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

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.

Page 1
Page 2

What is Logic

The three Laws of Thought

Matrix Truth Tables

Scientific Method

Legal Maxims

Caselaw .. Jokes

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 1^st 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.

2. What is logic?

3. 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.

4. 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.

5. 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”,

6. 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.

7. 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.

8. 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 1^st and 2^nd premisses.

9. 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:

10. 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.

11. 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.

12. 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.

13. 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.

14. 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. }

2. 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 P, or P implies P, where 'P' is a proposition

5. 'P' is a propositional variable.

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

2. 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 = 'É' if P then P, or P implies 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 Ú ~ P { Either P is true OR not P is true. }

• 3. The law of identity. P É P { P implies 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.....

2. 4. The Three laws of Thought.

• The modern formulations, they are as follows:

'not' = '~', 'and' = '·' , 'or' = '' Ú', and 'if ..... then = 'É' if P then P, or P implies 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 Ú ~ P. Either P is true or not p is true.

• 3. The law of identity. P É P. P implies P, itself.

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.

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

2. 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).

The two columns to the right side below are actually the truth table for the contradictory function.

P

~P

T

F

F

T

~

(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.

P

Ú

~P

T

T

F

F

T

T

T

P É

P

T

~P É

~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 s true.

and conjunction ( P · Q · R · S · T ) that states either P and Q and R and S and T is 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.

v O

v W

T

T

F

T

F

T

T

T

T

F

F

F

( · O

· W )

F

T

F

F

F

T

T

T

T

F

F

F

( · O

· W )

· Vd )

T

T

T

T

T

T

T

F