Intellectually Dishonest Atheists

As philosopher Edward Feser has pointed out, some atheists are simply not intellectually serious. They may be very ignorant or uneducated, directly dishonest, deeply confused, ill-informed, willfully obtuse, ideologically dogmatic, or just plain stupid; the end result is the same: it is not possible or fruitful to have a serious, rational discussion about God with such people. Here are some red flags which may alert you that you are dealing with an intellectually dishonest or defective atheist:

✅ 1. A persistent inability or refusal to distinguish God from a god or gods. This is a distinction 3 or 4-year-old children can easily grasp, so any atheist who claims not be be able to grasp it is either severely intellectually impaired or lying. In almost all cases, the atheist is simply attempting to conflate God with a god in order to set up a strawman and/or trying to annoy you by belittling God—while ignoring the basic conceptual distinction that all European languages mark by differentiating the word “God” from the word “god” by capitalization. As the Stanford Encyclopedia of Philosophy explains, in the entry written by atheist philosopher J. J. C. Smart:

‘Atheism’ means the negation of theism, the denial of the existence of God. I shall here assume that the God in question is that of a sophisticated monotheism. The tribal gods of the early inhabitants of Palestine are of little or no philosophical interest. They were essentially finite beings, and the god of one tribe or collection of tribes was regarded as good in that it enabled victory in war against tribes with less powerful gods. Similarly the Greek and Roman gods were more like mythical heroes and heroines than like the omnipotent, omniscient and good God postulated in mediaeval and modern philosophy.

Theists have little to no interest in discussing gods, at least not when God is the topic of discussion. If an atheist wants to discuss gods, he is free to do so, but he cannot pretend talk of gods has any bearing on or relevance to a discussion about God.

✅ 1.1 A persistent inability or refusal to distinguish God from such things as imaginary friends, faeries, wizards, spaghetti monsters, Santa Claus, or other fabulous, fictitious, or mythological entities.

✅ 1.2 A persistent habit of paraphrasing religious ideas in ways which are deliberately ludicrous, derisive, or tendentious, e.g. describing the resurrected Christ as “a zombie,” or God as a “sky daddy.”

✅ 1.3 Persistent use of the fallacious “I just believe in one god less than you” rhetorical trope.

✅ 1.4 Persistent use of tendentious and irrelevant rhetorical mischaracterizations of Christianity, e.g. as “Bronze Age mythology.” Christianity, of course, dates from long after the so-called “metallic” ages, in fact from the prime of the Roman Empire, on of humanity’s civilizational high points. And Judaism, its precursor religion, derives almost entirely from the Iron Age up through historical times—not that the age of a teaching has any bearing whatever on its truth-value.

✅ 1.5 Persistent dishonest characterization of God as some kind of “cosmic tyrant” or “cosmic oppressor” (interestingly enough. the position of Satan).

✅ 1.6 Persistent dishonest characterization of God, especially in the Old Testament, as a moral monster.

✅ 1.7 A persistent inability or refusal to distinguish miracles from magic, usually paired with a tendency to attribute magical powers to nature, e.g. in such claims as “the universe created itself out of nothing” or “properties such as consciousness just emerge out of unconscious matter, because they do.”

✅ 2.0 Belief in scientism, the logically incoherent claim that “only scientific knowledge is valid/real/genuine knowledge” or that “only science or the scientific method can establish the truth-value of propositions,” claims which are neither themselves scientific nor established by science, and hence, self-defeating, and which entail such absurdities as “no human being knew anything before Europeans in the 1600s.”

✅ 2.1 Persistent claims that science, which studies physical nature by means of empirical observation and quantitative measurement, has any bearing on the question of the existence of God, who is by definition, beyond nature, not empirical, and not measurable in terms of quantity. Persistent insistence that claims about God must be proven “scientifically” or that any evidence for God must be “scientific” fall into this category.

✅ 2.2 The claim that Galileo Galilei’s run-in with the Roman Catholic Church in 1633 proves (somehow) that there is some kind of natural antipathy between either (a) science and religion, or (b) science and Christianity, or (c) science and Catholicism. This indicates a complete ignorance of the history of the Galileo affair, and is merely a recycled weaponized meme of the early Enlightenment.

✅ 2.3 Use of the non sequitur that the multiplicity of religions proves that no religion is true, either wholly or in part. By this logic, of course, one may also “prove” that no scientific theory is or can be correct, wholly or in part, since there are always rival theories.

✅ 2.4 Claiming or assuming that the atheist, a finite being who is not all-knowing, is not all-powerful, is not all-wise, and is not all-good, nevertheless is in an epistemic position to know with certainty what an all-knowing, all-powerful, all-wise, all-good being would or would not do or have done.

✅ 2.5 The belief the atheist knows the true or real origin of religion in human pre-history, a matter which, since it occurs far in human pre-history, we have no certain knowledge of, but only conjecture.

✅ 2.6 The peculiar belief held by some atheists that their total ignorance with respect to God and divine matters is in fact an infallible indication of their intelligence or wisdom or knowledgeableness precisely about the things about which they know nothing.

✅ 2.7 Repeated assertion of the evidently false claim “there’s no evidence for God.”

✅ 3.0 Persistent use of the burden of proof fallacy, that is, the rhetorical trope which combines an argument from ignorance (“my position is the default position,” i.e. “my position is true until proven false, so I need not argue for it) with special pleading that the atheist be allowed to use arguments to ignorance in support of atheism (i.e. “atheism is true because I am totally ignorant about God or divine matters”).

