Extending the Power of Logical Argument: Coherent Propositions and Truth Functions

While some may question the extensive application of logic (see e.g. my previous post on logical fallacies) to human disputation, it is important to bear in mind logical rigor doesn't come naturally to most humans. We are not all 'Mr. Spocks', after all, nor is it likely our significant others would want that. Hence, when we are confronted by a debate or having to make a logical and coherent case we have to be prepared to summon great energy and often investment of time to ensure: a) we don't mix 'apples' and 'oranges', and b) we consistently use each in its proper reference frame.

A certain level of rigor or discipline then must be applied to ensure coherent, critical thinking, especially taking care that  truth categories are not mixed up and that claims of truth aren't confused with attitudes to truth! Sadly, most who pontificate on matters of religion, or economics,  have probably never taken a logic or philosophy course in their lives, so end up flying by the seat of their pants - and end up crashing and burning.

The purpose of this post is to extend the power of logical argument beyond the basics laid out in recognizing assorted logical fallacies.  I do not promise the going will be 'easy' only that the energetic reader should be much better able to handle him (her-)self in a debate or argument afterward.

Preliminaries:

1) One cannot assume a "logical deduction" unless there exists a relationship between the premise and the conclusion such that we have a right to expect the conclusion IF we know the premise is true (cf. Russell, Introduction to Mathematical Philosophy, p. 145)

Said relationship then ought to be between analogous truth claims OR attitudes,  but not mixing up both.

2) From (1) it follows that two truth functions which have the same truth value for all values of the argument are indistinguishable. Thus, p and q are the negations of not-p and not-q.

In terms of propositional functions, let q = S(A) and p = S(B). Then if p = f(q) the contradictory hypothesis is p' = f(~q) .

Example: if p = f(q) = "The Bible is the actual word of God verbatim and cannot have either errors or contradictions"

BUT - if one error or contradiction is found in it, we must have: p' = f(~q) or:

"The Bible has a contradiction in it, so cannot be the actual word of God, but of mentally-limited humans."

3) Five basic truth functions exist (op. cit.)and are not all independent:

i) The 'negator': Not-p

Expresses that function of p which is true when p is false, and that which is false when p is true.

Note: The truth of a proposition or its falsehood is referred to as its "truth value". This can be either TRUE or FALSE, i.e. the true value of a true proposition is true, and the falsehood of a false proposition.

Thus: Mars has two Moons, Deimos and Phobos, is a true proposition, and

Saturn does not have 101 Moons, is a true proposition

ii) The disjunction: p OR q:

This is a function whose truth value is 'truth' when p is true and also when q is true. (It can be mechanically-electronically embodied by the logical OR - gate)

But the truth value is falsehood when both p and q are false.

iii) The conjunction: p AND q:

Has 'truth' for its truth value when BOTH p and q are true, otherwise falsehood.

It is denoted by the logical AND gate.

Example: p : "Solar flares erupt with large areas and temperatures in the millions of degrees"

q: "Solar flares result from magnetic instability in the associated plasma"

iv) Incompatibility: ~ (p /\ q)

E.g. p and q are not both true, or the negation of conjunction (iii). It is also the disjunction of the negations of p and q, i.e. not-p or not-q. The truth value appends 'truth' when p is false, and also when q is false. Likewise, the truth value appends falsehood if both are true.

v) Implication: p->q (p implies q) or "if p, then q"

Example: If the New Moon is aligned with the Sun we can get a total eclipse of the Sun

Here: p = alignment of Sun and New Moon

q = total eclipse of the Sun

This can be generalized in various ways, e.g.

