Joe, I should clarify the role played by this underlying syllogism in the given 'added determinants' argument.

All horses are animals,
and all horses have heads,
whence some animals (namely the horses, at least) have heads.

What is the precise utility of this syllogism? It serves to equate the respective units of the two terms involved - namely (all) horses and (some) animals. The common reference of these two terms is what makes logically possible the substitution of one term for the other.

Thus, the head of a (any) horse is at the same time the head of (some) animal. Thus, we can licitly argue that the head of a horse is the head of an animal.

And this is made possible entirely by means of Aristotelian syllogism. The modern critics of the latter are thus shown to be boasting of innovation without justification.

On the other hand, for instance, the argument "horses are animals: the majority of horses are the majority of animals" is invalid, because we cannot form an equivalent syllogism. We cannot predicate the term majority of horses; i.e. we cannot produce the minor premise "all horses are majority" - because, of course, majority here is a quantity of horses, not a predicate of theirs. Whence the desired conclusion "some animals are majority" is also nonsensical.

Regards, Avi

Something about you (optional) logician-philosopher

Avi, as usual, your input has shed light on the subject - thanks. Chapter 19 of your book is interesting and seems to extend the rather narrow province of the traditional categorical syllogism into many more forms of argument. Obviously, those who criticize Aristotle's logic are not aware of these 'extensions', which is why they think it is so limited. It's somewhat surprising to me that when the new and "improved" logic came along early in the 20th century, there was not more resistance to it, but perhaps that's because so few people knew (or really cared) that the traditional logic has essentially the same inferential power. Too many people are impressed by the apparent "rigor" of mathematical notation, it seems.

Returning to the horses head argument, the guy who posted the syllogism has responded to my objection that it had too many terms (by the way, you are right that my solution has 4 terms, not 3 - my bad) :

But this still has 5 terms, so isn't a valid categorical syllogism, although it is a valid argument which contains an implicit substitution.

Anyway, these are comments following an interesting blog post by philosopher Ed Feser, who I've mentioned before in relation to arguments about the existence of God. You might like to read the post, and maybe even add a comment.

The metaphysical presuppositions of formal logic

Hi Joe,

As you say, "too many people are impressed by the apparent "rigor" of mathematical notation." They do not realize that symbols are merely abbreviations of longer verbal statements - they add nothing to the the accuracy of the information they transmit. Indeed, they are poisonous to knowledge, in that they befuddle people, who tend to forget just what the symbol contains and what it does not contain. The mind, if we are careful, is forced to artificially keep returning to the underlying verbal discourse, to truly understand the symbol. Why cause people such fatiguing and prone-to-error detours? Many people give up on logic nowadays because of this unnecessary complication.

Symbolization should only occur, if at all, at the very end of the theoretical research and discovery process. It is not a reliable tool to start with.

Regarding the link you gave me - I am sorry but cannot follow it, because I do not want to get entangled in endless conversations with hostile elements. I am retired, and enjoy my rest. You are welcome to pursue the conversation with them, using the replies proposed above. I always appreciate your questions, because they get me thinking.

Best regards, Avi

Something about you (optional) logician-philosopher

Hi Avi,

I understand completely that you don't want to get involved in arguments - there are always 'trolls' around and it can be upsetting if you're the target of one. But the link I gave is to a blog post and participation in the comments following it is optional, so just ignore the comments section. If you had read the post I was going to ask your opinion regarding one or two of the points made, although I'm largely in agreement with the content.

I was thinking of posting your proposed syllogism but didn't want to do so without your permission, so thanks for giving that.

Glad to hear it! I value your opinions and the opportunity to ask questions concerning the content of your books, and other philosophical/logical topics. But I'll try not to pester you too much. :innocent: