The newest Jesus and Mo strip, “usage”, came with this message on Patreon (though not on the normal website:
Take-away pizza it is then.
I used to be a beg-the-question pedant, but there comes a time when you just have to go with it. ‘Assumes the conclusion’ is clearer anyway.
I’m still a beg-the-question pedant, but I agree with the artist that “assumes the conclusion” (the traditional meaning) is clearer, since everybody now thinks that “begs the question” means “raises the question.” Best to not use “begs the question” then, and use either “assumes the conclusion” or “raises the question.”
And, as usual, Mo commits the very act he’s decrying. . . .
It’s funny, the use of something versususage of something and god forbid the utilization of something are my pet peeves. More style than anything else, I suppose.
I too find some uses of these words objectionable but, on the other hand, there are subtle differences between them. Use seems more to refer to an actual occurrence, while usage refers to such occurrences collectively. A body of uses, if you will.
I can understand how the meaning was changed or taken over for something else. It gets much more usage this way even if it is wrong.
There are some subtle but important differences, I think. Linguists take usage to refer to the whole pattern of distribution of linguistic forms in discourse. Use, however, is often contrasted with mention—this is a point that we often talk about on this site in connection with the Woketariat’s total inability to distinguish employing a term of abuse for purposes of abuse from citing that term as an instance of a term of abuse. But usage would cover both uses and mentions of the term, because the given term shows up in discourse with one or the other denotation.
Yeah, “usage” is what fellas like Fowler and Follett concerned themselves with. “Use” is what the rest of us ordinary English speakers and writers do on a day-to-day basis.
And “useless” is what a (hopefully) few philosophers do when they try to criticize a correct formal logic argument by claiming it ‘begs the question’.
Of course it does, logic in the strict sense cannot pull a rabbit out of a hat. The closer the conclusion is to implying all the premisses, rather than being just a weaker conclusion from the premisses, that seems to show it’s a better argument. So making the only premiss be exactly the conclusion itself seems to be one of these ‘best’ arguments. Clearly that’s ridiculous.
Valuable arguments in formal logic are valuable for entirely different reasons.
But in every day discourse, the original meaning of a politician begging the question is a very good point to emphasize.
I do realize I’m veering off the topic of language usage. But the Jesus ‘n Mo here brings up something else which a few may find interesting.
Mark Liberman, one of the linguists at Language Log, agrees and, to my mind, gives the most astute advice on the matter:
Liberman’s entire piece on the matter is well worth reading.
To my ear, “beg the question” and “raises the question” aren’t equivalent. The first says that anyone who hears the statement will experience a strong urge to ask the question. The second merely says the question naturally follows from the statement.
Well, if you wish to insist on using “beg” in the first situation, you may want to go with “begs to have the question asked.” if you use “begs the question” alone, you risk having your listener or reader think that you don’t understand the petitio principii fallacy.
It hasn’t been a problem so far. 😉
Strictly speaking, to ‘beg the question’ in its original sense should not be called a ‘fallacy’. If something very close to the conclusion is assumed as an axiom or better said, as a premiss, the logical argument is likely correct, but pathetic. Of course politicians and advertisers do that all the time, and delude tens of millions who don’t realize the pathetically useless ‘logic’ there. The perpetrators try to disguise what they are doing with vagueness and many irrelevancies.
A so-called fallacy would normally be more like either incorrect logic, or, more of interest, a use of logic to show both some proposition and its negation are deducible (so EVERY proposition in the formal logical system is). That latter is probably better called a ‘contradiction’, or better: ‘the production of an inconsistency in that theory’ than called a ‘fallacy’. Note the word “deducible” as opposed to “true”.
There is certainly much good pure logic where what is assumed seems far from the conclusion, yet correctly carried out logic produces that conclusion.
It took a few centuries of effort–but perhaps Fermat’s last theorem in number theory as deducible from basic pure logic plus number theoretic premisses is the strongest example which lots of people have some familiarity with.
There I am indirectly making a somewhat controversial implication, that really there is no boundary where pure logic ends and pure mathematics starts.