"Unless p is false, q is true" OR

"Either p is false or q is true"


4) Further generalizations are possible using (1)-(3), e.g.

a) Negation is the incompatibility of a proposition with itself, or p/p

E.g. "the Apollo astonauts brought back Moon rocks made of green cheese"


b) Disjunction is the incompatibility of not-p and not-q or (p/p)[(q/q)

Example: "Saturn is not a very large or hot star"

c) Implication is the incompatibility of p and not-q, or p[(q/q)

Example: "If the Moon rises tonight, the Sun will not rise tomorrow"

d) Conjunction is the negation of incompatibility, e.g. (p/q)[

Example: "Saturn and Earth are both member planets of the solar system"

5) Gödelian Truth Limits:

Consider a simple statement of logical transitivity:

X = Y

Y = Z

therefore X = Z

What if instead we append an axiomatic statement that reads, in effect: "X=Y is unprovable-in-the-system". If this statement is provable-in-the-system, we get a contradiction, since if it is provable in-the-system, then it can’t be unprovable-in-the-system. This means the original axiom: "X= Y is unprovable-in-the-system" is false. Since in any consistent system nothing false can be proven in-the-system, the proposition is undecidable.


Now, given all these basics, let's see if we can apply them to the assertions or alleged propositions made by a recent blogger:

Example (1):

"All TRUTH is exclusive ! The truth that "two plus three equals five" is very exclusive too . It does not allow for any other conclusion ."

The basic and most fundamental error is that he mixes up an absolute general statement, with a particular one. "All Truth is exclusive" is in fact unprovable by the same set of axioms or axiomatic statements that would prove "2 + 3 = 5". The reason is that the first is a meta-statement about the WHOLE Truth system! To be more concise, the offender is rendering an ALL-inclusive truth statement about what he insisted is an absolute exclusivity! He claims "all truth is exclusive" but his statement itself is all-inclusive and implied to be the exception to his own proposition! Thus it violates the Gödelian Truth Limits (5).

It helps here to present a more concrete illustration and example, to show why the most general statement is false. We take here the original claim of Epimenides in his “all Cretans are liars” paradox:

"All Cretans are Liars"

If the speaker is a Cretan, then the statement is ipso facto unresolvable. If Cretan, he exists within the so-called abstract, formal system. Yet, he’s making a statement (meta-) about the system. Hence, is he lying? Or is he telling the truth? This cannot be resolved. An undecidable proposition, as Gödel’s Incompleteness Theorem (II) applies.

In like manner, the statement "All Truth is exclusive" emerges as an undecidable proposition at the very least. (And it may also be false in the framework earlier considered).

Scott Soames in his monograph Understanding Truth further clarifies the issue of more and less general schema to arrive at truth, and what is “materially adequate” p. 69:

“The characterization of individual instances of (different) schema has consequences for more general definitions of truth. If such instances (e.g. L1 statements) are thought of as partial definitions, then the task of defining truth for an entire language may be seen as finding a way of generalizing the partial definitions so as to cover every sentence of the language.”

In other words, in order to make the claim: "All Truth is exclusive" one would have to: a) have access to ALL COMPLETE truth statements that can exist in the universe, and b) show that no two of them exhibit disjunction, or incompatibility of other problems. In addition, one would have to articulate his proposition as compatible with the claim: in other words, one cannot formulate an all-inclusive truth statement to apply to one for which "All Truth is exclusive". This is not feasible, because no human mind is capable of formulating an absolute exclusive truth statement via an all-inclusive truth claim.

Consider the following statements referring to solar flares, and note the L1 hierarchy that presents:

1) A class X solar flare occured on the Sun last Tuesday.

2) A class X-7 solar flare occurred on the Sun at 22h 33m GMT last Tuesday.

3) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday.

4) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday and lasted a total duration of 1440 seconds.

5) A class X-7, optical class 2B solar flare occurred on the Sun at 22h 33m GMT last Tuesday, peaked 543 seconds after inception, and lasted a total duration of 1440 seconds.

Now, are ALL of the above statements (referencing the same event) EXCLUSIVELY true? Or better, are they all EQUALLY true? If not, why not? Can one therefore have true statements which do not express the entire truth but rather only a partial truth? Obviously, the answers are in succession: NO - they can't all be exclusively true (on account of factual intersection), NO - they are not all equally true (since they embody different levels of knowledge about the event), but YES - one can have TRUE statements which only convey a partial truth.

