my right arm from the top part of the belt, the full story has pictures. Additionally I photographed the policeman's view of cars in the same position I had to be,in order to stop me, and they all show it is not possible to determine fully whether I was wearing it correctly or not, but at best, under superhuman eyesight, one could only see perhaps, if it were true, the absence of the top part of the belt. The clipped area was in direct line with the engine, and he would need X ray eyes to determine that. In the event, I requested a Newton hearing, to determine the truth of facts, prior to the hearing itself, but the CPS had withdrawn their case, at a cost to the police or court, of £625.

Returning to the formal logic in the propositions P1 and P2, as you can see, they derived from an obvious starting point of a contradiction, but really belonged to the class of contrarieties, which is dealt with elsewhere, because the truth table matrix for contrarieties is unlike that of contradictions, whereby P1 and P2 (or else NOT P1 as this started out), can be jointly false, IE; he stopped me to have some fun at my expense.

A subsequent complaint and investigation with the Police complaints authority revealed a contradiction in he event that the statement given by the investigative member asserted hat the PC had stopped me for the tax dis, but then noticed the seat belt being incorrect. The two aspects of the statements show them to be contradictory IF both true, because the reason for the act has to be P1, and not P2 or vice versa, but since the truth relied on empirical corroboration, they were contraries, the truth of one did NOT ENTAIL the falsity o the other. Both could be false, but both could not be true together in time. There is a truth table matrix for contrarieties that will establish this, following the three laws of thought.







7 But on the other hand there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate. This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false; but neither what is nor what is not is said to be or not to be.-Again, the intermediate between the contradictories will be so either in the way in which grey is between black and white, or as that which is neither man nor horse is between man and horse. (a) If it were of the latter kind, it could not change into the extremes (for change is from not-good to good, or from good to not-good), but as a matter of fact when there is an intermediate it is always observed to change into the extremes. For there is no change except to opposites and to their intermediates. (b) But if it is really intermediate, in this way too there would have to be a change to white, which was not from not-white; but as it is, this is never seen.-Again, every object of understanding or reason the understanding either affirms or denies-this is obvious from the definition-whenever it says what is true or false. When it connects in one way by assertion or negation, it says what is true, and when it does so in another way, what is false.-Again, there must be an intermediate between all contradictories, if one is not arguing merely for the sake of argument; so that it will be possible for a man to say what is neither true nor untrue, and there will be a middle between that which is and that which is not, so that there will also be a kind of change intermediate between generation and destruction.-Again, in all classes in which the negation of an attribute involves the assertion of its contrary, even in these there will be an intermediate; for instance, in the sphere of numbers there will be number which is neither odd nor not-odd. But this is impossible, as is obvious from the definition.-Again, the process will go on ad infinitum, and the number of realities will be not only half as great again, but even greater. For again it will be possible to deny this intermediate with reference both to its assertion and to its negation, and this new term will be some definite thing; for its essence is something different.-Again, when a man, on being asked whether a thing is white, says 'no', he has denied nothing except that it is; and its not being is a negation. Some people have acquired this opinion as other paradoxical opinions have been acquired; when men cannot refute eristical arguments, they give in to the argument and agree that the conclusion is true. This, then, is why some express this view; others do so because they demand a reason for everything. And the starting-point in dealing with all such people is definition. Now the definition rests on the necessity of their meaning something; for the form of words of which the word is a sign will be its definition.-While the doctrine of Heraclitus, that all things are and are not, seems to make everything true, that of Anaxagoras, that there is an intermediate between the terms of a contradiction, seems to make everything false; for when things are mixed, the mixture is neither good nor not-good, so that one cannot say anything that is true.