✅ 3.1 Chronological bigotry, i.e. the absurd belief that human beings who lived prior to (say) Richard Dawkins were one and all somehow mentally inferior to anyone living today, up to and including the greatest minds of the past. This would also include the belief that all human beings in the past were incapable of skepticism or critical thinking, or were somehow exceptionally gullible or credulous in a way we, the Enlightened Moderns, are not.

✅ 3.2 “Arguments” that consist wholly of posting atheist memes, e.g. “Eric the God-Eating Penguin.”

✅ 3.3 “Arguments” that consist of no more than exercises in blasphemy or obscenity.

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“Fallacies” aren’t what you think they are—and they aren’t very useful.

If you spend any amount of time online following or taking part in debates, you’ll eventually see someone accuse someone else of committing or employing “a fallacy.” What exactly does this mean?

The superficial thing it means as that the accuser is claiming that there is something wrong with the other person’s argument—specifically that the conclusion they are drawing doesn’t follow from the premises they are using; and so (by definition) their argument is logically invalid—where “logically invalid” just means “it is possible that the premises are true and the conclusion is false.”

But people often assume or act as if a fallacy were something more than this, that it is a kind of meta-error that makes arguments erroneous, that it is a kind of formal invalidity maker. But “fallacies” are no such thing.

What is a “fallacy”?

There is fairly wide agreement about what one is, some kind of error in reasoning, but if you take a close look at how logicians both professional and popular define “fallacy,” you will quickly see that there seems to be no “something more than just an error” that people seem to think there is. Here’s a representative list of definitions:

“A fallacy is a deceptive error of thinking.” – Gensler, Introduction to Logic

“A fallacy is a mistake in reasoning.” – Kreeft, Socratic Logic

“A fallacy is a flaw in reasoning.” – yourlogicalfallacyis.com

“A fallacy is an error in reasoning.” – The Nizkor Project

“A fallacy is the use of invalid or otherwise faulty reasoning or ‘wrong moves’ in the construction of an argument.” – Wikipedia

“Fallacies are deceptively bad arguments.” – Stanford Encyclopedia of Philosophy

“A fallacy is a kind of error in reasoning.” – Internet Encyclopedia of Philosophy.

What makes an argument valid or invalid?

There are two basic principles of logic that you must grasp to understand this, and one false principle that you must recognize as false. Let’s start with the correct principles:

(V1) An argument is valid if and only if it instantiates any valid argument form.

(V2) An argument is invalid if and only if it fails to instantiate any valid argument form.

This principle is INCORRECT:

(F1) An argument is invalid if it instantiates an invalid argument form.

Reasoning is movement of the mind from premises to a conclusion, from point A to point B. An argument is valid if it can get from point A to point B by any possible route; it is invalid only if one cannot rationally get from A to B at all. Note that the fact “you can’t get from A to B by route F” doesn’t entail “you can’t get from A to B at all.” This is why (F1) above is a FALSE PRINCIPLE: The fact that a given argument A instantiates a given invalid argument form F shows nothing at all about the validity of A; A can, in principle, instantiate any number of invalid argument forms and still be valid—it only has to instantiate just one valid argument form to be valid.

Consider: “You can’t reach the North Pole by going south; therefore, you can’t reach the North Pole.” “You can’t reach the North Pole by going east; so you can’t reach the North Pole.” “You can’t reach the North Pole by going west; so you can’t reach the North Pole.” “You can’t reach the North Pole by going southeast; so you can’t reach the North Pole.” “You can’t reach the North Pole by going southwest; so you can’t reach the North Pole.” ETC.

The fact that there are innumerable directions by which you cannot reach the North Pole doesn’t show anything at all about whether you can reach the North Pole.  The fact that there is one direction you can travel in which will get you to the North Pole—namely, north—shows that you can, in fact, reach the North Pole. The only thing that matters is that there is a way that succeeds.

And logic is just like that. If there is a valid route from A to B, it doesn’t matter whether there is an invalid route from A to B, or many, or an infinite number (which there are: there are always an infinite number of invalid routes from A to B you can propose).

AN EXAMPLE: Consider the following argument:

  1. q ⇒ q
  2. q
  3. ∴ q

This argument instantiates the invalid argument form affirming the consequent. Is it invalid? No. Why not? It also instantiates the perfectly valid form modus ponens.  So it really doesn’t matter that it instantiates an invalid form, since it also instantiates a valid form—which is all that matters.

THE UPSHOT: people think that IF they have correctly identified an invalid argument form that an argument instantiates, THEN they have shown something about the argument’s validity.  But they haven’t. That no more works than what is sometimes called the “fallacy fallacy,” which is to hold that showing that an argument for conclusion C is invalid shows that conclusion C is false. But this doesn’t work. An argument for C can be invalid and C still be true.  And it is just as wrong to hold that showing an argument A instantiates an invalid argument form F shows that argument A is invalid.

Sophia vs Jacob: A Hypothetical Twitter exchange

Suppose Sophia and Jacob are having a Twitter exchange, and Sophia makes an argument, to which Jacob responds by typing (in all caps of course) “BANDWAGON FALLACY!” and ‘helpfully’ providing Sophia with a link to yourlogicalfallacyis.com’s description of the Bandwagon fallacy:

1. Jacob hasn’t shown anything about Sophia’s argument. All he has done is say the name of an alleged fallacy. If Jacob’s position is that an argument is proven to be invalid on the condition that someone says the name of a fallacy, then he’s in pretty dire trouble. Sophia can simply elect to accept Jacob’s rule and proceed to “refute” all Jacob’s arguments by saying the names of various fallacies; or she can ask him to prove his rule is correct—and defeat every argument he attempts to give for it by saying the names of various fallacies; or if Sophia is feeling particularly snarky, she can post one of my cards to Jacob, which uses the rule he is implicitly appealing to to defeat itself. When someone thinks they can refute your argument by saying the name of a fallacy, this is the name of the fallacy you say to refute their argument that they have refuted your argument by saying the name of a fallacy:

evecardfallaciesnominalfallacyfallacy

THE UPSHOT HERE is that Jacob has still failed TO DEMONSTRATE HIS CLAIM that Sophia has made an error in her argument. All Jacob as done so far is argue “I have said the name of an error; therefore your argument is in error.