Now, if one can have partial truth statements then one can still access truth or true valued assertions at some level.

Let's go on:

Example (2):

"The same is true for value statements , such as "Racism is wrong" and "People should not be cruel." These views do not tolerate any alternatives . "

The problem here is that he has not proven the values are actual truth values, as opposed to the subjective values of a moralism in his own mind. In particular, he's violated Precept (1): "One cannot assume a "logical deduction" unless there exists a relationship between the premise and the conclusion such that we have a right to expect the conclusion IF we know the premise is true". But he has formulated no premise, because he's not defined either "racism" or "cruel" - he simply assumes everyone knows exactly what he means! Hence, he leaves us no testable proposition that can be put into any logical relationship, far less link a premise to a conclusion.

Questions then occur: E.g. : Is drawing or portraying President Obama as a witch doctor with a bone through his nose, racism? If not, why not ? The first step in setting out a premise that portends a "truth value" is therefore to carefully define one's terms, don't assume everyone knows what you mean!

So, IF he defines both "racism" and "cruelty" and then integrates them into a premise, tied to a conclusion that relates them- we may then consider whether "These views do not tolerate any alternatives". (In which case, depicting President Obama as a witch doctor with a bone through his nose may not meet the criterion of an "alternative" to him, hence can be "tolerated" - but as he's framed his case, we can't say so because it's too vague.)

Example (3)


"All truth CLAIMS are exclusive . For example , if humanism is true , then all non-humanisms are false . If atheism is true , then all who believe in God are wrong . Every truth claim excludes its opposite ."

As I already showed (Example (1)) the first statement is an undecidable proposition by virtue of en embedded contradiction. Thus, we behold an all-inclusive truth statement intended to apply to the proposition that "all truth is exclusive"! Thus it is a meta-statement about truth claims, not a statement within an axiomatic system concerning a class of truth claims. Thus, it is a non sequitur to flip from this most general, undecidable proposition to saying "thus if humanism is true all non-humanisms are false". In addition, it's an oversimplification, since one can have a conjunction (3(iii)) such that a truth value exists when BOTH p and q are true. (And again, we note he's neither defined "humanism" nor "non-humanism" so we've no idea what he means.)

But let's use the conjunction of propositions to show discrete and particular possibilities that defy his simple conclusions. It is known that in its most generic sense "humanism" means :

That philosophy or coherent attitude supportive of human values, i.e. those values that elevate, sustain and integrate a society beyond its merely physical or mechanical operations

Thus, our society provides physical infrastructure - such as roads, sewers, water mains, etc. and also mechanical contrivances (buses, or cars, trains) to help the people survive but humanism allows support systems beyond these basics, for example, decent and affordable health care. The reason is that a society without quality affordable health care (accessible to all) cannot function to its optimum. If too many are ill, then they can't be productive and if not productive, the society deteriorates because too few must work to care for the many who are ill or otherwise disabled.

The underlying conjunction here (p and q) is:

p: Humans are worthwhile beings to support in other ways besides purely mechanicalq: All humans have the same essential needs for humane support, so all should thereby be provided with said humane support

Since (p -q) defines the conjoint truth value, then "non-humanisms" would have to mean non-humans and would thereby be ab initio excluded from the proposition putatively concerning HUMANS. Hence, the claim of "non-humanisms" implicit in a human domain is a falsehood since it wouldn't apply to humans anyway! (Though one can argue that an "extended humanism" would also confer health care on animals in need, or at least certain classes of them, i.e. personal pets)

The statement about atheism is also invalid, because it reduces atheism to one meaning, ignoring all others. (For example, implicit atheism, and agnostic atheism). It would be like me writing: "If evangelical Christianity is true , then all other Christians who believe in God are wrong". This is arrant nonsense. Moreso since it hinges on the claimant providing the necessary and sufficient conditions for his (exclusive) deity to exist - thereby showing why its conditions supersede those of other Christians. To append a truth value to the statement then, a specific definition of atheism is needed, not an open-ended term that invites any reading.

