Comments on: A Logical Problem http://www.themattscott.com/2009/08/28/a-logical-problem/ ramblings-theology-my thoughts Thu, 11 Mar 2010 17:01:28 -0800 http://wordpress.org/?v=2.9.2 hourly 1 By: JPeaslee http://www.themattscott.com/2009/08/28/a-logical-problem/comment-page-1/#comment-5073 JPeaslee Sat, 12 Sep 2009 01:50:52 +0000 http://www.themattscott.com/?p=525#comment-5073 I think it's not valid because "some" implies that some aren't, which according to the major and minor premises, isn't true.<br><br>But I really don't know, I can't stand that kind of stuff. I think it's not valid because “some” implies that some aren't, which according to the major and minor premises, isn't true.

But I really don't know, I can't stand that kind of stuff.

]]> By: Derek F. http://www.themattscott.com/2009/08/28/a-logical-problem/comment-page-1/#comment-5048 Derek F. Fri, 28 Aug 2009 14:15:00 +0000 http://www.themattscott.com/?p=525#comment-5048 I think I got my major and minor premises mixed up in your example. It would actually be the following:<br><br>Major Premise: All green things are immortal.<br><br>Mior Premise: All horses are green.<br><br>Conclusion: All horses are immortal. I think I got my major and minor premises mixed up in your example. It would actually be the following:

Major Premise: All green things are immortal.

Mior Premise: All horses are green.

Conclusion: All horses are immortal.

]]> By: Andrew Martin http://www.themattscott.com/2009/08/28/a-logical-problem/comment-page-1/#comment-5047 Andrew Martin Fri, 28 Aug 2009 14:07:45 +0000 http://www.themattscott.com/?p=525#comment-5047 Gotta walk before you can run :-). Start with two-valued stuff, then you can look at intiutionistic logics, linear logics, belief revision nonmonotonic logics and the rest later. <br><br>Derek's right: you need/have a very precise meaning of the terms "sound" "valid" etc. <br><br>Where are the symbols? I'd be expecting to set up sentences like<br><br>((∀h)H(h)⇒I(H) )⇒((∃h)H(h)∧I(h))<br><br>and be able to evaluate if they are deducible and/or universally valid. Gotta walk before you can run :-) . Start with two-valued stuff, then you can look at intiutionistic logics, linear logics, belief revision nonmonotonic logics and the rest later.

Derek's right: you need/have a very precise meaning of the terms “sound” “valid” etc.

Where are the symbols? I'd be expecting to set up sentences like

((∀h)H(h)⇒I(H) )⇒((∃h)H(h)∧I(h))

and be able to evaluate if they are deducible and/or universally valid.

]]> By: Derek F. http://www.themattscott.com/2009/08/28/a-logical-problem/comment-page-1/#comment-5046 Derek F. Fri, 28 Aug 2009 13:26:27 +0000 http://www.themattscott.com/?p=525#comment-5046 It's been a while since I've looked at syllogisms. I'm thinking that your professor may mean that the student's conclusion is not the proper inference from the major and minor premises. Going back to your example, it looks like this: <br><br>Major Premise (predicate of conclusion): All horses are green.<br><br>Minor Premise (subject of conclusion): All green things are immortal.<br><br>Conclusion (natural inference from premises): All horses are immortal. <br><br>The keyword is "all." If ALL horses are green, and ALL green things are immortal, then the proper natural inference from these specific premises is that ALL (not just some) horses are immortal. "SOME horses are immortal" is also true, but it is not the primary conclusion that arises from the premises: it is a corrollary truth that can be inferred from the conclusion, but it is different than the conclusion. <br><br>I believe the term "valid argument" has a very specific denotation in regards to syllogisms. It means "an argument in which the conclusion is naturally deduced from the premises." The prhase "some horses are immortal" is not the natural conclusion: it is an inference from the conclusion. Once we know this conclusion, we can create another syllogism which makes sense of that student's thinking: <br><br>All horses are immortal.<br><br>"Some horses" is included within the group "all horses." <br><br>Some horses are immortal. <br><br>The trick is in the precision of the language. I think that's right, but I'd double check. Does that make sense? And by the way, you're not talking about Tom Pynn, are you? It's been a while since I've looked at syllogisms. I'm thinking that your professor may mean that the student's conclusion is not the proper inference from the major and minor premises. Going back to your example, it looks like this:

Major Premise (predicate of conclusion): All horses are green.

Minor Premise (subject of conclusion): All green things are immortal.

Conclusion (natural inference from premises): All horses are immortal.

The keyword is “all.” If ALL horses are green, and ALL green things are immortal, then the proper natural inference from these specific premises is that ALL (not just some) horses are immortal. “SOME horses are immortal” is also true, but it is not the primary conclusion that arises from the premises: it is a corrollary truth that can be inferred from the conclusion, but it is different than the conclusion.

I believe the term “valid argument” has a very specific denotation in regards to syllogisms. It means “an argument in which the conclusion is naturally deduced from the premises.” The prhase “some horses are immortal” is not the natural conclusion: it is an inference from the conclusion. Once we know this conclusion, we can create another syllogism which makes sense of that student's thinking:

All horses are immortal.

“Some horses” is included within the group “all horses.”

Some horses are immortal.

The trick is in the precision of the language. I think that's right, but I'd double check. Does that make sense? And by the way, you're not talking about Tom Pynn, are you?

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