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Re: The Horse's Head argument

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) :


'A thing which belongs to a horse' and 'a thing which belongs to an animal' aren't actual terms. To show why, let's reformulate the syllogism.

Horses are a kind of animal.
Horseheads are heads that belong to a horse.
Horseheads are heads that belong to an animal.

This says precisely the same thing as the other syllogism, except now, everything uses 'is.'

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

Re: The Horse's Head argument

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

Re: The Horse's Head argument

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.

I always appreciate your questions, because they get me thinking.

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: