Is is Is

I have noticed of late that when an atheist is confronted by one of the several paradoxes of logic that haunt atheism, instead of addressing the issue, the atheist finds it simpler to jettison logic. In such sad attempts, the atheist employs the very laws of logic he denies.

What desolation atheism eventually produces in the soul!

In the dry, dim, gray world where life has no author, hence no meaning, no purpose, no point, no escape, is a world so empty and unwelcoming that eventually even immaculate Reason herself gathers her white robes, quenches her bright torch, and wings away.

A short reminder of the law of logic is in order, and perhaps a word as to why, despite their great boast to be unsentimental and clear-eyed paragons of reason, those who abandon God find it increasingly difficult not to abandon nature, human nature, human virtue, and human reason as the implications of that first abandonment play out.

Logic is based on the law of identity, or, in layman’s terms, based on the idea that anything is what it is.

Whatever else may or may not be true about a thing, we know that whatever it is it, it is what it is.

Existence exists. Reality is real. A is A. “Is” is “is.”

Logic is the study of literal statements for their self consistency. A statement is a representation. A statement is true if and when what it says is so, indeed is so; and when what it says is not so, is not so.

Some definitions:

A statement is valid when it can be put into a form that does not deny what it affirms. A conclusion is necessary when, if the premiss is true, the conclusion must also be true. When two statements stand in this necessary relation to each other, they are said to be logical, whether true or not; and if not necessary, illogical.

If the conclusion does not necessarily follow from the premiss, it may or may not be true, even if the premiss is known to be true. If offered in a proof, a conclusion that does not necessarily follow is called a fallacy. A fallacious conclusion, let it be emphasized, may or may not be true, but even if true,  it is not necessarily true.

A formal fallacy are when the statements are not composed in the form that shows the logical necessity between premiss and conclusion. Formal fallacies include converse error (also called affirming the consequent), inverse error (also called denying the antecedent), the fallacy of four terms, the fallacy of the undistributed middle, and the fallacy of the illicit major.


  • It is a converse error to reason that if sidewinders are poisonous, and Cleopatra was poisoned, therefore a sidewinder bit her. The syllogism does not preclude asps.
  • It is an inverse error to reason that, if scorpions are poisonous, but no scorpion stung me, I am not poisoned. The syllogism again does not preclude asps.
  • It is a fallacy of four terms to reason that, if sunsets are pink, and pink is light red, that ergo sunrise is light red. The syllogism fails to establish that sunrises and sunset share a color in common. (This is an example of a true but fallacious conclusion).
  • It is the fallacy of the undistributed middle to reason that if all Spaniards are Iberian and all Portuguese are Iberian, ergo all Portuguese are Spanish.  The syllogism does not establish a common middle term precluding non-Spanish Iberians.
  • It is the fallacy of the illicit major to reason that if all Spaniards are Iberian and no Portuguese are Spanish, ergo no Portuguese are Iberian. Again, the syllogism does not establish a common term between major premise and conclusion precluding non-Spanish Iberians.

These fallacies can be summarized in a single diagram, showing the four types of proposition (universal or particular; affirmative or negative) and the four types of implication (contradictory, contrary, subaltern, subcontrary).


Two propositions are contrary when while one or both may be false, they cannot both be true. Two propositions are contradictory when if one is false, the other must be true. Two propositions are subcontrary when both may be true, but both cannot be false. Finally, when a universal statement (“the superaltern”) proves the truth of a particular (“the subaltern”), but not conversely, the particular is said to be subaltern to the universal.

Each of the formal fallacies above is a confusion of these four type of implication, as, for example, the fallacy of of the converse conflates superaltern with subaltern. (In the example above, sidewinders being poisonous snakes only means some poisonous snakes are sidewinders, not all.)

And so on for the other formal fallacies.

Informal fallacies include all errors in reasoning due to carelessness, ambiguity, and inattention to the subject matter.

