### The Logic Forum Discussion Area

Logic
Author
Comment
Re: Negation of a relational quantified term?

Contraposition of All dog-owners are kind persons All not(kind person) are non(dog-owners). It is not dog that is distributed in the original subject, but dog-owners. The negative term non(dog-owner) means not any dog-owner. A dog-owner in either case is an owner of some dog (dog undistributed).

Given your ONLY two premises, all dog-owners are kind and some dogs are beagles, you cannot draw the desired conclusion by substitution or any other means, for reasons already explained.

Non(dog-owner) cannot be changed to non(beagle-owner), because according to your statement, only some beagles are dogs (i.e. you refused all beagles are dogs). You cannot be sure that the beagles you have in mind are the dog variety, and therefore you cannot place the term beagle in lieu of the term dog.

Re: Negation of a relational quantified term?

Avi Sion
Contraposition of All dog-owners are kind persons All not(kind person) are non(dog-owners). It is not dog that is distributed in the original subject, but dog-owners. The negative term non(dog-owner) means not any dog-owner. A dog-owner in either case is an owner of some dog (dog undistributed).

Given your ONLY two premises, all dog-owners are kind and some dogs are beagles, you cannot draw the desired conclusion by substitution or any other means, for reasons already explained.

Non(dog-owner) cannot be changed to non(beagle-owner), because according to your statement, only some beagles are dogs (i.e. you refused all beagles are dogs). You cannot be sure that the beagles you have in mind are the dog variety, and therefore you cannot place the term beagle in lieu of the term dog.
Given your ONLY two premises, all dog-owners are kind and some dogs are beagles, you cannot draw the desired conclusion by substitution or any other means, for reasons already explained.

Avi, with respect, you CAN draw the conclusion I derived, but not using standard syllogistic, because it doesn't allow for complex terms (including relational ones). I'm a little surprised that you're taking this line because in your book you mention both complex terms and substitution, and in fact you've also demonstrated in another thread on this forum that such inferences are possible.

Here:

http://pub12.bravenet.com/forum/static/show.php?usernum=1014493548&frmid=6526&msgid=900296&cmd=show

Also, the conclusion can be derived using modern predicate logic fairly easily, and since you deny that modern logic is no way superior to the traditional logic (and I agree, by the way), it follows that the conclusion can also be drawn from those two premises ALONE using term logic.

Non(dog-owner) cannot be changed to non(beagle-owner), because according to your statement, only some beagles are dogs (i.e. you refused all beagles are dogs). You cannot be sure that the beagles you have in mind are the dog variety, and therefore you cannot place the term beagle in lieu of the term dog.

I was objecting to your inference that "all beagles are dogs" can be drawn FORMALLY from "some dogs are beagles". You don't need me to tell you that All B is D cannot be inferred from Some D is B.

The philosopher Hanoch Ben-Yami has written an interesting book called "Logic & Natural Language", which you can download from here :

http://publications.ceu.edu/publications/ben-yami/2004/15107

There is also the work by Fred Sommers and George Englebretsen. They developed a "new syllogistic" which is capable of anything modern predicate logic can do, and more. It uses a simple algebra of plus and minus signs, but there's no reason why it can't be expressed using the standard notation of traditional logic (and in fact that's what I'm working on, because I know most people are put off by mathematics).

Re: Negation of a relational quantified term?

Joe, sorry to disappoint you. But so far you have not managed to convince me. I'm not taking any line - I'm open-minded. But so far you have not shown me a convincing proof. Try formulating your thesis without dogs and beagles and without owners. Just symbols A, B, C, etc. for the terms, but still in ordinary language for the rest of it. You will, I wager, see for yourself that it can't be done.

One more comment I can make is that you do not realize that the negation of a complex term of the sort you have put forward is broader than you conceive. For example, the negation of [a creature that likes some dogs] is not [a creature that dislikes all dogs] - for it includes all other things in the universe. Or to put it differently, or more narrowly, not to like is not to dislike, because there is a third alternative, viz. indifference. Similarly with your other terms.