2. Suppose Jacob mans up and really does try to show that Sophia’s argument fits the alleged pattern of the “bandwagon fallacy.” And let’s suppose he succeeds. Well, he still hasn’t shown anything about the validity or invalidity of Sophia’s argument. We’ve allowed that he has shown that Sophia’s argument instantiates a type of reasoning that, as an informal fallacy, can be invalid, but it is the nature of informal fallacies (aka material fallacies) that they are sometimes errors and sometimes not. I’ve written a lot about this, mostly for Twitter. If you like, you can have a look at what I have to say about material fallacies HERE.  But just to give some examples:

(a) an appeal to authority is sometimes erroneous, sometimes not; appeal to experts in their fields or a scientific consensus are not errors of reasoning. In the 1990s, Andrew Wiles proved Fermat’s Last Theorem is indeed a theorem.  How do I know this? Because a few dozen of the the few thousand people capable of understanding Wiles’ proof checked it very carefully and agreed. So, my belief that Wiles’ proof of Fermat’s Last Theorem is sound is based entirely on the authority of some of the world’s foremost mathematicians. I could verify Wiles’ proof for myself, but it would require around a decade of mathematical study before I’d be in a position to—and frankly I don’t have the time or inclination. That is what expert mathematicians are for. If we were disallowed from appealing to authority, we’d have to establish all knowledge for ourselves at all times, which would completely defeat the point of the division of intellectual labor, and completely wreck science, since no established scientific “conclusions” could ever be appealed to.

(b) an argument from parts to whole is not always an error.  If you argued that “every brick in the Yellow Brick Road weighs 3.5 kg, so the entire Yellow Brick Road weighs 3.5 kg” you’d be making an error (and if you want to call it “fallacy of composition” go ahead).  But if you argued “every brick in the Yellow Brick Road is brick, so the Yellow Brick Road is a brick road” or “every brick in the Yellow Brick Road is yellow, so the Yellow Brick Road is yellow” you wouldn’t be making an error.

(c) An appeal to universal human experience is not an “ad populum fallacy,” for example in the case of such claims as: “minds exist” or “human beings by nature are divided into two sexes” or “time has three dimensions, past, present, and future” or “anger and fear are emotions found in human beings” or Euclid’s Common Notions: “The whole is greater than the part” or “equals added to equals are equal” or “things which are equal to the same thing are equal to one another.”  The point here is that there really are COMMON NOTIONS, as Euclid uses that term, namely, things which all human beings know or can recognize that do not stand in need of any formal proof, because they are too simple or too obvious to have one (this is also called the consensus gentium, “the consensus of the whole species”—I’ve discussed how it differs from an ad populum error HERE.

THE UPSHOT HERE is that Jacob has still failed to TO DEMONSTRATE HIS CLAIM that Sophia has made an error in her argument, even if he has shown that her argument instantiates the form some informal fallacy or another. All Jacob has done so far is argue “Your argument instantiates a form which may or may not be an error; therefore it is in error!

3. But let’s make it a bit easier on Jacob, and suppose that he has detected in Sophia’s argument not an informal fallacy but a formal fallacy, such as affirming the consequent. Now, formal fallacies are different from material or informal fallacies in that they are invalid just in virtue of their form, and so do not depend on the situation, context, or content as to whether they are valid or invalid. They are simply invalid. Period.

Now, let us suppose that Jacob succeeds in showing that Sophia’s argument does indeed instantiate the invalid argument form called affirming the consequent (P⇒Q; Q; ∴P). Has Jacob now shown that Sophia’s argument is invalid? No, he has not. He has not, because to do so, he would have to be appealing to principle (F1): An argument is invalid if it instantiates an invalid argument form, which as we have seen, is a false principle.

Sophia is therefore entirely within her epistemic and logical rights to says to Jacob, after he has demonstrated that her argument instantiates the form of affirming the consequent, “So what? You still haven’t shown my argument is invalid. You wasted a lot of effort on showing something that has no logical bearing on whether my argument is valid or invalid.”

THE UPSHOT HERE is that Jacob has still failed TO DEMONSTRATE HIS CLAIM that Sophia has made an error in her argument, even if he has shown that her argument instantiates the form even of a formal fallacy. All Jacob has done so far is argue “Your argument instantiates a formally invalid argument form, an error; therefore it is in error.” And this argument is an enthymeme that requires the false principle (F1) as its hidden premise, and so is unsound.

4. Jacob’s problem is that, in order to show that Sophia’s argument is invalid, he has only two options: (A) the direct logic-indifferent method, in which he can show that Sophia’s argument is invalid by showing that, while her premises are true, her conclusion is false.  This isn’t really a “method” at all—it is simply showing that Sophia’s argument is a case of the very definition of an invalid argument, namely, an argument with true premises and a false conclusion; or (B) Jacob can attempt to show that there is NO logically valid argument form which Sophia’s argument instantiates (remember, her argument only needs to instantiate ONE to be valid), in any formal-logical system, including those which have not yet been discovered or constructed.  In other words, to use method (B) Jacob would have to prove the nonexistence of a logical form which Sophia’s argument instantiates. And as most people are well aware, it is damn-near impossible to prove absolutely the nonexistence of something (showing it to be contradictory is the only way I know that this can be done).