Informal fallacies include all fallacies of accident or converse accident or any fallacy conflating a generality with a universal; and include plurium interrogationum (also called complex questions, trick questions, multiple question, fallacy of presupposition); and include post hoc ergo propter hoc, petitio principiiignoratio elenchi; and the various forms of ad baculum, ad verecundiam, ad ignorantiamad misericordiamad populum; and, of course, the ever popular ad hominem.

I will not weary the reader with examples of each: social media and mainstream news sources will provide them abundantly.

I will say only that only pointy-headed prigs and bookworms avoid ad hominem arguments; nor can you prove ad ignorantiam arguments are wrong; nor is it safe for you to deny an ad baculum argument; that if ad populum arguments were bad, everyone would not use them so often.

Finally, ad verecundiam is the strongest form of argument, as many eminent people will attest.

Let it be emphasized that all informal fallacies, if and when their exceptions are kept in mind, are not wrong.

Indeed, all the informal fallacies are fallacies, not because they are wrong, but because they are generally right.

One generally should not take the word of an unreliable witness with a proven history of untruthfulness, nor rely on the expertise of an expert whose self-interest very likely inclines him to lie; experts generally can be trusted regarding the subject matter of their authority; one generally should avoid what it not in one’s self interest; generally if one event follows another, there is causation, not coincidence, involved; and the reason why people look to the majority to take their cues is that the wisdom of many people together, in the general case, is more sound than the wisdom of one alone. It is generally safe to rely on experts, on tradition, on popular opinion, or on self-interest.

But what is generally right, what is right by and large, is not right universally, and is not necessarily right.

That is what makes an informal fallacy a fallacy. It gives a proof, but not a proof beyond doubt. It persuades, but it is a judgment call, not a logical certainty.

Logic deals not with what is likely to be true, but with what necessarily must be true. That is its great strength and great limitation.

Hence a syllogism can be formally correct, and yet still suffer from an informal logical fallacy, hence not necessarily be true, even when the premisses are true.

To reiterate,

  • valid argument has a correct formal structure. A valid argument is one where if the premises are true, the conclusion necessarily follows.
  • sound argument is one that has a formally correct argument that also contains true premises.

An argument with an unstated premiss could also be sound, if the unstated premiss is true. Such arguments are called enthymemes.

In all these cases, logic deals with literal statements only. Figures of speech, poems and parables, myths and metaphors, rhetoric and riddles, puns and plays on words all employ some degree of ambiguity or double meaning to make their point.

There are degrees of ambiguity in everyday speech which need not, indeed, ought not be replaced by statements of more precision, because no listener is likely to be confused. One need not clarify what is already clear.

Common speech contains layers of meaning which, when no confusion exists, it would be unhelpful, or even counterproductive, to make explicit. We often use understatement or exaggeration to make a point, which, taken literally, would render the statement absurd.

It is commonplace to make statements indirectly, by implication, as when one might say “I am not happy about this” to express anger in an understated way. If taken literally, however, this converse expression only denotes a lack of happiness, not the presence of anger.

As someone whose speech by nature and training are more precise than the norm, I cannot even count the times when, making some statement I meant to be taken literally, I offended the listener, who thought I meant to imply the converse in some coy and indirect way.

An example likely to provoke vehement objection is to say “police lives matter.” In the lunacy of modern political correctness, this is taken (or mistaken) to be a denial that black lives matter.

As a matter of logic, one cannot conclude that if police lives matter, black lives do not, unless one holds the two types of lives mutually exclusive. This is the informal fallacy of presupposition (akin to being asked whether you have stopped beating your wife yet). It is also the informal fallacy of a false dilemma, as if being asked to chose between only two options, when three or more exist.

An informal fallacy of ambiguity also exists here: the word “matter” has no matter to it. If an officer shoots a knife-wielding attacker in the act, surely the life of the victim he saves matters, due to her innocence, not her skin hue.

It is also the formal error of denying the antecedent. “If police lives matter, and blacks are not police, therefore their lives do not matter” follows the same form as “If pigs are mammals and bears are not pigs, therefore bears are not mammals.”

However, most arguments fail not because of formal errors, but merely because of ambiguity, that is, of being overbroad, or resting on a fatuous distinction, or mere vagueness.

To condemn a race for the actions of a few is a generalization; to assert that men can be women on the grounds of an alleged distinction between sex and gender is fatuous; to promote social justice denouncing justice is merely vague, and, in this case, using words that have an emotional connotation but no clear denotation.

Ambiguity is fatal to logic but is facile in common speech.

When the novelist says “it was the best of times, it was the worst of times” the audience is meant to understand that the times were best in one sense of the term, and worst in another sense.

This use of one word to refer to two ideas must be resolved before logic can be applied to the statement. Logic, indeed, need only be raised in a discussion when the audience does not grasp the precise meaning of the terms.

Logic deals with the ideas to which words point, not with words as such. Words are the shrine, workhouse, and playground of the poet, not the logician.

The poet uses words indirectly, to express in words what cannot otherwise be expressed in words. If the love of the poet is like a red, red rose newly sprung in June, does he mean she is fair and soft to the eye, sweetly scented? Does he mean she is thorny? To analyze the poem as a syllogism would be silly, and rob the words of grace and meaning.

But the politician, if he promises to raise the minimum wage while lowering the unemployment rates is not engaging in poetry, but flimflam.

The role of logic is to detect the connections between the concepts being addressed, to discover any hidden contradictions.

More to the point, the philosopher, in his own mind, is tempted to defraud himself when he ponders the deep questions of life, for these concepts are subtle, and implications profound, and human nature being what it is, the temptation to deceive ourselves with self-flattery or self-doubt is overwhelming, and only heroic fortitude and saintly humility stands a chance to outwrestle such a hydra.

Judging from history, the number of philosophers who used their airy speculations into life’s deep matters to justify their own self-indulgence increases sharply in the modern age. The fine and unobvious errors in logic of philosophers like Rousseau, Nietzsche, Marx, and Ayn Rand led to gross and obvious sins in their personal lives.

Now, let it be noted that no word, not even the most precise terms of physics or geometry, can be utterly free of ambiguity. There is no such thing as perfectly precise.  Unreasonable doubts always have room to arise. The most we can hope for is to satisfy reasonable doubts.

For example, we all know noon is distinct from midnight, and day from night, but we also know that dusk and dawn involve an hour or more of twilight before the sun clears the horizon at various latitudes, so which minute precisely divides night and day is a matter open to dispute: civil, nautical, and astronomical twilight are defined differently as when the sun is six or twelve or eighteen degrees below the horizon.

Non-sailors and non-astronomers do not need this degree of precision in daily life, so the question of how to define dawn to the very minute is unlikely to arise.

Hence, as a general matter, the logician need not define any term until needed. He need not know what a Snark is, nor a Boojum, but if he is told all Boojums are Snarks, and all Snarks are fond of bathing machines but slow at taking jests, to know Boojums share that fondness and that slowness.

Again, this conclusion is as certain as the premisses on which it stands, no more and no less. The certainty is not because the logician knows anything about Snarks. The word is a nonsense word.

But the logicians knows that “is” is “is” — which allows him to know that what is true categorically is true in the particular, and this applies not just to Snarks and Boojums, but to all topics and terms, real or imaginary, if the term is unambiguous.

If we know that “is” is “is” what else can we deduce from this? It seems a very small foundation indeed on which to erect a tower of thought, but all rational thoughts of rational creatures have this as their ultimate first premiss.

If ‘is’ is ‘is’ then ‘is’ is not ‘is not’ — or, in other words, no statement can be true when it denies what it asserts.

No matter what the assertion is, it cannot be true when it is also false. From the law of non contradiction we can deduce the law of exclusion: A or not-A. If A is true, its direction contradiction not-A is not. If not-A is true, A is not.