Finally, the appended proposition:

"Every truth claim excludes its opposite ."

Has already been shown invalid, since it omits consideration of the fact that conjunction is the negation of incompatibility, e.g. (p/q)[. If one can have any conjunction, uniting propositions of truth p and q, then clearly a contingent truth claim p does not exclude its co-contingent q. As a more or less trivial example:

p: "Every photon of light is a particle"

q: "All light is waves"

In fact, as noted before in a previous blog:

http://brane-space.blogspot.com/2010/06/more-on-heisenberg-microscope-in.html

Both statements can be true, provided the optical limits of observation are made clear. It is this very example, underscored by quantum mechanics, which displaces the either-or exclusionary absolutism of the claim. In other words, the actual experiments of QM show that observables in the form of propositions can be BOTH and not merely one OR the other! This is the very basis for the development of quantum logic, see e.g.

http://brane-space.blogspot.com/2009/09/foray-into-quantum-logical-and.html

Looking At Some Logical Fallacies

In the American political, economic and religious landscape it is rare to find people who are able to rigorously argue or debate their case or claim - whether for cutting Social Security, or starting a new war, or defending the existence of a supernatural Being. In many cases, the person isn't aware of the logical pitfalls as he endlessly debates his skeptic opponent. This blog post serves to highlight some common logical fallacies one can encounter.

1) Circular reasoning: Or circular logic, is a logical fallacy in which the proponent-claimant begins with what he ought to be proving:

Example: “God does not need a cause because He had NO BEGINNING”

In this example the related debate is on the proof of God's existence, and the disputant has insisted that a causeless cosmos is no more exotic or unusual than claiming a causeless deity, and we already observe the universe in existence.

Further, since  a "causeless God" is a much more extraordinary claim than a causeless cosmos, e.g.  http://brane-space.blogspot.com/2009/09/debunking-anders-primary-cause-fantasy.html

then much greater argumentative heft must be summoned to defend it. The example shown, however, reveals "God" is trotted out as part of the premise, and the causeless attribute is added as a separate part. Thus,  the religionist's argument is useless because the conclusion is one of the premises. Circular logic cannot prove a conclusion because, if the conclusion is doubted, the premise which leads to it will also be doubted.

Since I dispute a causeless God's existence, then I dispute the entire content of the premise.

Related to this, actually a sub-category of circular reasoning, is "begging the question".  In fact, there is no "question" to follow or beg but rather it refers to the specious circular argument under consideration. As in the case of our example shown, it means assuming that ("causeless God") which one ought to be proving. It is believed to have originated in the 16th century as a mistranslation of the Latin petitio principii "assuming the initial point". Alas, the misuse has since fallen into the public-mass domain and many people use it erroneously to mean raising the question.

Example: "This (vote to cut food stamps) begs the question of whether the Democrats are really serious about supporting the middle class."

One who is invoking logical fallacies would do better simply  to avoid the term altogether and use circular reasoning instead.

2) Non -sequitur:

This fallacy is based on assuming or asserting that some proposition is validated based on a prior claim. One clever one sometimes used is that:

 "Believers can’t violate real logic  because “God is the author of logic and reasoning”.

A non-sequitur. Also, no proposition since it's not founded on any a priori true statements of or demonstrable facts. As Scott Soames notes (‘Understanding Truth’, Oxford Univ. Press, 1999, p. 18):  "A sentence or utterance cannot be true potentially (or subjected to belief) if it says nothing or expresses no proposition."

Logic, reason and its derivatives – the articulation of propositions and conclusions which are demonstrated by consistent experience and verification in the material world, are neither germane nor relevant- for example - to claiming the existence of an entity presumed “infinite” and also “omniscient”. Such a deity would neither have any use for logic or be able to appreciate it, far less originate it – since the necessary and sufficient conditions for its existence obviate it.

Consider: Logic requires the isolation and separation of objects in order to relate them to propositions. In this way both generalizations and deductions can be made.

A logical sequence might be (give propositions p, q, and r):

If p, then q

If q, then r

Hence p-> r

(Hence, p implies r)

However, to do this necessitates that the objects connected to the propositions p, q, and r be isolated from each other by category.

Now, let’s associate each in a concrete way with a proposition:

p = A hydrogen nebula forms dense with dust

q = The hydrogen nebula experiences gravitational collapse

r= a proto-star forms

Thus, each proposition is associated with separate (discrete) object (p (H-cloud), q(denser cloud via collapse), r( proto-star)

This template example may explain why religious believers have so much difficulty proving the existence of a supernatural Being.  The claimed entity - putatively infinite - cannot be resolved into separate parts for integration into a consistent logical argument.

3) Post hoc ergo proper hoc:

Example:

"Jim got seriously ill and had to be hospitalized. I prayed for him and he got better after five days. Therefore, my prayers made him better."

This is quite common and easily exposed. It basically means a person has connected some event in a causal fashion with an event that has gone before – though there is no proof whatever of causal nexus.

It is often observed after disasters, when there are few survivors, and they claim that they “experienced a miracle” by escaping alive. In fact no connection exists between the plane crash or whatever, and their survival. They were merely lucky – to perhaps be sitting in the right seat at the right time, nothing more.

One of the most common examples, however, concerns prayer and alleged “effects” as embodied in the example statement.. Someone prays for ‘X’ and ten minutes or ten hours or ten days later something happens that was “prayed for”. (E.g. someone recovers from a bad cold or flu) Because the event, although a coincidence, occurred after the prayer,  it is believed that prayer caused the manifestation.

4) Slippery Slope:

Examples:

"If we legalize marijuana across the country, our people will collectively lose the ability to want to do anything- and they'll just tune out  - so we can be taken over by anyone!" 

"If the Russians get away with taking Crimea, they will go after all their former Soviet bloc states next!"

Those who invoke slippery slope arguments want to convince you that legalizing marijuana, or cultivating atheism, will launch the most stupendous catastrophes in the history of humanity or the cosmos. Biblical plagues of locusts, diseases, famines…not to mention terrorist attacks, will rain down on one and all. Families will be torn asunder. Functioning society will crash.

 The base thread in all slippery slope arguments is the assumption, or perhaps more accurately the false assumption, that some despised outlook or behavior will lead inexorably to a vastly worse outlook or behavior. Although these tactics are insipid on their face, since no concrete evidence is ever presented to support them (or if it is, it’s specious), they’re invoked because people can be so easily misled by appeals to fear. All that’s required is a preconceived negative image, e.g. an MJ user zoned out and oblivious to the world around him, and the recipient of the disinformation will be ready to accept just about any claim.

History shows, time and time again, that appeals to slippery slope reasoning often do much more harm to innocent people than they do to advance a case for some agenda- whether preventing nationwide legalization of MJ, refusing to vote an atheist into public office, or starting a war with Russia over the Crimea annexation.

5)  Ignotum per Ignotius:

Example:  "The human eye is far too complex an organ to have come about in any way other than intelligent design."

Of all the fallacies, I think this is the most endemic and pervasive within the U.S. cultural war landscape. This dates from as far back as 1925, when Christian “design” model creationists argued the best “cure for atheism” was the structure and design of the eye. Well, hardly! Since, after all, the eye “sees” optimally at a particular wavelength (~ 5500 Å) of light, precisely because it evolved on a planet with a star whose maximum radiation output is at that wavelength!