THE UPSHOT HERE is that all appeals to fallacies as a way of refuting arguments or proving invalidity all seem to be instances of (B)—and they all fail because they can’t actually do the work of demonstrating invalidity.  THE MOST they can accomplish is to raise a doubt about the validity of an argument by suggesting that the argument in question has nothing more to it than the invalid form it instantiates.  That is to say, that the person making the argument is appealing to the invalid form as a valid form, which he or she means to establish validity, either in the mistaken belief that it is valid or disingenuously as a rhetorical move.  But if the person making the argument says “No, I see that pattern is invalid, but that’s not what I’m claiming makes my argument valid,” then an appeal to fallacy really can’t DO anything else. People WANT to say “No! Your argument instantiates an invalid argument form! It’s invalid!” But they can’t logically say that. That’s (F1) again, and (F1) is false—obviously false, even: “You can’t get from A to B” obviously does not follow from “You can’t get from A to B by route F.”

Why aren’t “fallacies” very useful?

A fallacy is usually a name given to some general type of error or mistake. The problem with this is that errors do not, strictly speaking, have ‘types’—there are no general forms of error, because error by its way of being is indefinite and indeterminate—and what is indefinite and indeterminate is cannot be defined or determined rigorously.

Fallacies aren’t very useful because they CAN’T DO MUCH.

Naming a fallacy certainly doesn’t show anything about an argument’s validity or invalidity.

Showing that an argument fits the form of a informal fallacy doesn’t show anything at all, since material fallacies aren’t always fallacious—that depends entirely on the content, and you’d still have to show that the argument in question is in error, something which, if you are able to do it, makes the citation of the “fallacy” completely redundant and superfluous, and if you can’t do it, makes the citation of the “fallacy” completely toothless and pointless.  So in the case of informal fallacies, citing the fallacy accomplishes nothing either way; everything turns on whether you can demonstrate an actual error in the argument. EITHER WAY, the citation of the fallacy adds nothing and does nothing.

Showing that an argument instantiates a formally fallacious argument form also doesn’t show anything about the validity of the argument. Because (F1) is false, from the fact that a given argument A instantiates a given formally invalid argument form F, NOTHING FOLLOWS ABOUT THE VALIDITY OR INVALIDITY OF A.  So, once again, if you are going to get anywhere, you’d have to show an error in the argument itself, and the appeal to the fallacy (1) does not show any error, nor (2) add anything to the demonstration of error if one is able to show an error in the specific argument. So in the case of formal fallacies, citing the fallacy accomplishes nothing either way; everything turns on whether you can demonstrate an actual error in the argument. EITHER WAY, the citation of the fallacy adds nothing and does nothing.

Basically, citing a fallacy or appealing to a fallacy is just a roundabout way of saying “Your argument is in error”—and this is something that still needs to be shown. Either can you can show an error, in which case the citation of the fallacy is superfluous and adds nothing; or you cannot show any error, in which case the citation of the fallacy is pointless and accomplishes nothing.

EITHER WAY, the citation of a fallacy ADDS NOTHING and DOES NOTHING. 

ADDENDUM:

It is with satisfaction and pleasure that I learn that Peter Geach, one of the greatest logicians of the 20th century, and a philosopher I respect extremely highly, makes the same point that I do: that ‘fallacies’ understood as invalid argument forms are not invalidity-makers of arguments:

GeachValidInvalid

As Geach notes, if it were the case that invalid argument forms were invalidity-makers, then all arguments would be invalid, since all arguments can be reformulated an the conjunction of all their premises with &s, leaving us with the invalid form

  1. p1 & p2 & p3 & p4 & … & pn
  2. ∴ q

or more simply

  1. p
  2. ∴ q

which gives us a simple modus tollens

  1. If instantiating a logically invalid argument form makes an argument invalid, no arguments are logically valid.
  2. But some arguments are logically valid.
  3. ∴ Instantiating a logically invalid argument from does not make an argument invalid.

Q.E.D.

Philosophers are (or should be) interested in truth, not originality, so I am always pleased to find points that I make in philosophers I respect.

Retortion

Philosophers test things. We test arguments for logical validity and soundness. We test propositions for coherence and truth-value. We test concepts and definitions. Testing things is built in to the activity of philosophy.  This is the meaning of the famous Socratic ἔλεγχος (elenchos), which is translated as “refutation” or “cross-examination,” but really just means “a careful scrutiny or examination of something.”  If that something is a claim, and that claim doesn’t withstand testing, then refutation will be the result, as it typically was with Socrates, since most of his interlocutors’ claims didn’t hold up under testing.

Philosophers have many means of testing claims.  One of the best techniques for testing very broad or universal claims or principles is the technique of retortion.  It is one of the most useful and one of my personal favorites. ‘Retortion‘ is Latin for ‘turning something back on itself’ (this is what we do when we ‘retort’ to someone—we turn words back on them).  In the case of philosophy, retortion means applying a universal principle to itself to test whether it passes its own test or meets its own standard.

Many claims are such that they are self-stultifying, that is, in some critical way or another, they undermine themselves.  A self-destructive or self-refuting claim is a claim that, if it is true, must be false, for example “There is no truth”—if this claim were true, it would be false.  A self-undermining claim is one that, while it doesn’t itself entail its own falsity, does entail that the claim is unwarranted, and so cannot be known to be true or asserted as true, for example “No human being knows anything to be true”—if this claim were true, we could not know it to be true.

