About 0:50 in his video “Libertarianism and Property Rights from First Principles”, Shane Killian states that the Law of Non-Contradiction is “the foundational principle of all logic and reason.” That’s going a bit far. To be sure, the LNC is one of the first principles of all logic and reason, but so is the Law of Identity, the Law of Difference (aka the Law of the Excluded Middle), and the Law of Ground (aka Principle of Sufficient Reason). However, this is a minor point, so let’s let it go.
The problem is that Shane gets the LNC wrong. He states it as follows: “Something cannot be A and not-A at the same time.”
He then adds “Also, if something is A, it cannot be B, if A and B are mutually exclusive.” This latter part is not necessary and is actually an argument:
1 ~(A & ~A) [LNC]
2 A [Posit]
3 B ⇒ ~A [Posit]
4 B [Posit]
5 ~A [3, 4]
6 A & ~A [2, 5]
7 ∅ [1, 6]
This too is a minor side issue. Here he’s just trying to add something that follows from the LNC as part of it. But since it does really follow, we can let that go too. I point out these two small errors because they tend to show that Shane doesn’t actually have a very good grasp of logic. And that’s a problem when you are trying to make a purely logical argument.
So here is the real problem with Shane’s statement of the LNC. He states it as “Something cannot be both A and not-A at the same time.”
But the actual Law of Non-Contradiction runs “A thing cannot be both A and not-A at the same time and in the same respect.”
Let’s do some quick sources:
“It is not possible for the same thing at the same time both to belong and not belong to the same thing in the same respect.” – Aristotle, Metaphysics Γ 4, 1005b 18ff.
“[The] law of non-contradiction states that the same property cannot at the same time both belong and not belong to the same object in the same respect. So “S is P” and “S is not P” cannot both be true at the same time – unless we take “S” or “P” differently in the two statements.” – Harry J. Gensler, Introduction to Logic
“[The LNC] states that contradictory statements cannot both be true in the same sense at the same time.” –Wikipedia
We could go on (and on), but we need not. The point is clear. Shane has left out the crucial clause of the LNC “in the same respect.” And it isn’t hard to see why this clause is necessary. For example, I am charged with a crime, and found to be not guilty; however, I really did commit the crime. Thus I am both guilty of the crime, and not guilty of the crime at the same time. If Shane’s formulation were correct, this would be impossible. But here the “respect” clause kicks in: I am, at the same time, guilty of the crime in respect to my having done it, but not guilty of the crime in respect to my legal status of having been found not guilty.” We could multiply examples at will.
Now, at about 1:55, Shane attempts to apply his incorrect version of the LNC to the propositions “Consistency is preferable” and “Consistency is not preferable.” He states “One or the other must be true, but both cannot be.” But unfortunately he is wrong. And he is wrong because of the respect clause of the LNC. For one thing, he uses the term “preferable” as if it were an absolute, and not a relative, term. But “preferable” is relative to the preferences of beings capable of having them. One person may prefer something which another does not.
But even worse, there are situations in which consistency is manifestly NOT preferable—e.g. when one has bad, evil, or insane principles, inconsistency might be much preferable to consistency. If one lived in a society with a particularly unjust law, it would be preferable if this law were applied inconsistently, because it would do less harm overall than a thorough and totally consistent application of the law would.
We may also cite Emerson’s famous remark:
Clearly, Emerson means something like “Consistency is not preferable, when it is foolish.” I take him to be describing those people who adopt one or more principles which they then hold to be completely incorrigible regardless of the amount of evidence produced against them. They will reject any argument and any evidence that contradicts the previously accepted principle—in the name of “consistency is preferable.”
Or, to take a rather different example, in Lewis Carroll’s Alice in Wonderland and Through the Looking Glass every character, as far as I can tell, behaves with complete logical consistency. And they are all (as the Cheshire Cat notes) quite mad. The charm of these books is in part this juxtaposition of total logical consistency with complete madness.
Or, again, to take another wildly different example, General Relativity and Quantum Mechanics are mutually inconsistent. Each one seems to logically entail that the other is false. However, we simply don’t know which one is false, if both are false, in what way one or both are false, or if there is some over-arching theory that could reconcile the two. Given our limited knowledge and the fact that without General Relativity we cannot deal with large-scale cosmic phenomena at all, and without Quantum Mechanics, we cannot deal with small-scale subatomic phenomena at all—it seems that our (provisional) acceptance of these two mutually inconsistent theories is preferable to throwing out one or both of them on the simple ground that they are inconsistent. So in this case “Consistency is preferable” may be true in respect to our wanting to reconcile Relativity and Quantium theory, but “Consistency is preferable” may be false if it were taken as a directive to throw out one or both of the theories in order to have “consistency.”
On the other hand, it is obvious, I take it, that one ought to have consistent beliefs, and if one’s beliefs can be shown to contain a contradiction, then one needs no reevaluate one’s beliefs, because at least one of them is false.