What is the logical fallacy of ignotum per ignotius? Basically it translates from the Latin to mean: “seeking to explain the not understood by the less well understood.” In this case, attempting to account for the alleged grandiose “design” of the human eye by appeal to totally unknown constructs (e.g. a supernatural or unknown "designer"). This, after all, would have to be the subtext if the eye’s design is being viewed as “a cure for atheism”. (E.g. the atheist is compelled to surrender evolution via natural selection, since the inherent nonrandom survival features are alleged to be unable to account for the splendid design).

The problem with this line of argument is that it invokes a less well-known or understood mechanism (“the designer”) to account for a structure or organ whose origin may not be fully apprehended at this moment. But who or what is this designer? The proponents of the various forms of creationism (including the now fashionable intelligent design) won’t say, but it doesn’t require an Einstein to infer they are interjecting a supernatural agent. That is, “God.”

The problem is that all intelligent design (ID) has done is to subsume naturalistic evolution's observations then magically assert they are produced by "intelligent design", since no random process could possibly arrive at such intricacy in a billion years. Thus, rather than accept a fairly well understood random process ID’ers opt to nix it in favor of a much less well understood “designer” about whose specifics, attributes they are totally silent.

All they can offer up is the canard that: “X, Y or Z structures display irreducible complexity, hence there must be some unseen intellect working behind the scene to create it!" This is pure nonsense as well as a circular argument- but most important commits ignotum per ignotius fallacy. (Note that very often logical fallacies are committed in sets, though one particular transgression stands out.)

To paraphrase the philosopher David Hume[1]:

"No testimony is sufficient to establish a miracle, unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish."

For example, consider the example of the eye again. Is the falsehood of its intelligent design more miraculous than the fact it attempts to establish: that the eye is the product of intelligent design? Arguably no. While the falsehood would leave natural selection as a primary agent, it is (as we saw) in no way is “more miraculous” or incredible than the initial ID proposal! As I noted earlier, by the time natural selection appears, a selection effect in the genome is already solidified. So no "random chance exists", .e.g
http://brane-space.blogspot.com/2010/08/if-youre-going-to-quote-dawkins-do-it.html

6) Arguing from authority:

Example: "Read John 3:16! If you don't believe in the Lord Jesus Christ as personal Savior you are going to Hell!"

If you’ve ever argued with orthodox Christians, you know how often they cite chapter and verse from their Bible to try to force an argument to their side.  The tendency has become so predictable it resembles a kind of dog whistle response whenever an unbeliever appears in view. The Fundies (especially) salivate-drool and aren't even aware they're doing it. You start a rational argument with a hard core believer, and within five minutes he’s trotting out the old canard:

“The fool hath said within his heart there is no God!”

If that citation doesn’t work, look for him to go back to his biblical or scriptural grab bag for some other forlorn, antiquated quote (say like John 3: 16) , all in an effort to convince you that you, Mr. or Ms. Heathen, are going against two thousand year old authority and God’s holy writ! The favorite quotes, by the way, seem to be all those dealing with “Hell” in the New Testament, or related to the end times and the “Beast” written about in Revelation. All of these, as well as the psychotic personality portrayed in the Old Testament, disclose (god-) concepts fashioned by human minds. Martin Foreman hits the nail squarely on the head when he writes[2]:

“No self-respecting human author, far less an all-knowing deity, would suggest (the Bible) is worthy to be considered a holy text”

Catholics at least are somewhat less predictable than Protestants, maybe because Catholics were forbidden to read the Bible for centuries, so didn’t develop the incredible fetishism and obsessive dependence displayed by many evangelical Protestants


7) Red Herring:

In any argument or debate with a diehard cultural warrior, the most anticipated tactic is always the red herring. This tried and true ruse represents an effort to re-direct a debate away from its central issue to a marginal or peripheral one.

Examples:

“Look at all the crime, the murders and the drugs going on! If it weren’t for atheists we’d have none of these!”

"Socialism has always failed because it seeks to steal from those who create the jobs, and produce the goods!"


"The Russians just used NATO expansion as an excuse to justify their invasion of the Crimea!"