Retortion can also be fruitfully employed in regard to ethical principles and other practical principles or imperatives.  As my readers who follow me on Twitter know, I regularly encounter a claim to the effect of “The person who makes a claim has the burden of proof to prove that the claim they are making is true.”  Now, this is not a claim I accept at face value, but I always assume the person making the claim actually accepts it (otherwise they are trying to bind me with a rule of argument that they are exempt from, which is clearly unfair, and which I am therefore right to refuse).  But if the person making this claim does accept it, it follows—by way of retortion—that he has the burden of proof to prove that the burden of proof does lie with the one who claims, since he is claiming this.  And if you follow me on Twitter, you also know that there are all manner of reactions to this—to me, perfectly reasonable—request to obey their own principle, but so far, actually attempting to prove the claim to be true has not been among the reactions. (Of course, it cannot be proven to be true, because it isn’t. They’d do much better if they said “This is a procedural rule I’d like to adopt for this discussion. Would you agree to this?” I wouldn’t agree to it, and would propose an alternative, but this would be the way to go about it.)

Roger Scruton has a rather well-known quote which makes use of retortion to good effect:

scrutontruth

There are innumerable principles which at first glance seem to be profound or important insights that go down like wheat before the scythe of retortion:

“No one can know any metaphysical truths, only scientific ones.”  How do you know this metaphysical truth?

“Only scientific statements are valid.” That isn’t a scientific statement, so it isn’t valid.

“Everyone’s opinion is equally valid.” Is my opinion that opinions are not equally valid valid?

“We can never be certain of anything.” Are you certain of that?

“No one can have knowledge about God.” How do you know this about God?

“Truth is determined through empirical observation.” What empirical observation determines this to be true?

“What is true for me may not be true for you.” It is true for me that anything true is true for everyone.

“No truth is immutable.” So that truth is mutable, and may have changed.

“No belief can be ultimately justified.” Is that belief ultimately justified?

“It’s always wrong to make moral judgments.” Overheard by philosopher Mary Midgley at a party.

Examples could be multiplied indefinitely, from the lowest banalities of “there is no truth” up to clever and interesting logical paradoxes such as “The set of all sets that do not contain themselves does not contain itself” or “This statement is only false and not true.”

Remember: a very good cognitive habit is to always apply the retortion test to any principle presented to you as absolute or universal. 99 times out of 100, this will burn said principle to the ground. Your interlocutor may get annoyed with you, but that isn’t your fault or your problem. If he is reasonable, he must understand the force of the objection, and seek to reformulate his principle in a rationally cogent manner.

“You Can’t Prove a Negative” Part 2

As I wrote in my post “You Can’t Prove a Negative”, this claim—that you can’t prove a negative—is a silly urban legend of logic that needs to die.

So it came up again on Twitter, and someone was kind enough to direct me to an essay by another philosopher addressing this same absurd bit of “folk logic” (as he aptly calls it). I also think his view that “you can’t prove a negative” is largely a view held by people who  have “a desperate desire to keep believing whatever one believes, even if all the evidence is against it.” In other words, “you can’t prove a negative!” is code for “you can’t prove I’m wrong, so I’ll continue to think I’m right!”

I think it is worth reblogging, so here is Steven D. Hales “You Can Prove a Negative”:

________________________________________________________________

THINKING TOOLS: YOU CAN PROVE A NEGATIVE
Steven D. Hales

A principle of folk logic is that one can’t prove a negative. Dr. Nelson L. Price, a Georgia minister, writes on his website that ‘one of the laws of logic is that you can’t prove a negative.’ Julian Noble, a physicist at the University of Virginia, agrees, writing in his ‘Electric Blanket of Doom’ talk that ‘we can’t prove a negative proposition.’ University of California at Berkeley Professor of Epidemiology Patricia Buffler asserts that ‘The reality is that we can never prove the negative, we can never prove the lack of effect, we can never prove that something is safe.’ A quick search on Google or Lexis-Nexis will give a mountain of similar examples.

But there is one big, fat problem with all this. Among professional logicians, guess how many think that you can’t prove a negative? That’s right: zero. Yes, Virginia, you can prove a negative, and it’s easy, too. For one thing, a real, actual law of logic is a negative, namely the law of non-contradiction. This law states that that a proposition cannot be both true and not true. Nothing is both true and false. Furthermore, you can prove this law. It can be formally derived from the empty set using provably valid rules of inference. (I’ll spare you the boring details). One of the laws of logic is a provable negative. Wait… this means we’ve just proven that it is not the case that one of the laws of logic is that you can’t prove a negative. So we’ve proven yet another negative! In fact, ‘you can’t prove a negative’ is a negative  so if you could prove it true, it wouldn’t be true! Uh-oh.

Not only that, but any claim can be expressed as a negative, thanks to the rule of double negation. This rule states that any proposition P is logically equivalent to not-not-P. So pick anything you think you can prove. Think you can prove your own existence? At least to your own satisfaction? Then, using the exact same reasoning, plus the little step of double negation, you can prove that you aren’t nonexistent. Congratulations, you’ve just proven a negative. The beautiful part is that you can do this trick with absolutely any proposition whatsoever. Prove P is true and you can prove that P is not false.

Some people seem to think that you can’t prove a specific sort of negative claim, namely that a thing does not exist. So it is impossible to prove that Santa Claus, unicorns, the Loch Ness Monster, God, pink elephants, WMD in Iraq, and Bigfoot don’t exist. Of course, this rather depends on what one has in mind by ‘prove.’ Can you construct a valid deductive argument with all true premises that yields the conclusion that there are no unicorns? Sure. Here’s one, using the valid inference procedure of modus tollens:

1. If unicorns had existed, then there is evidence in the fossil record.
2. There is no evidence of unicorns in the fossil record.
3. Therefore, unicorns never existed.