8 In view of these distinctions it is obvious that the one-sided theories which some people express about all things cannot be valid-on the one hand the theory that nothing is true (for, say they, there is nothing to prevent every statement from being like the statement 'the diagonal of a square is commensurate with the side'), on the other hand the theory that everything is true. These views are practically the same as that of Heraclitus; for he who says that all things are true and all are false also makes each of these statements separately, so that since they are impossible, the double statement must be impossible too.-Again, there are obviously contradictories which cannot be at the same time true-nor on the other hand can all statements be false; yet this would seem more possible in the light of what has been said.-But against all such views we must postulate, as we said above,' not that something is or is not, but that something has a meaning, so that we must argue from a definition, viz. by assuming what falsity or truth means. If that which it is true to affirm is nothing other than that which it is false to deny, it is impossible that all statements should be false; for one side of the contradiction must be true. Again, if it is necessary with regard to everything either to assert or to deny it, it is impossible that both should be false; for it is one side of the contradiction that is false.-Therefore all such views are also exposed to the often expressed objection, that they destroy themselves. For he who says that everything is true makes even the statement contrary to his own true, and therefore his own not true (for the contrary statement denies that it is true), while he who says everything is false makes himself also false.-And if the former person excepts the contrary statement, saying it alone is not true, while the latter excepts his own as being not false, none the less they are driven to postulate the truth or falsity of an infinite number of statements; for that which says the true statement is true is true, and this process will go on to infinity. Evidently, again, those who say all things are at rest are not right, nor are those who say all things are in movement. For if all things are at rest, the same statements will always be true and the same always false,-but this obviously changes; for he who makes a statement, himself at one time was not and again will not be. And if all things are in motion, nothing will be true; everything therefore will be false. But it has been shown that this is impossible. Again, it must be that which is that changes; for change is from something to something. But again it is not the case that all things are at rest or in motion sometimes, and nothing for ever; for there is something which always moves the things that are in motion, and the first mover is itself unmoved.


Let this, then, suffice to show (1) that the most indisputable of all beliefs is that contradictory statements are not at the same time true, and (2) what consequences follow from the assertion that they are, and (3) why people do assert this. Now since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing. For of contraries, one is a privation no less than it is a contrary-and a privation of the essential nature; and privation is the denial of a predicate to a determinate genus. If, then, it is impossible to affirm and deny truly at the same time, it is also impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in a particular relation and one without qualification.





Formal logic and Dialectical logic. The source of the traditional mechanistic theory of development in positivist thought is said to reside in the so-called 'laws of nature and correct thinking' as stated by Aristotle. Somerville (1967) nicely contrasts the Aristotelian view of correct thinking (a.k.a., formal logic) with the dialectical view of correct thinking (a.k.a., dialectical logic). His point is that what is called "Aristotelian logic" is not to be identified with "logic itself" or with the logic of things (pp. 42-43).

The Aristotelian laws are as follows: (1) Law of Identity: Each existence is identical with itself; (2) Law of Noncontradiction: Each existence is not different from itself; and (3) Law of Excluded Middle: No existence can be both itself and different from itself.

In contrast to the above view, materialist dialectics holds that the basic rules of correct thinking should reflect a universe not in which the static and changeless is at the core but in which change is at the core. The dialectical laws of correct thinking, which subsume the Aristotelian principles, are as follows: (1) Law of Unity and Struggle of Opposites: Every object or process develops into something else, not only because it is affected by some eternal force but also because the very components out of which it is made force changes (change is built-in to its existence); (2) Law of Transition from Quantitative to Qualitative Change: Development cannot take place without discontinuity; and (3) Law of Negation: Every new stage, while synthesizing in itself the progressive trend of previous stages, contains within itself the preconditions for further development (see Conforth, 1952). In brief, the first law says that everything has a history; the second, that the history is qualitative as well as quantitative; the third, that this kind of history does not stop (Somerville, 1967, p. 67).

These laws are presented as conclusions arrived at on the basis of the factual evidence rather than as a priori principles. Even though these principles are regarded as universal (i.e., found in everything), it is not claimed that the specific laws of each particular level of reality can be deduced from them. While dialectical logic provides broad methodological guidelines it "does not obviate the necessity of finding, in each new case, the specific cause, the concrete pattern of change" (Somerville, 1967, p. 74). Materialist dialectics therefore provides a strategy of approach to the empirical investigation of phenomena rather than a detached catalogue of contradictions (e.g., cause/effect, necessity/chance, possibility/reality, essence/appearance) to seek. What the specific contradictions of particular objects (or general levels of nature) are and how they are resolved are questions for empirical scientists in the various fields of knowledge to discover (Konstantinov, 1974, p. 146).




