Hi Smith.
David Stove’s contention that “almost every logical truth which anyone knows, or could know, is either not purely formal, or is singular or of low generality” is itself a claim to formality and generality, and therefore self-contradictory and surely false – for a start. Behind that is a mass of misrepresentations of logic and fake examples.
Let us consider the example, given by Bill Briggs: “in which formal transposition fails, let p = “Baby cries” and q = “we beat him”, thus “If p then q” = “If Baby cries then we beat him”. But then by transposition, not-q = “We do not beat Baby”, not-p = “he does not cry”, thus “If not-q then not-p” = “If we do not beat Baby then he does not cry,” which is obviously false.”
Well, the conclusion is false here because the premise is false, not because the inference process is false. “If Baby cries then we beat him”? 1) Is this a generality? Who is “we”, the whole world or a certain family or some families? 2) Is this a real if-then statement? It cannot be, because “we beat him” is a volitional act, so logically it cannot be an inevitable consequence of “baby cries” but at best a probable consequence. That is, at best, “If Baby cries then we are likely to beat him”. So, this is not a true example of a formal and general if-then statement, nor therefore a correct example of if-then contraposition. The example given is, thus, fallacious nonsense.
Furthermore, the contraposite there presented is misleading. The real contraposite of “If Baby cries then we beat him” is not “If we do not beat Baby then he does not cry,” but “If we did not beat Baby it can be assumed that he did not cry,” i.e. “if we did not beat him it is because he did not cry.” In cases like this, when dealing with human actions and reactions, I would recommend use of the form “when-then” rather than “if-then”, i.e. with natural (de re) conditionals rather than logical (de dicta) conditionals (see my book Future Logic (part 4) for a study of de re conditioning: http://www.thelogician.net/FUTURE-LOGIC/De-Re-Conditioning-IV.htm.
It is fashionable to attack logic, but such attacks are all illogical bunk.
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Hi Avi, thanks. I had a feeling there was something fishy about it, but couldn't put my finger on where the error was.
Hi Smith, thanks.
I haven't read Stove's'The Rationality of Induction', so I do not know what he advocates in it. I ought to read it, but I have a pile of books I still want to read waiting for me.
If you're interested in Induction, I strongly recommend my book 'Hume's Problems with Induction', which should inoculate anyone against fallacious claims regarding this subject.
You can read it online here: http://www.thelogician.net/LOGICAL-and-SPIRITUAL-REFLECTIONS/Hume/Hume-Problems-with-Induction-A.htm. Or you can buy it at amazon.com or at lulu.com in softcover or e-book form.
If you leave your e-mail address at www.thelogician.net, I will add you on to my mailing list for future announcements.
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You can download David Stove's 'The Rationality of Induction' from here :
https://drive.google.com/file/d/1vQL9QsQfdimuiBAdhVQfRpOhqx_twP_d/view
That example comes from the chapter 'The Myth of Formal Logic', which has other examples. Here's one :
Joe,
First, the very idea that one can debunk “formal logic” by means of formal logic (i.e. using symbolic terms) is itself self-contradictory and absurd. Second, the idea that, by allegedly showing with a single example (or even many) that some seemingly logical argument(s) are self-contradictory, one can thereby declare the whole wide enterprise of formal logic to be false and worthless is again absurd – refuting one argument form does not imply refutation of all other (unconnected) argument forms. So, in both these instances already, one can immediately see that your critic of formal logic (David Stove) is a sophist.
Thirdly, consider Stove’s alleged refutation.
1) He says: "All men are mortal entails "If Socrates is a man then Socrates is mortal"; which in turn entails "If Socrates is a man then it is not the case that Socrates is an immortal man". So, entailment being transitive, "All men are mortal" entails "If Socrates is a man then it is not the case that Socrates is an immortal man".”
Yes, If All men are mortal and Socrates is a man, then Socrates is mortal; that is a syllogism: 1/AFF. If Socrates is mortal, then Socrates is not immortal; that is an obversion. As regards “immortal man” – this is a compound statement of the given Socrates is a man and the inferred Socrates is mortal (or not-immortal).