In fact, none of the above are remotely related to, or effects from, the cause imputed. More atheists aren't going to increase crime (there are fewer atheists per capita in prisons than any other group), nor are socialists going to "steal" from those who create jobs,  nor did Russia occupy Crimea out of an "excuse" - i.e.  the NATO expansion is real and was threatening to them.

In each case the red herring exploiter seeks to take attention off the real causes of whatever problems are under discussion and deflect them to a specious scapegoat or smokescreen cause. Thus, poverty and extreme economic inequality aren't examined as the primary sources of crime, drugs etc. - but instead atheism is blamed.  Similarly, an inefficient, capitalist economic model isn't examined  (based on the Pareto distribution) for why its sundry aspects fail in a low aggregate demand society. Instead,  Socialists are blamed for trying to "steal" the means of production - when in fact the alleged job creators are merely sitting on their money and doing nothing- leaving millions jobless - yes, who would have jobs under Socialism because tax monies would be used for capital works- alternate energy programs and not launching wars or specious spending.

In like manner, the Russians have been blamed for "aggression" on Crimea- when in fact it is the U.S. that has driven NATO expansion (at the behest of Lockheed and other defense companies eager for contracts) right to Russia's border- hence posed a threat to them.  But it's more convenient to use the Russians as the scapegoat than to take a cold, hard look at one's own belligerent and exceptionalist nationalist policies.

These sorts of red herring examples, while egregious in their own right, also force the demonization of the selected scapegoats  - whether atheists, Socialists, or Russians. Each is to be identified as walking, talking moral scourges who inflict a tendency to evil-doing on any vulnerable person in the society, or on other  "innocent" nations (e.g. case of USA)  who are themselves moral exemplars  - or so they'd have you believe.

8) No True Scotsman:

It was humanist Philosopher Antony Flew, in his Thinking about Thinking, who first made people aware of the "No True Scotsman" Fallacy.

As he put it:

"Here we have Angus, a Glaswegian (inhabitant of Glasgow), who puts sugar on his porridge, and who is proposed as a counter-example to the claim “No Scotsman puts sugar on his porridge”.

Then the ‘No true Scotsman’ fallacy would run as follows:

(1) Angus puts sugar on his porridge.

(2) No (true) Scotsman puts sugar on his porridge.

(3) Therefore:Angus is not a (true) Scotsman.

And:

(4) Therefore:Angus is not a counter-example to the claim that no Scotsman puts sugar on his porridge.

Thus the 'No true Scotsman fallacy' , while postulating a false exception that is exclusively "real" or "true",   is actually a way of reinterpreting evidence in order to prevent the refutation of one’s position. Proposed counter-examples to a theory (or verifiable claim) are dismissed as irrelevant solely because they are counter-examples. Hence, they are depicted by the fallacy as not really what the theory or claim is about. The fallacy thereby entails discounting evidence that would refute a specious singular proposition, concluding that it hasn’t been falsified when in fact it has.

Another example:

"NO REAL American criticizes his own country or government!"

Again, the premise is that criticism of one's country means one cannot be a real citizen of it. This is irrespective of all the things the criticizing citizen may do (e.g. voting, national service, i.e. volunteering in Peace Corps, contributing to his community) that discloses powerful discounting evidence.   But as in the other manifestations of the fallacy, all evidence is reinterpreted to prevent the refutation of the specious position - which often also adopts the banner of a false patriotism. (For this reason, Samuel Johnson once said "Patriotism is the last refuge of a scoundrel.")


Next time you engage a person in debate, be cognizant of how he or she may attempt to use one or more of these fallacies on you!


[1] David Hume: An Enquiry Concerning Human Understanding, Sec. X “Of Miracles”, Prometheus Books, 1988, p. 103.

[2] Martin Foreman, “Good News for Atheists- The Bible is NOT the word of God,” reprinted in Freethought Springs, March, 2007 from the series by M. Foreman: If God Existed, He Would be an Atheist.