So Shane is wrong to say that “Consistency is preferable” and “Consistency is not preferable” is a “true dichotomy” (to use his term) that one could decide on the basis of a priori reasoning. Shane attempts to prove that “Consistency is not preferable” is itself a consistent principle, and therefore self-defeating, since if it were true, we should reject it, since it is consistent.
Now, I’m the last person to object to principle being shown to be false by way of retortion (that is, applying the principle to itself in such a way that shows it defeats itself). But what Shane has actually done is shown that “Consistency is never preferable in any respect” is a self-defeating principle. He has not shown that “Consistency is not preferable at some times and in some respects.” (Note that he hasn’t even shown that “Consistency is not preferable” is self-defeating by his own incorrect statement of the LNC, since he should have stated it “Consistency is never preferable at any time.” Even by his own misstatement of the LNC, he has not shown that consistency isn’t preferable at some times and not at others—he simply dropped the time clause, as if “preferable” could be treated as an eternal, invariant property (without any argument for such).
Shane’s argument is meant to be a logical step by step argument, starting with Principle 1: The Law of Non-Contradiction. That would be, I admit, a good place to start. You couldn’t find a better first principle. But Shane gets the Law of Non-Contradiction wrong. So his Principle 1, on which his entire argument rests, as a misstatement of the Law of Non-Contradiction, is false. So we really don’t need to see anything more to know that the rest of his argument is worthless, since it rests entirely on a false first principle.
We have seen how he attempts to derive Principle 2: The Principle of Consistency from his Principle 1, but his argument fails both because he has got Principle 1 wrong (by omitting the in the same respect clause) and even gets the argument wrong with respect to his own incorrect statement of it (by omitting the at the same time clause)—therefore his Principle 2: The Principle of Consistency is not established.
I didn’t go further than this. There is no need to do so. Shane is next going to attempt to establish a Principle 3: The Burden of Proof on the basis of Principle 2, but since he has not established Principle 2, and Principle 1 is false anyhow, there’s really no point in going further with his argument.
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.
I sat down to write a blog post about this, and realized that I had already done it. Here’s the original: Personal Moral Relativism Collapses into Emotivism, via David S. Oderberg. But I can give a more succinct account here, for easy reference.
Here’s the basic point: Anyone who claims that moral judgments of the form “X is wrong” reduces to personal opinion, personal belief, personal view, etc. seems to be saying something incoherent. That is, the attempt to reduce moral judgments to the status of personal belief or opinions fails because it ends up being incoherent.
Why is this the case?
(1) Anyone who makes a claim like “A proposition of the form ‘X is wrong’ (e.g. ‘rape is wrong’) stated by P means only that ‘P believes that X is wrong’ or ‘In P’s opinion, X is wrong’,” is claiming that ‘P believes that X is wrong’ or ‘In P’s opinion, X is wrong’ gives the analysis or meaning of the expression “X is wrong.”
This analysis necessarily fails because “X is wrong” is supposed to be explained as “P believes that X is wrong” which contains the the proposition “X is wrong” embedded within it—and so this embedded portion of “P believes that X is wrong” still needs to be explained. If it is true that “X is wrong” means “P believes that X is wrong” then the “X is wrong” embedded inside “P believes that X is wrong” means “P believes that X is wrong,” which yields the analysis “P believes that P believes that X is wrong.” And “P believes that P believes that X is wrong” itself still contains the embedded “X is wrong” and so becomes “P believes that P believes that P believes that X is wrong” … which still contains the embedded “X is wrong,” which is therefore never explained at any level. All that is done is to set off an infinite regress which explains nothing at any point.
So attempting to analyze or give the meaning of “X is wrong” as someone’s belief or opinion or view that “X is wrong” is failed pseudo-analysis of moral propositions, being both infinite and failing at every point to give the meaning of “X is wrong.”
(2) Alternately one could attempt to analyze “X is wrong” stated by P as “P disapproves of X.” But now one needs to give the analysis or meaning of “P disapproves of X”—it should be clear that “P disapproves of X” cannot mean “P thinks that X is wrong” because this analysis would be both circular and generate same infinite regress problem above.
(3) One could hold that “X is wrong” stated by P means “P disapproves of X” where “P disapproves of X” is treated as a brute psychological fact without any rational content—it need not be analyzed because it has no rational content. But if the relativist makes this move, he is embracing emotivism, which entirely removes moral judgments from the sphere of reason altogether, which is not what the relativist meant originally when he said that moral judgments were personal judgments. He did not, presumably, mean at first to deny that they are judgments. He only wanted to claim that they were “personal” judgments. But clearly one cannot coherently hold that “all moral judgments are really only personal judgments and are also not judgments at all.”
The UPSHOT: The “personal relativist” needs to give a coherent analysis of moral judgments of the from “X is wrong” that (a) does not set off an infinite non-explanatory regress, (b) is not circular, and (c) does not collapse his position into a different position entirely, viz. emotivism.