However, it is NOT true that All men are mortal BY ITSELF IMPLIES If Socrates is a man then Socrates is a not-immortal man. All we can say is that All men are mortal and Socrates is a man TOGETHER IMPLY that Socrates is a not-immortal man. Nesting is possible; i.e. one can say: If all men are mortal, then if Socrates is a man it follows that Socrates is a not-immortal man. But the nested hypothetical cannot be dissociated from its condition (that All men are mortals); and treated as an independent truth thereafter.
2) Thus, when Stove then claims: “Conjoin that conditional with the necessarily true conditional, "If Socrates is an immortal man then Socrates is a man". Hypothetical syllogism then gives you, "If Socrates is an immortal man, then it is not the case that Socrates is an immortal man".” – he is engaged in an illicit process, treating a conditional conditional as a categorical conditional.
If all men are mortal, then if Socrates is a man it follows that Socrates is a not-immortal man.
Plus: If Socrates is an immortal man then Socrates is a man.
Does NOT according to formal logic yield the conclusion: If Socrates is an immortal man, then Socrates is a not-immortal man.
To repeat, that is because the hypothetical syllogism is not as Stove depicts it, but a conjunction of the major premise “If all men are mortal AND Socrates is a man, then Socrates is a not-immortal man” and the minor premise “If Socrates is an immortal man, then Socrates is a man”. The middle term in the major premise (mortal AND man) is thus MORE SPECIFIC than the middle term in the minor premise (just man), and NO valid conclusion can be drawn.
Stove commits THE FALLACY OF FOUR TERMS, and thus shows his utter ignorance and stupidity, if not his utter dishonesty (“there is nothing untoward so far”!). Instead of proving that (as he puts it) “formal logic is a myth“, he demonstrates how important it is to study it truly and not get misled by sophistry.
Many evil people try hard to debunk logic, because they wish for the triumph of irrationality. This is the agenda of the Woke crowd, and of their sick predecessors since the so-called Enlightenment. It is fashionable – but all wrong.
Avi
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As regards the argument that 'if baby cries, then we beat him' implies the contraposite 'if we do not beat baby, then he does not cry', which is false.
Here you should ask the question, why is the inference claimed false?
1) Baby cries – we then beat him - presumably invariably?. But this is a volitional act, and the beater may not always be present anyway when Baby cries. So, is the premise always true, for a start?
2) Is it correct to say that if Baby is not beaten, he does not cry? Surely, when baby starts crying he was not yet being beaten, which is why the beater then started beating him! If he was already being beaten, then one can understand why he cried, and also one may wonder whether the continued beating was related to the crying!
Etc. Etc. As you can see, there are many difficulties in these “if-then” statements – they are not really clear and consistent if-then statements, and so one can understand that they lead to doubt.
Truly this “philosopher” David Stove is an idiot, who is looking for ways to attack logic while lacking an understanding of logic.
(Joe, I wrote this thinking you had written the related question - but now realize it is an old post by Smith, not you. Still I leave the comment for others to see.)
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Hi Avi, I take your points about trying to 'disprove' logic using logic, and of course you are right to say that using one or two examples doesn't show that there is no such thing as formal logic (although to be fair to Stove, he does acknowledge that there are many 'logical truths').
Following the argument closely, I see that you are correct. As you say, where it goes wrong is using the compound term 'immortal & man'. It seems reasonable that 'if Socrates is a man then it is not the case that Socrates is an immortal man' is implied by 'All men are mortal', but when you take the contrapositive of the conditional you end up with 'if Socrates is an immortal man then Socrates is not a man', which is contradictory.
To be honest, I don't know what to make of Stove or his 'agenda'. He's not one of the woke liberals for sure, because he was a conservative and banned from Sydney university for being politically incorrect. He wrote an essay called 'The Intellectual Capacity of Women', which didn't go down too well. He seemed to take great delight in offending as many people as possible, but could be very funny sometimes, usually at the expense of famous philosophers. I particularly like his comment on Plato and universals :
Hi Joe.