Much deeper and more interesting is Godel’s 2nd incompleteness theorem telling us that we cannot be convincingly sure that the logic plus number theory just mentioned won’t itself lead to a contradiction. We could be sure of the opposite if such an inconsistency is ever found. But I’m confident for other than purely logical reasons that it won’t happen.
‘Begging the question’ in the original sense in formal logic is an utterly useless concept within that discipline. Mathematicians are well aware of that, despite the existence apparently of an uncountable lot of philosophy professors who are utterly confused about it. I won’t name names, but happen to have some direct experience of at least 5 or 6 otherwise reputable philosophy journals polluted with that kind of nonsense in the past few decades. In many universities, they do not force even their graduate students to learn sufficient formal logic, or that wouldn’t have happened.
Sorry for the length, but this is almost a personal matter to me, and cannot be formulated without a reasonable number of sentences.
Why would that be controversial? Do you mean that people propose a precise boundary? Why?
No, it’s more that philosophies of mathematics (other than logicism of Frege, Russell, etc. which said—as I implied there—that logic and math are not really distinct) chiefly formalism (Hilbert) and intuitionism (Brouwer) said it’s not, that math is something essentially different than logic. That’s looking back at the 1st part of the 1900s and omitting many other important names and shades of opinion. So any one such philosophy is necessarily controversial, as is anything else any philosopher says, it seems.
And I have no pretensions of knowing much philosophy, as well as forgetting a lot more math than I’d like to admit! But having an opinion comes for free.
Rather than boundaries between countries, it’s more like separate islands(?) or the same island(?), using a geographical simile.
Partly because of Godel incompleteness, and if you’ve looked at these things, a sort of informal boundary in a sense is that logic ends with 1st order, and math begins with higher order or with 1st order set theory uninterpreted.
Seems to me that “fallacy” is another word whose meaning depends on usage, and it’s not hard to see a meaning which fits widespread usage and counts circular arguments as fallacious. Namely, “fallacies” are arguments that aren’t rationally convincing. A circular argument is dialectically pointless, even though its conclusion does follow deductively.
Are “circular argument” and the older meaning of ‘begging the question’ (at least nearly) the same thing to you? I’d tend to think the word ‘fallacy’ is rather generally referring to anything that is wrong rationally, the last word there itself being used very generally and perhaps not very precise as well. But I agree every word’s “meaning depends on usage” as you say, and so is a function of time. And a future new meaning (I resist the temptation to say the stupid ‘going forward’!) can sometimes be a dumb, but always unstoppable, adoption.
Once again, too many replies from me in this thread.
Yes, I intend “circular argument” to cover the old meaning of “begging the question”. And I think this is the most common, standard meaning of “circular argument”, but I could be wrong about that.
The phrasing I always found the most appealing was locate the conclusion in the premises. It makes the point clearly, but has the slightly elevated tone that makes begs the question (in its original sense) a favorite in the groves of academe.
@Peter Hoffman: is your point this, that ‘begging the question’ isn’t so much a fallacy as it is a tautology, and that the fallacy is the downstream belief that the tautology actually established a secure conclusion?
My reply to a reply to your #3 maybe replies here also. However…
To begin I was more concerned’ about the looseness of the word ‘fallacy’.
But that segued into the difference between formal logic and everyday discourse. In the former, despite a certain amount of puffing up from philosophers, the notion of begging the question in its original sense is of virtually no interest. A logical conclusion cannot be ‘stronger’ than its combined premisses.
It is far more subtle to evaluate how good an argument is. But if the conclusion is almost obviously among the premisses, the argument itself could be just as easily false as true in whatever (non-logical!) sense false and true are intended by the arguer—there is always an unspoken, but mutually assumed, pile of side conditions. One must evaluate carefully all the premisses used, and often in a way which is much harder and more subtle than pure logic.
There are a couple of points here that may be relevant in connection with what you’re saying.
(i) A proof in some logic—classical, intuitionistic, resource-sensitive or whatever—is basically always about entailment. If the entailment goes both ways, then you’ve established a tautology. And that’s considered a result, something to be proud you could do! A proof for a De Morgan equivalence, e.g.