Written out, these basic rules can be expressed thus:

  1. ‘Is’ is ‘is’
  2. ‘Is not’ is ‘is not’
  3. ‘Is not’ is not ‘is’
  4. ‘Is’ is not ‘is not.’

Written as categorical statements :

  1. A is A. This is the Law of Identity.
  2. Not-A is Not-A. This is also the Law of Identity.
  3. Not-A is not A. This is the Law of Either-Or.
  4. A is not not-A. This is the Law of Noncontradiction.

The same can be written as if-then statements:

  1. If A then A. This is the Law of Identity.
  2. If not-A then not-A. This is also the Law of Identity.
  3. If not-A then not A. This is the Law of Either-Or.
  4. If A, then not not-A. This is the Law of Noncontradiction.

These laws apply to any and all statements where A is A, that is, unambiguous statements.

A statement can be more or less accurate depending on how precisely it is worded, and how well those who heed the statement know what the speaker means by those words.

Formal logic studies the implications of statements based on their form, regardless of content. Logic will tell you whether an idea is valid, that is, consistent with itself.

To know whether the content is apt, true, sound, proportionate, or reasonable requires the more difficult faculty of wisdom, also called right reason. Right reason tells you whether an idea is true, that is, consistent with nature.

Right reason also tells you whether you are being honest with yourself, showing the patience and fortitude needed to be a philosopher. Right reason tells you whether an action is truehearted, that is, virtuous, and hence consistent with nature.

The reason why, even to this day, we use phrases about taking defeat philosophically, is that philosophy is meant, not to fritter away time discussing laws of logic, but to use logic to reach right reason, to distinguish true virtue from vices in disguise, to strip ourselves from our own hypocrisies, and, in short, to bring the burning light of honesty to the very place deep inside of us where it is least welcome.

Philosophy is meant to undermine and overthrow pride, particularly intellectual pride. The example of Socrates shows how unpopular the effort is.

Modern philosophy differs from Medieval philosophy in two significant respects: first, it is devoid of Christianity, hence of theology and metaphysics; second, it is garbage.

The examples mentioned above of Rousseau, Nietzsche, Marx, and Rand are sufficient to display the tendency of postchristian philosophy to inflate, rather than overthrow, the great beast of pride. Rand, for example, waxes indignant against those who break contracts or act with the slightest lapse of integrity, but dismisses with an airy wave of the hand objections to adultery. As if the covenant of marriage were less sacred than a contract for goods.

Prechristians had no such tendency. Pagan philosophers of old averred that right reason held her lamp over the high, hard path to virtue, and that, by right reason, we can obtain prudence, the first of virtues; knowing prudence, we can learn justice, which is prudential judgement; applying justice to our own unruly soul fathers the virtue of fortitude, allowing a man to be longsuffering and courageous; and fortitude governing the appetites and passions gives birth to temperance.

The men of the classical world knew little or nothing of faith, hope, and charity, and did not list these as virtues. For this reason, the brilliance of Athens and the glories of Rome arose amid melancholy, stoical, but pitiless men.

These men were resigned to serve cruel and capricious gods, to serve city or serve Caesar with grim finality, marching to wars of conquest, keeping slaves and catamites, exposing infants, and divorcing wives, eventually to fall into the realm of Hades as mere shadows.

The noblest Roman history ever brought forth, Cato of Utica, ended his life on his own swordpoint, dying as honor demanded, even as the most glorious Roman, Caesar, perished beneath the knives of his friends, for the sake of a freedom that the city never regained.

Romans build the godlike architectural wonders of the Colosseum, and there held hellish games where gladiators or wild beasts shed human blood for the amusement of idle crowds.

The Roman devised the most sound and just laws of antiquity, with divisions of power between Consul and Senate, Assembly and Tribunate, then voted bread and circuses to the mob, devalued their coins, and granted permanent dictatorial powers to an Emperor, welcoming his boot on their own prone neck.

In a world ruled by pagan gods, divine parricides and adulterers, and ruled by iron-faced Fates whom even these gods could not defy, nothing more can be hoped for.