Someone might object that that was a bit too fast  after all, I didn’t prove that the two premises were true. I just asserted that they were true. Well, that’s right. However, it would be a grievous mistake to insist that someone prove all the premises of any argument they might give. Here’s why. The only way to prove, say, that there is no evidence of unicorns in the fossil record, is by giving an argument to that conclusion. Of course one would then have to prove the premises of that argument by giving further arguments, and then prove the premises of those further arguments, ad infinitum. Which premises we should take on credit and which need payment up front is a matter of long and involved debate among epistemologists. But one thing is certain: if proving things requires that an infinite number of premises get proved first, we’re not going to prove much of anything at all, positive or negative.

Maybe people mean that no inductive argument will conclusively, indubitably prove a negative proposition beyond all shadow of a doubt. For example, suppose someone argues that we’ve scoured the world for Bigfoot, found no credible evidence of Bigfoot’s existence, and therefore there is no Bigfoot. A classic inductive argument. A Sasquatch defender can always rejoin that Bigfoot is reclusive, and might just be hiding in that next stand of trees. You can’t prove he’s not! (until the search of that tree stand comes up empty too). The problem here isn’t that inductive arguments won’t give us certainty about negative claims (like the nonexistence of Bigfoot), but that inductive arguments won’t give us certainty about anything at all, positive or negative. All observed swans are white, therefore all swans are white looked like a pretty good inductive argument until black swans were discovered in Australia.

The very nature of an inductive argument is to make a conclusion probable, but not certain, given the truth of the premises. That just what an inductive argument is. We’d better not dismiss induction because we’re not getting certainty out of it, though. Why do you think that the sun will rise tomorrow? Not because of observation (you can’t observe the future!), but because that’s what it has always done in the past. Why do you think that if you turn on the kitchen tap that water will come out instead of chocolate? Why do you think you’ll nd your house where you last left it? Why do you think lunch will be nourishing instead of deadly? Again, because that’s the way things have always been in the past. In other words, we use inferences — induction — from past experiences in every aspect of our lives. As Bertrand Russell pointed out, the chicken who expects to be fed when he sees the farmer approaching, since that is what had always happened in the past, is in for a big surprise when instead of receiving dinner, he becomes dinner. But if the chicken had rejected inductive reasoning altogether, then every appearance of the farmer would be a surprise.

So why is it that people insist that you can’t prove a negative? I think it is the result of two things. (1) an acknowledgement that induction is not bulletproof, airtight, and infallible, and (2) a desperate desire to keep believing whatever one believes, even if all the evidence is against it. That’s why people keep believing in alien abductions, even when flying saucers always turn out to be weather balloons, stealth jets, comets, or too much alcohol. You can’t prove a negative! You can’t prove that there are no alien abductions! Meaning: your argument against aliens is inductive, therefore not incontrovertible, and since I want to believe in aliens, I’m going to dismiss the argument no matter how overwhelming the evidence against aliens, and no matter how vanishingly small the chance of extraterrestrial abduction.

If we’re going to dismiss inductive arguments because they produce conclusions that are probable but not de nite, then we are in deep doo-doo. Despite its fallibility, induction is vital in every aspect of our lives, from the mundane to the most sophisticated science. Without induction we know basically nothing about the world apart from our own immediate perceptions. So we’d better keep induction, warts and all, and use it to form negative beliefs as well as positive ones. You can prove a negative — at least as much as you can prove anything at all.

Steven Hales is professor of philosophy at Bloomsburg University, Pennsylvania.

“Of all people, the atheist is the most unfortunate”

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St. Nektarios of Ægina

Of all people, the atheist is the most misfortunate person because he has been deprived of the only good thing upon the earth: faith—the one true guide toward the truth and happiness. The atheist is a most misfortunate person because he is deprived of hope: the essential staff needed to journey through life’s lengthy path. The atheist is a most misfortunate person because he is deprived of human love, which caresses the aching heart. The atheist is a most misfortunate person because he has been deprived of the divine beauty of the Creator’s image, which the Divine Artist has etched within man and which faith unveils.

The eye of the atheist sees in creation nothing other than the operation of natural processes. The brilliance and magnificent beauty of the Divine Creator’s image remain hidden and undetectable to him. As he glances aimlessly at creation, nowhere does he discover the beauty of God’s wisdom, nowhere does he see God’s omnipotence, nowhere does he observe God’s goodness and providence, nowhere does he discern the Creator’s righteousness and love for creation. His mind is neither capable of ascending higher than the visible world nor reaching beyond the boundaries of physical matter. His heart remains anesthetized and indifferent before God’s ever-present divine wisdom and power. Within it, not even the slightest desire to worship the Lord exists. His lips remain closed, his mouth silent, and his tongue frozen. His soul voices no hymn, doxology, or praise as an expression of gratefulness to God.

The peace of the soul and the serenity of the heart have been removed by disbelief; instead, mourning has inundated the depth of his being. The delight, which the faithful person experiences from executing God’s divine commandments, and the great pleasure that he enjoys from an ethical way of life are unknown feelings for the atheist. The elation which faith bestows to the believer has never been felt by the atheist’s heart. The assurance that arises from faith in God’s providence, which relieves man from the anxiety of life’s worries, is a power unknown to him.

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The joy poured upon the entire universe has abandoned the heart of the atheist because God has fled from his heart. The ensuing void has instead been filled by sadness, dejection, and anxiety. The atheist lives in a dispirited state; listlessness has taken hold of his soul. He wanders astray in the lightless and expansive night of this present life without even one ray of light to illumine his crooked paths. There is no one to lead him or guide his footsteps. All alone, he passes through the arena of life with no hope of a better future. He walks amidst many traps, but there is no one to free him from them. He is caught within these snares and crushed by their weight. In times of difficulty and sorrow, there is no one to alleviate or console him.