~(p /\ q) ≡ ~p \/ ~q
establishes formally that if it’s not the case that the conjunction of two propositions is true, then at least one of them must be false, and conversely. And a proof of this equivalence—a tautology, because it holds regardless of the truth of p and q—is something that logicians value; it’s a hard-won skill, something that very few students in their first logic course can do from scratch, even using a friendly system like sequent-style natural deduction. Proofs of tautologies, and entailments generally, are what the first level of logic is all about; they’re the bread and butter of the discipline. The problems seem to come when, in informal reasoning, people try to derive what you’re calling a ‘stronger’ conclusion than the initial premises. So one of the difficulties with situating actual logic in the context of a real-world argument is that people don’t realize what the limits of logic are: they can’t give you something you didn’t start with (though using some of the standard rules, like EFQ, do let you arrive at (at least initially) completely counterintuitive conclusions).
(ii) Even more baffling for a lot of people is that absolutely valid logical reasoning can yield a conclusion which is an empirical crock. The distinction between validity and soundness is one that people will eventually get if you bang away at it enough, but a lot of the time, the discussants don’t ‘get’ the idea of ‘garbage in, garbage out’. The ‘side conditions’ you refer to are going to bear directly on the soundness of the argument, not necessarily its validity, and the problem is that you can have people arguing with each other who have very different, maybe mutually incompatible sets of such side conditions. And it’s very unusual to see people change their minds about those.
A lot of times, people accuse each other of arguing illogically when none of them are being illogical—they just disagree on what the facts are!
Also for Sastri below.
I did sort of insult some philosophical logicians (who deserve even worse IMO!), but certainly not all of them. Here’s a few excellent ones, who are at this point co-authors of an excellent book: George Boolos, Richard Jeffries and John Burgess. Unfortunately only the last is still alive, so he updated and helped with a 3rd edition of what had had two authors. However, that book, principally what’s called 1st order logic, is really at least at a 2nd level, not for beginners in formal logic. Actually Burgess has an excellent little 3rd level book called Philosophical Logic, not used nearly as often as it should be for grad students.
So that’s an example of people (but not of what you wanted, Sastri).
I bring it up here mainly because I think, Type Logician, that you are more on the philosophical than the mathematical side, with using that triple bar symbol, which goes back to Bertrand Russell or earlier, whereas the 2-sided horizontal arrow () is universal among mathematical logicians, for exactly the same thing.
Sorry for the wonkish stuff, as Paul Krugman always says. I’m not going to go into a thorough reply, but do say that I agree on your use of ‘tautology’, if, as it seems to say, it is meant strictly within propositional logic to mean a formula which is true in all interpretations, in this case, for all choices of truth evaluations. So something as simple in the more advanced (but including propositional) 1st order logic, an extremely easy logically valid formula such as ‘for all x, x=x’ is definitely not called a tautology. 1st order is distinguished by having variables, and for the 1st time in 2200 years, went beyond Aristotle and the medievals and their syllogisms, far beyond, thanks mostly to Frege around 1880-90.
I think it’s fine and valuable for people not having gone into formal logic themselves to think about and discuss logic informally. However, there is considerable scope for misunderstanding each other without the careful definitions of words such as tautology, validity, soundness, etc. which formal logic starts with, even in that case, describing completely the formal (better, symbolic) language they will stick to for the duration of the discussion.
So the schoolmarm concludes with an exercise, showing that surprises even occur at a very basic level:
Show that [(A–>B) or (B–>C)] is a tautology.
The damn thing sure looks wrong, looks like we are claiming that for any A , B , C, either the 1st implies the 2nd, or else the 2nd implies the 3rd. It doesn’t say that–the exercise is NOT asking you to prove that either A–>B is a tautology, or B–>C is a tautology.
I won’t promise to mark your homework.
But there’s a nice example for Sastri!
Sorry, my bad mistake: Sastra, not Sastri.
Just one note, PH—I did try the double-headed arrrow, but it doesn’t work! It’s invisible when you try to use it—something about the typographic rules in force on this blog: it looks to me like the equal sign within the double arrows is misread as a failed typesetting instruction. Notice that your parentheses following your comment here are empty—i assume you tried to do the same thing that I first did. I wound up using the triple horizontal simply because the standard biequivalence symbol is unavailable (I suppose -||- would have done the trick as well).
