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.
      

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.

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

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.

The third law of Thought, the law of identity.

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 )

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.

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.

THREE– the 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.

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.

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.....

(2) Aristotelian Logic and Syllogisms. Framing a question that gets closer to the truth.

It's better to ask your opponent to deny a proposition than affirm it.

Denying entails part of the whole truth while affirming permits considerable

modulation of meaning if the question is not framed by all-embracing definitions, otherwise known as a frame of reference.

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,

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

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.

(3) Formal Logic.

(4) The Three laws of Thought.

• As Aristotle wrote them, 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. 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.

• 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.

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.

(5) Essential tools of integrity.

(6) Minimal Truth tables.

(7) Knowledge, Truth, Probability and Belief.

(8) A few unacceptable consequences of formal reasoning unless extremely careful.

_____________________________________

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.