And yet, in the postchristian age, not even the stoic dignity and fortitude of the pagans can be found.

Temperance, such as a man who suffers from same-sex sexual attraction, in any sane age, would be called upon to exhibit, or any fool lured to an hour pleasure by addictive drugs or pornography, even such a minor example of temperance as a maiden dressing modestly so as not to enflame unwelcome attention from mashers and cads, in the postchristian world is denounced as internalized oppression, and even the mild suggestion that adults display self-command is dismissed as violently and vehemently wicked.

Fortitude is actively discouraged. The sight of seeing a fit and well muscled young black man, tall and proud, driven to cringing and weeping fear like a wimpy little girl by the sight of a garage-door rope pull, or hearing a wrong pronoun, or reading a book by Mark Twain, or seeing the logo on a bottle of maple syrup, are but a very few examples of how entirely hollow, craven and weak postchristianity attempts to make all men. In the modern world, everyone is a victim, everyone is a pathetic wretch unable to work, to achieve, to overcome.

Justice is injustice, in the postchristian world, and prudence is sin. In all these cases, a simple act of logic would restore these virtues to their proper dignity and role. The arguments are not complex. A schoolboy could follow them.

A schoolboy could follow them; but not a schoolboy who has been taught that words have no meaning, logic is deception, and only emotions are real, and, at that, only emotions that are dark, violent, unjustified, disproportionate, inapt, uncontrolled, and aimed at revenge for imagined offenses. That boy has no tools by which to check his thoughts. The lamp has been quenched.

Without a Supreme Being, there is no answer to the question of why to be good on days when it is not useful. There is no reason to suspect reason is reasonable, nor that the world deduced by abstract reasoning, as in math or physics, is real, and certainly not that abstract reasoning called formal logic. If there is no Word of God, there is no reason words have meaning.

If neither marriage is sacred, nor any vows, nor human life, there is no answer to why to be faithful to family, clan, and nation, nor why to protect the weak, feed the poor, or save the innocents infant from murder. Sodomy becomes a matter of pride, and infanticide becomes a matter of constitutional right.

More to the point, honesty in thought and word and deed become matters of temporary convenience, and honor vanishes. No businessman need fret if his cheats his customers, and no scientist need fret if he falsified his results. Whatever is convenient or politically correct replaces honest speech with elliptical jargon and jabberwocky. Words stop.

Such is the central need of logic to the human soul. Without it, right reason cannot be reached. Without reason, virtue becomes vice.

A wordless world is a world of shouts and slogans, emotion and mad passion, but no meaning, no logic, no philosophy. It is a world of beasts, but beasts who are more bestial to each other than any natural beasts.

Men in such a state will devolve (as the father of science fiction once imagined) into shambling cannibal troglodytes, and into their disarmed, hapless, and gracile victims: livestock rather than rational creatures.

Our elite may not as yet be literally eating men like Soylent Green, but they consume our lives and lifeworks without a qualm of hesitation, and harvest the organs of slain unborn in a fashion more grisly than mere cannibalism.

Without God, philosophy is lost. Without philosophy, men become Morlocks or their Eloi livestock.

Some atheist philosophers make bold but convoluted attempts to explain why a moral law imposes an imperative on all rational creatures in the absence of a lawgiver; or explain how human reason, emerging from unreason by the blind and unintelligent crapshoot of Darwinian evolution, is a reliable instrument able to conform to the regularities in nature and detect them; or, indeed, how there are regularities in nature to detect, if nature is a dead conglomerations of accidents rather than a living work of art.

Abolishing the Supreme Being while preserving dependent lesser beings, denying creator while affirming creation, are feats of intellectual acrobatics increasingly rare to see ventured. The architects of towers without foundations, free to float among airy clouds but unable to stand upright, grow ever more few.

The only sound foundation of any philosophy is reason, but if creation is accidental, is it irrational, nor has any being within it cause to be otherwise.