And my background is mathematical logic: deductive calculi (the Lambek and typed λ-calculi), higher-order linear logic and category theory, which give me the tools I need for my empirical research, and which I’ve taught to advanced undergraduate and graduate classes at my university. Don’t be misled by the triple horizonal; it’s not a tribal emblem! And maybe fewer assumptions about who you’re talking to and what they do for a living?
😉
You’re exactly correct about my 2-sided arrow disappearing into Neverland. (Mine was just a single line, not double—I make a fuss about the semantic language and the formal language not overlapping—talk about wonking out!) I hadn’t even noticed that, failing to proofread when the correction option appeared, until you now point that out. And I don’t know how to make the ‘triple equal’ sign except in LaTeX.
Certainly also no negativity intended in guessing a philosophical slant for you, but guessing incorrectly. Godel himself regarded his work as philosophical, though even A.C. Grayling in his recent history of philosophy doesn’t seem to put him there. I really like that book though it includes less on logic history than I’d hoped for. And we were certainly happy that Lambek ended up in Canada. Do you by any chance know Phil Scott in Ottawa?–he was a Ph.D. student here, not under me, and a good friend, who did a lot with Lambek in the subsequent 40 years.
In my case, I imagine anyone here that bothers to notice is aware that my job (paid) was mathematics, and (unpaid) still is—I’m now paid each month to not have dropped dead before the deadline a month earlier! So my new really bad joke is to (very un-uniquely) have a moving deadline for not dropping dead.
Peter—I imported that symbol from a small unicode reservoir I’ve gathered to use in this kind of situation (didn’t have a double-headed arrow in it and didn’t want to thrash around trying to find one, and long ago gave up on getting LaTeX to shake hands with the formats that undergird most blogs). I haven’t read Grayling’s book on the history of phil, but I loved The God Argument. And I don’t know Phil Scott (though his work on theoretical computer science is held in very high regard in my research community) but Lambek was the inspiration for a lot of my previous work—a prince of a man; you up there were so luck to have him for so long.
And I hope you keep ahead of that deadline for the next hundred years!
Because I’ve little to no formal training in logic, these sorts of academic discussions usually prompt an inquiry regarding the provision of concrete examples, so the kids at home can follow along.
For example, a debate on the Existence of God might be able to begin with an agreement that “God” will be defined as “That which, if it exists, exists necessarily.” I’m less sure about beginning a debate with “God, because He exists, Necessarily Exists.” The conclusion looks like it flew over the premises and went straight to the definition.
I suspect that any theists insisting on the second definition will end up complaining that the atheist can’t ever “get it” because they don’t even understand what God Is.
A bit of above reply is also to this.
As far as god’s existence goes, claiming it to be deducible within logic, the famous ontological argument of Anselm seems to be the grandaddy. There are many words written on that, and famous philosophers e.g. Kant and Descartes, plus from Godel an argument within higher (not 1st) order logic which also needs modal logic. He never published it but it’s in the final, 3rd, volume of his complete works, compiled by many, but Solomon Feferman gets the most credit for terrific work.
Godel’s logic itself is certainly correct. But the premisses used are very dubious, to put it mildly. I think it illustrates what I said above of difficult extra-logical considerations often being the chief germane thing, not the formal logic’s correctness, e.g. the matter of ‘begging the question’ in its original sense.
I’m sending in too many on this one! Sorry.
Almost forgot: I’m sort of proud of a put-down re certain unnamed’s nonsense on Anselm:
“Many believe that discomfort is far more closely related to constipation than conceivability is to existence.”
I’m yet another beg-the-question pedant, but using it with either meaning just means that you’ll annoy or confuse the other fraction of the population. Conclusion: don’t use it.
Why can’t we talk about something with a clear right or wrong answer, like its vs. it’s, so I can feel properly superior?
This lifelong Latin student is also a beg-the-question pedant. I see this issue coming from a misunderstanding of the translation into an older form of English from the Latin, petitio principii, which I might translate as “asking for (begging) the foundational principle (that which is in question).” In other words, the person committing this logical fallacy is saying in essence, “At the outset of my argument, grant me what I should prove.”
Getting ahead of yourself