For the record, in more formal terms, Stove's error can be expressed as follows:
If Q and R, then S (= if Q, then (if R, then S)
If P, then R, "therefore" (according to Stove) If P, then S
This is of course an invalid syllogism, because the middle term is different in the major premise (Q and R) and in the minor premise (R): and the former is narrower in scope than the latter.
When I accused Stove of being Woke, I deliberately used a currently fashionable word, even knowing that it is not exactly the right word to use in this context (since it has a much wider application). My point was that this contemporary fashion is not that new. Today the focus is, for instance, on creating confusion between the male and female genders and claiming that one can go from one to the other at will or that there are many gradations in between or beyond them. Not long ago, reason was assailed by means of 'deconstruction'. A few centuries back, Hume and after him Kant attacked reason is various subtle ways, denying causation or soul for instances. In ancient Greece, the Sophists did their best to confuse people. My point is that this is a clear trend. The assault on reason is not an accident. Rather it is the work of people who have a definite, deep-seated will to find fault with reason (making unreason seem logical).
Clearly, Stove's argument was an instance of this evil intent. Had he wished to find the truth of the matter, he would have thought about the validity of his argument a bit more carefully, and found out for himself its fallaciousness. Any high-school kid who has studied logic knows the fallacy of four terms. But Stove was evidently eager to stick his sword in logic's back. So, even if Stove is a political conservative, he is in relation to the art and science of logic clearly on the side of the bad guys (the anti-logic crowd).
As regards his statement about Plato and universals, this is a bit facile - and indicative of Stove's superficiality. In truth, our ability to perceive or conceive, or merely intuit, similarities and differences between concrete or abstract things is a great wonder, a marvelous mystery. Most people don't realize it. That Plato was one of the first, if not the first, to truly realize this, and to try and find some answer to how it comes about, is one of the reasons why he is rightly regarded since antiquity as one of the greatest philosophers that ever was.
As for the use of the term entailment rather than implication, I generally avoid the former and use the latter. Some people use the former for the conclusions of arguments and the latter for straight if-then statements - but that to my mind is silly hair-splitting, intellectual snobbery. In truth, the relation of premises and conclusions is one of implication - there is no difference which justifies using a distinct term for it.
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Hi Joe,
Regarding the Stove argument you quote, I read the symbol (d) as referring to the major premise only, thus getting:
“If A and B are true, and C is claimed to follow from them jointly but is false, then C does not follow from A and B.” This principle is a universally true statement for all deductive arguments, according to formal logic. This is therefore a true major premise (called (d) by Stove).
“The preceding principle (i.e. (d)) is false” is therefore surely FALSE by formal logic. This is therefore a false minor premise by Stove.
It follows that we cannot even suppose the “The preceding principle (i.e. (d)) is false” to be true, and no paradox or logical problem of any sort arises. Stove’s ‘conclusion’ is thus worthless.
(Note in passing that Stove uses the terms valid/invalid instead of true/false, showing that the does not even clearly know the distinction between these concepts.)
But reading your analysis, it is evident that you probably have pinned down more precisely what he was up to - sowing confusion between the whole argument and the mere major premise thereof, making his minor premise a sort of self-reference. I suspect that Stove is not consciously engaging in sophistry, but is merely too unintelligent to see the errors he commits.
I agree with your assessment of him: "Looking at Stove's articles and books, he is a very negative philosopher who seems to be content to criticize others; as far as I can see he hasn't produced any original work". I wonder if he deserves to be called a "philosopher" - he is obviously a hater rather than a lover of wisdom.
As for the word entailment, I admit that I use it occasionally as a weaker term than implication. Perhaps we should say entailment when dealing with inductive (probabilistic) 'implication', so as to distinguish this from deductive (100% firm) implication.
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