Introduction and instructions

Dear Students,

Welcome to HU Logic. You are free to comment on the blog, ask questions, interact with each other or with me, or do anything related to our class. I will give some extra credit to students who are active on the blog to various degrees.

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Predicates in search of nouns

According to standard categorical logic, statements of the form All S are P must have some sort of noun-phrase in the predicate.  Thus ‘All dogs are mammals’ is fine, but ‘All dogs are four-legged’ is not.  Why is this a requirement? Standard categorical logic is based on Aristotelian logic and inherits some of Aristotle’s assumptions. So one reason for the noun-requirement is that given Aristotelian metaphysics predicates without nouns are incomplete. To understand why, we first need to keep in mind that  predicates (parts of language) correspond to  properties (parts of the extra-linguistic—that is, non-linguistic—world).  Predicates without nouns are incomplete because, according to Aristotle,  properties  must inhere in objects in order to exist.  There are no free-floating properties—properties without some subject that they attach to.  Thus, statements like ‘All dogs are four-legged’ while grammatic...
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Relations and Multiple Quantifiers in Predicate Logic

Thus far we have been using only one-place predicates. These are predicates that only require one name (put differently, these are properties that only require one object) to complete them. For example, _____ is red = Rx _____ is heavy = Hx _____ is a wife = Wx ( ∃ x)Rx is true if and only if there is at least one thing in the universe that is red. ( ∃ x)Hx is true iff there is at least one thing in the universe that is heavy, and so on. (x)Rx is true iff everything in the universe is red, and so on.  But, as we all know, there are predicates that are more than one place. In other words, there are predicates that require more than one name to complete them (put differently, there are properties-- better-called relations--that require more than one object). For example ____ is heavier than ____ = Hxy ____ is taller than ____ =  Txy ____ loves ____ = Lxy ____ is between ____, _____ = Bxyz (∃ x) (∃y )Hxy is true iff there is something ...
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Why Validity Matters

In this post, we will briefly consider two famous arguments that are in need of lots of interesting work to make them valid and persuasive. Rather than do that work here, I just want you to see the original arguments and how you are now in a good position to see their defects as stated. I am not saying that they cannot be remedied. But the attempted remedies are trickier than meets the eye. Put differently: once we recognize that the original arguments are not valid, the force of the arguments begins to diminish a bit.  The Logical Problem of Evil Lots and lots of people think that the existence of evil is a real problem for the existence of God. But clearly stating the problem is not as easy as some have thought, and once the problem is clearly stated the ways out of it are more numerous than initially believed. Here's a first stab at the problem: 1st try:  Evil exists. Therefore, God does not exist.  Obviously, that won't do. Something else must be added....
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