The Logic Forum Discussion Area
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.
Thanks. I wasn't sure that entailment meant the same thing as implication, especially as logicians (some, anyway) use the double turnstyle symbol for it. And according to Wikipedia, it means different things in different contexts. I don't know why modern logicians are so obsessed with symbols; logic is not mathematics, and it just puts people off who may have otherwise been interested in learning the subject. Not only are symbols not really necessary most of the time, but there seems to be no set of symbols which are used consistently.
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.
Agreed. Abstraction is an amazing ability and is the one thing which sets us apart from other animals. 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.
The other example in 'The Myth of Formal Logic' is a so-called paradox, similar to the liar paradox:
... (the) syllogistic rule: '"All F are G and x is F" entails "x is G", for all x, all F, all G.'
That is a purely formal judgement of validity with as good a claim on our belief as any.
Here I offer, not a counterexample, but a counterexample-or-paradox, the paradox being an obvious relative of the Liar. ...
(d)
All arguments with true premisses and false conclusion are invalid.
(d) is an argument with true premisses and false conclusion.
______________________________
(d) is invalid.
If (d) is invalid then our syllogistic rule is false straight off. If (d) is valid, then its conclusion is false, and so one of its premisses must be false. Then the problem is to find the false premiss. The first premiss is true. So is the second part (we are supposing) of the second premiss. The falsity must therefore be in the first part of the second premiss: but where? Indeed, since the conclusion, if false, is necessarily false, and since the first premiss is necessarily true,and the second part of the second premiss is necessarily true: please find the necessary falsity which is asserted by the first part of the second premiss, (the part which says both premisses are true).
This is a trick, because (d) refers to the whole argument, but the second premise is a PART of the argument which refers to the WHOLE argument, which is not yet complete. I've seen this kind of 'paradox' before, and it isn't really a true paradox. Arguments which refer to themselves are just sophistry.
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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