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Fallacies
– Classical Fallacies1
Classical |
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 |
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.
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A very different Fallacy list by Questor © Fallacies of conduct. Click fallacy above or 13 below. |
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Get the primer free for your computer, a pdf file click here..... |
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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 |
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Chapters ready for reading have 1st letter in Pale red as Preamble.
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I have not restricted this treatise to the customary boundaries of theoretical disciplines, for two reasons.
Go straight to the Fallacy list.
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{ Hamlet. Excellent, i' faith; of the chameleon's dish. I eat the air, promise-cramm'd. You cannot feed capons so. }
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:
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.
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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.
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”.
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.
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Get the primer free for your computer, a pdf file click here.....
'not' = '~', 'and' = '·' , 'or' = '' Ú', and 'if ..... then = 'É' if P then P, or P implies P, where 'P' is a proposition.
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.
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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. |
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P |
~P |
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T |
F |
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F |
T |
It follows that the matrix below is for the negation of the contradictory function above.
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~ |
(P |
~P) |
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T |
T |
F |
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T |
F |
T |
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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.
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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.
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P |
Ú |
~P |
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T |
T |
F |
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F |
T |
T |
The third law of Thought, the law of identity.
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T |
P É |
P |
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T |
~P É |
~P |
This states that
where P is true, it is identical with itself; ....... P ( P implies P ) and
where Not P is True, it is identical with itself; ....... Not P ( Not P implies Not P )
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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.
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Disjunctive proposition.
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v P |
v Q |
v R |
v S |
v T |
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T |
F |
F |
F |
T |
F |
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F |
F |
F |
F |
F |
F |
Conjunctive proposition
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· P |
· Q |
· R |
· S |
· T |
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T |
T |
T |
T |
T |
T |
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F |
T |
T |
F |
T |
T |
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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.
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v O |
v W |
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T |
T |
F |
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T |
F |
T |
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T |
T |
T |
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F |
F |
F |
TWO – the Absence of Oxygen AND Water, ( in the body ).
The sufficient condition, is the more powerful in this table since
'T' represents the result of Life being TRUE.
This shows all conditions where both ingredients are present / absent JOINTLY,
when both are absent, life is absent. When either one is absent life is absent
We know that BOTH are a sufficient condition from this table,
since all other possibilities show life absent when one is absent. This shows both are
jointly part of a more complex cause.
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( · O |
· W ) |
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F |
T |
F |
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F |
F |
T |
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T |
T |
T |
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F |
F |
F |
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.
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( · O |
· W ) |
· Vd ) |
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T |
T |
T |
T |
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T |
T |
T |
F |
This entire section is being overhauled and added to in depth, please revisit fairly frequently, though the unfamiliar tra