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The rediscovery of term logic

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Discovered something interesting about logic just tonight in fact. A recent logician, Fred Sommers, has rediscovered term logic. But he's done better, he's enhanced it. Now it is on par with the predicate logic of Frege and Russell. This is significant.

First, the new term logic and predicate logic are comparable in really only one way: They both involve translations into an algebraic like syntax. But the term logic syntax is much easier, and possibly more expressive. I've been fooling with predicate logic for about ten years now, and I still don't get the hang of it. Worse, it seems I do a better job reasoning if I skip the whole "translate into predicate syntax" step in the first place. The term logic syntax is just symbol algebra with only plus signs and minus signs. It's much more superfiscial, in the way that predicate logic is supposed to be deep and reveal the True Logical Form of the proposition. If anything, Sommers refutes this thesis.

I was going to introduce the new logic, but read Sommers' Foreward in this book for a summary: http://books.google.com/books?id=F5a-US69x78C&lpg=PA1&pg=PR9#v=onepage&q&f=false. In a separate paper, which I'll have to trace, Sommers explains many of the advantages of his term logic, for instance that it deals with mass nouns appropriately and shows inferences that may even be impossible to express in predicate logic. But as of this writing, there might be pitfalls in the logic that I'm not yet aware of. For instance, how does it deal with multiple generality? And I haven't seen anything about modal logic, but I doubt it's that difficult to incorporate.

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Posted

In the mid-1960s I turned to the problem of our deductive competence.

How, for example, do ten-year-olds, innocent of “logic,” recognize the

logical equivalence of ‘No archer will hit every target’ and ‘Every archer

will miss some target’? What makes everyone instantly certain that (A)

‘Every colt is a horse’ and (B) ‘Someone who owns a colt doesn’t own a

horse’ are jointly inconsistent?

Modern predicate logic (MPL) formally justifies such common, intuitive

logical judgments, but its justifications do not explain how we make them.

F. Sommers

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