Feelings of love and gratitude remain unknown mysteries for the atheist. The atheist, having appointed matter as his principal governor, limited man’s true happiness within the narrow confines of temporary pleasures. Consequently, he constantly seeks to enjoy these pleasures and is ceaselessly concerned and preoccupied with them. The beauty of virtue is completely foreign to him. The atheist has not tasted the sweetness and grace of virtue. The atheist is oblivious to the source of true happiness and has raced toward the fountains of bitterness. He has been filled to satiety by ephemeral pleasures; satiety in turn has induced in him disgust; disgust has resulted in ennui; ennui has given rise to affliction; affliction has developed into pain; and, finally, pain has led to hopelessness. All the pleasures have lost their glitter and beauty because all of the world’s pleasures are transient, and, as such, are incapable of rendering the atheist fortunate.

Man’s heart was created to be filled by the greatest good; therefore, only when it enjoys this good does it leap and rejoice—because this good is God. God, however, has fled from the heart of the atheist. The human heart has infinite desires because it was created to embrace the infinite God. However, since the atheist’s heart is not filled with the infinite God, it can never be filled or satisfied with anything—even though it perpetually groans, seeks, and desires to do so. The pleasures of the world are incapable of filling the heart’s emptiness. The pleasures and delights of this world quickly evaporate, leaving within the heart dregs of bitterness. Similarly, vain honor and praise are accompanied by sorrows.

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The atheist is unaware that man’s happiness is found not within the enjoyment of earthly pleasures but in the love of God—Who is the greatest and eternal good. He who denies God denies his own happiness and eternal bliss. The poor atheist struggles through life’s hard and toilsome journey, fearfully walking toward the end of his life without hope, headed for the grave that happily waits for him. The sweet waters of joy and happiness flow beneath his feet, while he, as another condemned Tantalus,1 is incapable of quenching his thirst and watering his tongue that has been dried and withered by atheism—for the waters flowing from the life-giving spring of faith recede from his lips.

The atheist has become a misfortunate slave subjugated to a harsh tyrant! How was your happiness stolen? How was your treasure seized? You lost your faith, you denied your God, you denied His revelation, and you rejected the abundant wealth of His divine grace.

How wretched is his life! It consists of a series of torments. His eyes see nothing joyful in nature. The natural world seems to him sterile and barren. It neither provides him with joy nor generates within him feelings of delight. None of God’s works smile at him. A mournful blanket covers the grace and beauty of the creation, which no longer contains anything attractive. His life has become an unbearable burden and a perpetual, unendurable misery.

Despair already stands before him as an executioner, and a merciless tyrant tortures this fearful man. Disbelief has corrupted the ethical powers of his soul; he has run out of courage and is now too week to resist. He is led, like a helpless being, by disbelief and handed over to the frightful bonds of despair. Unmerciful and uncompassionate despair, in turn, violently and harshly severs the thread of his pitiful life, and hurls him into the depths of perdition and darkness, from where he will resurface only when the voice of his divine Creator—Whom he denied—calls him to give an account of his disbelief, at which point he will be condemned and sent to the eternal fire.

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Χριστὸς ἀνέστη

The Spiritual Disorder of Atheism: St. Nektarios

 

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St. Nektarios of Ægina

Atheism is a mental disorder: it is a terrible ailment of the soul that is difficult to cure. Atheism is a passion that severely oppresses whomever it seizes. It holds in store many misfortunes for its captive, and becomes harmful not only for him but also for others who come into contact with him.

Atheism denies the existence of God. It denies that there is a divine Creator of the universe. It denies God’s providence, His wisdom, His goodness, and, in general, His divine qualities. Atheism teaches a falsehood to its followers and contrives false theories concerning the creation of the universe. It professes, as Pythia upon a tripod, that the creation is an outcome of chance, that it is perpetuated and preserved through purposeless, random interactions, that its splendor transpired spontaneously over time, and that the harmony, grace, and beauty witnessed in nature are inherent attributes of natural laws. Atheism detracts from God, Whom it has denied, His divine characteristics, and, instead, bestows them and His creative power to lifeless and feeble matter. Atheism freely proclaims matter to be the cause of all things, and it deifies matter in order to deny the existence of a superior Being, of a supreme, creative Spirit Who cares for and sustains all things.

On account of disbelief, matter becomes the only true entity; whereas the spirit becomes non-existent. For atheism, the spirit and the soul are egotistical inventions of man, concocted to satisfy his vainglory. Atheism denies man’s spiritual nature. It drags man down from the lofty height where he has been placed by the Creator’s power and grace, and lowers him amongst the rank of irrational animals, which he accepts as ancestors of his distinguished and noble lineage. Atheism does all this in order to bear witness to the words of the Psalm: “Man, being in honor, did not understand; he is compared to the mindless animals, and is become like unto them” (Ps. 48:20).

Atheism detracts faith, hope, and love from the world, these life-giving sources of true happiness for man, it expels God’s righteousness from the world, and denies the existence of God’s providence and succor.

Atheism accepts the laws that exist in nature, yet denies Him Who has appointed these laws. Atheism seeks to lead man to an imaginary happiness; however, it abandons and deserts him in the middle of nowhere, in the valley of lamentation, barren of all heavenly goods, void of consolation from above, empty of spiritual strength, bereft of the power of moral virtue, and stripped of the only indispensable provisions upon the earth: faith, hope, and love.

Atheism condemns poor man to perdition and leaves him standing alone as prey amidst life’s difficulties. Having removed love from within man, atheism subsequently deprives him of the love from others, and it isolates him from family, relatives, and friends. Atheism displaces any hope of a better future and replaces it with despair.