11. Non-Contradiction and Metaphysics

Two frequent themes of Aristotle's account of science are (1) that the first principles of sciences are not demonstrable and (2) that there is no single universal science including all other sciences as its parts. "All things are not in a single genus", he says, "and even if they were, all beings could not fall under the same principles" (On Sophistical Refutations 11). Thus, it is exactly the universal applicability of dialectic that leads him to deny it the status of a science.

In Metaphysics IV (Γ), however, Aristotle takes what appears to be a different view. First, he argues that there is, in a way, a science that takes being as its genus (his name for it is "first philosophy"). Second, he argues that the principles of this science will be, in a way, the first principles of all (though he does not claim that the principles of other sciences can be demonstrated from them). Third, he identifies one of its first principles as the "most secure" of all principles: the principle of non-contradiction. As he states it,

It is impossible for the same thing to belong and not belong simultaneously to the same thing in the same respect (Met. )

This is the most secure of all principles, Aristotle tells us, because "it is impossible to be in error about it". Since it is a first principle, it cannot be demonstrated; those who think otherwise are "uneducated in analytics". However, Aristotle then proceeds to give what he calls a "refutative demonstration" (apodeixai elenktikôs) of this principle.

Further discussion of this principle and Aristotle's arguments concerning it belong to a treatment of his metaphysics (see Aristotle: Metaphysics). However, it should be noted that: (1) these arguments draw on Aristotle's views about logic to a greater extent than any treatise outside the logical works themselves; (2) in the logical works, the principle of non-contradiction is one of Aristotle's favorite illustrations of the "common principles" (koinai archai) that underlie the art of dialectic.

See Aristotle's Metaphysics, Dancy 1975, Code 1986 for further discussion.

12. Time and Necessity: The Sea-Battle

The passage in Aristotle's logical works which has received perhaps the most intense discussion in recent decades is On Interpretation 9, where Aristotle discusses the question whether every proposition about the future must be either true or false. Though something of a side issue in its context, the passage raises a problem of great importance to Aristotle's near contemporaries (and perhaps contemporaries).

A contradiction (antiphasis) is a pair of propositions one of which asserts what the other denies. A major goal of On Interpretation is to discuss the thesis that, of every such contradiction, one member must be true and the other false. In the course of his discussion, Aristotle allows for some exceptions. One case is what he calls indefinite propositions such as "A man is walking": nothing prevents both this proposition and "A man is not walking" being simultaneously true. This exception can be explained on relatively simple grounds.

A different exception arises for more complex reasons. Consider these two propositions:

  1. There will be a sea-battle tomorrow

  2. There will not be a sea-battle tomorrow

It seems that exactly one of these must be true and the other false. But if (1) is now true, then there must be a sea-battle tomorrow, and there cannot fail to be a sea-battle tomorrow. The result, according to this puzzle, is that nothing is possible except what actually happens: there are no unactualized possibilities.

Such a conclusion is, as Aristotle is quick to note, a problem both for his own metaphysical views about potentialities and for the commonsense notion that some things are up to us. He therefore proposes another exception to the general thesis concerning contradictory pairs.

This much would probably be accepted by most interpreters. What the restriction is, however, and just what motivates it are matters of wide disagreement. It has been proposed, for instance, that Aristotle adopted, or at least flirted with, a three-valued logic for future propositions, or that he countenanced truth-value gaps, or that his solution includes still more abstruse reasoning. The literature is much too complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker, Waterlow.

Historically, at least, it is likely that Aristotle is responding to an argument originating in the Megarian School. He ascribes the view that only that which happens is possible to the Megarians in Metaphysics IX (Θ). The puzzle with which he is concerned strongly recalls the "Master Argument" of Diodorus Cronus, especially in certain further details. For instance, Aristotle imagines the statement about tomorrow's sea battle having been uttered ten thousand years ago. If it was true, then its truth was a fact about the past; if the past is now unchangeable, then so is the truth value of that past utterance. This recalls the Master Argument's premise that "what is past is necessary". Diodorus Cronus was active a little after Aristotle, and he was a Megarian (see Dorion 1995 for criticism of David Sedley's attempt to reject this). It seems to me reasonable to conclude that Aristotle's target here is some Megarian argument, perhaps an earlier version of the Master.