Here is philosopher Davis S. Oderberg saying essentially the same thing:
First there is the semantic problem: A proposition of the form ‘Doing X is wrong’ uttered by P (for some action or type of behavior X and some person P) is, according to the personal relativist, supposed to mean no more nor less than ‘P disapproves of doing X’: the latter statement is claimed to give the meaning or analysis of the former. But ‘P disapproves of doing X’ cannot, on this analysis, be equivalent to ‘P believes that doing X is wrong’, since ‘Doing X is wrong’ is precisely what the relativist seeks to give the meaning of; in which case the analysis would be circular.
On the other hand, the relativist might again analyze the embedded sentence ‘Doing X is wrong’ in ‘P believes that doing X is wrong’ as ‘P believes that doing X is wrong’, and so on, for every embedded occurrence of ‘Doing X is wrong’, thus ending up with an infinite regress: ‘P believes that P believes that P believes . . . that doing X is wrong.’ This, of course, would he no analysis at all, being both infinite and leaving a proposition of the form ‘Doing X is wrong’ unanalyzed at every stage.
Such an obvious difficulty might make one wonder that any relativist should support such a way of trying to analyze ‘Doing X is wrong’; but if he is committed to the idea that morality is a matter of opinion or personal belief, it seems that he tacitly invokes just such a pseudo-analysis. The only other route the relativist can take is to assert that ‘P disapproves of doing X’ needs no further gloss: it is a brute statement of disapproval that does not itself invoke the concept of wrongness (or rightness, goodness and the like). But then personal relativism collapses into emotivism, the theory that moral statements are just expressions of feeling or emotion and only appear to have the form of judgements that can he true or false. Emotivism is a different theory from relativism, however, and more will he said about it in the next section. Unless the personal relativist can give an analysis of disapproval that is neither circular, nor infinitely regressive, nor collapses his theory into emotivism, he is in severe difficulty; and it is hard to see just what such an analysis would look like.
Many people are mistaken about the etymology of the word “atheism.” They think it comes from an alpha-privative negation a- joined with theism, that is, they think
atheism = a- theism
atheism = the negation of theism
That is not where atheism comes from, however. ‘Atheism’ is in fact an older word than ‘theism.’ It comes originally from the Greek ἄθεος meaning ‘godless’ or ‘without god’. The -ισμός is a later addition, which means “doctrine of” or “teaching of.” Hence
atheism = ἄθεος -ισμός = atheos -ism
atheism = the doctrine or teaching of Godlessness, i.e. the teaching that there is no God.
Here’s a breakdown of the history:
As noted above the new redefinition of atheism as “lack of belief in God” was a bit of philosophical slight of hand (or more precisely slight of language, or even more precisely sophistry, perpetrated Antony Flew and a few of his atheistic fellow travelers starting in the early 1970s. Flew was probably the most consistent atheist apologist in philosophy through most of the 20th century—and it is worthwhile to note that late in his life, when retired and finally with enough leisure to read Aristotle carefully for the first time, Flew was rationally forced to reverse his lifelong position and embrace rational theism. Maybe he should have read Aristotle earlier in his career? Kudos to Flew for having the intellectual and philosophical integrity to publicly reverse himself on the very position he had built his entire philosophical career maintaining. That extraordinary act of philosophical courage and integrity almost makes me forgive him for perpetrating this pernicious bit of sophistry:
ADDENDUM: I’m not making this up. Of course I’m not, because I don’t just make stuff up. But for those atheists reading this who just assume that I am making it up, here’s a link to what the Stanford Encyclopedia of Philosophy has to say about it, in response to atheists’ persistent attempts to bully them into changing their definition:
Hint: They say the same thing I do. The “redefinition” of atheism was an argument strategy by Antony Flew, one which was never accepted as any sort of consensus, and one for which there are excellent reasons to reject.
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.
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.
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:
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.
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:
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.”
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.
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:
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
or more simply
which gives us a simple modus tollens
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.
As my friend Chris Lansdown has noted, not only is the “burden of proof” not useful in discussions, it actually renders all discussion and argument impossible, if it is taken seriously.
Consider someone who claims that his opponent has the burden of proof. By his own principle that “the one who claims has the burden of proof,” he has the burden of proof to prove his claim that his opponent has the burden of proof.
Suppose he attempts to do so. In order to prove this, he will have to make an argument. In order to make an argument, he will have to assert other claims, namely, the premises of the argument he offers as a proof.
But in asserting these new claims as premises, he immediately, by his own principle, acquires a burden of proof to prove his claims. So he will need to prove his new claims, the premises, as well.
But to prove his premises, he will need to make an argument for each premise, and every argument he makes will require more still more premises—that is, claims—and with every new claim he asserts, he acquires—by his own “the one who claims has the burden of proof” principle—a new burden of proof to prove each of the new claims.
This very obviously results in an infinite regress, where you have to prove the proof and then prove the proof of the proof and then prove the proof of the proof of the proof etc. ad infinitum. And since this endless task cannot be completed by any human being, it would destroy any meaningful conversation before it even begins.
Thus, literally the ONLY way to have a rational discussion about ANYTHING is to DISREGARD the nonsensical pseudo-logical principle that “the burden of proof is on the one who claims.”