Atheism is awful! It is the worst of all spiritual illnesses!

 

Agrippa’s Trilemma aka Münchausen’s Trilemma

Whenever a proposition is asserted to be true, we can ask “how do we know this proposition is true?”

Agrippa’s Trilemma is one of the most ancient philosophical problems.  If one is challenged on the truth of a given assertion, one may attempt to demonstrate or prove one’s assertion to be true.  But any demonstration or proof which is given will make use of premises of which it may again be asked “Are they true?”  This generates a problem of proving one’s proofs or demonstrating one’s demonstrations, and results in the following trilemma, called Agrippa’s Trilemma:

  1. There is an infinite regress in which every demonstration requires a demonstration of its own, with the result that this never comes to an end, and so no demonstration is ever accomplished, nothing is demonstrated, and one merely arbitrarily stops at some point; or
  2. A circular demonstration is given in which something is ‘demonstrated’ to be true on the basis of its own truth or the assumption that it is true; or
  3. Demonstration comes to an end in one or more undemonstrated and indemonstrable axioms or first principles, the truth of which, because it is undemonstrated and indemonstrable, remains unknown, thus undermining the warrant of any demonstration made on the basis of such axioms or first principles.

Agrippa’s Trilemma is also sometimes called Münchausen’s Trilemma, after the legendary Baron Münchausen, who was able to free himself and his horse from a swamp in which they had become mired, by the expedient of pulling himself and his horse up and out by lifting himself by his own hair:

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This technique, often called “bootstrapping” in English (from the idea of lifting oneself up by pulling on one’s own bootlaces), seems most akin to number 2 of Agrippa’s Trilemma, the circular demonstration, insofar as Baron Münchausen is both the lifter and the one being lifted at the same time.

The essential problem is that an infinite regress seems to undermine the possibility of any demonstration, a circular demonstration seems fallacious by its very nature, and any appeal to axioms or ἀρχαί (first principles) can be interpreted as arbitrary, because the legitimacy of the appeal cannot be demonstrated.

Is Agrippa’s Trilemma inescapable?

As with so many cases in philosophy, this is one of those limits of λόγος or discursive reason that thinking will run up against if pressed far enough. The best answer to it seems to be the kind of refutation that Aristotle calls retortion, which means “to turn something back on itself.” In this case, the poser of the Agrippa’s Trilemma seems to be assuming that demonstration or discursive proof is the standard of all truth-warrant, or even that “it is the case that we are caught in Agrippa’s Trilemma.”  But how does he know this to be true?

It seems entirely reasonable not to accept Agrippa’s Trilemma until it is demonstrated that it is a correct representation of our epistemological situation.  But how exactly does the proponent of the Agrippa’s Trilemma propose to demonstrate its validity as a representation of our epistemological situation without himself falling prey to it?

Either he can, or he cannot.

If he can, then Agrippa’s Trilemma is defeated by whatever means the proponent of Agrippa’s Trilemma uses to demonstrate it, which did not fall prey to it. But this cannot happen, since the Trilemma purports to show that all demonstration is impossible; thus a demonstration of the validity of the Trilemma would defeat itself (insofar is it would necessarily require a fourth method of demonstration, thus defeating the trilemma).

On the other hand, if the proponent of Agrippa’s Trilemma cannot demonstrate that it is a correct account of our epistemological situation, then we are justified in simply refusing to accept it, as something undemonstrated.  And so again, the Trilemma is defeated.

The classical answer, besides the argument to retortion showing that the Trilemma is self-defeating, is to hold that it reduces truth-warrant to demonstration, whereas there are other ways in which truth is warranted besides demonstration. As Aristotle puts it, “it is a sign of lack of education not to know of what one ought to seek a demonstration and what not”:

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The classical answer, to which I adhere, is that in addition to λόγος or discursive reason, human beings also have the cognitive power of νοῦς or νόησις (Latin: intellectus) which is a kind of direct mental “seeing” of certain basic truths, which are self-evident.  “Self-evident” means something which to understand it and to understand that it is true are one and the same.  Note that self-evident does not mean “obvious.”  A thing might be difficult to understand and so not obvious immediately or to everyone, but still be such that, once understood, it is seen to be necessarily true (e.g. that the sum of the angles of a Euclidean triangle is equal to two right angles is self-evident, but not obvious).

Despite our possession of νοῦς, human cognition is nevertheless essentially discursive. The human νοῦς, according to Socrates, Plato, and Aristotle, is essentially connected to or entangled in λόγος or discursivity (and so to language and linear, temporal thinking-through or διάνοια), such that the human νοῦς ought to be regarded as much inferior to that of God.  Aristotle in de Anima calls the human νοῦς, “the so-called νοῦς,” as if it were almost not worthy of the name.  It is also worth noting that the Christian philosophical tradition holds that the human νοῦς is not merely finite or limited as compared to that of God, but has also been darkened or impaired or damaged by the Fall of Man; although it has not been erased or obliterated entirely.  Saint Paul’s expression at 1st Corinthians 13:12 is usually taken as a characterization of the human noetic condition

For now we see through a glass, darkly, but then face to face. Now I know in part; but then shall I know, even as also I am known.

We see through a glass, darkly” seems not only a beautiful expression, but a true one. Human cognition is neither perfect nor blind. We are creatures that both by nature and our fallen state are “in-between” perfect knowledge and complete ignorance.

As Pascal says of humanity, “We know too much to be skeptics, and we know too little to be dogmatists.”

It seems, as always, all roads of merely human wisdom lead back to Socrates, whose human wisdom was the wisdom to know what he did not know, and the resultant endless search for the wisdom he did not have called philosophy.

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