Constructive Dilemmas

Here are two very famous arguments that are easily put in the form of a constructive dilemma. I will give extra credit to those who write up substantive comments on either or both of these.


Pascal's Wager
1. If God exists, I have everything to gain by believing in Him and if God does not exist, I have nothing to lose by believing in Him. 
2. Either God exists or God does not exist. 
3. Therefore, I have everything to gain or nothing to lose by
believing in Him. 

The Euthyphro Dilemma
1. If God willed the moral law arbitrarily, then he is not essentially good and if God willed the moral law according to an ultimate standard beyond himself, then He is not God (because there is something beyond Him).
2. But God willed the moral law either arbitrarily or according to a standard beyond him.

3. Therefore, either God is not good, or He is not God.

Comments

Post a Comment

Popular posts from this blog

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 ...
Read more

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...
Read more

Meta-Logical Themes: Soundness of Propositional Logic

We have been studying propositional logic (PL) for some time now. PL is about whole or complete propositions and their relationships to each other in terms of truth-preservation. That is, PL investigates the relationships between sets of true propositions to other propositions. How can we be sure that if we are given a set of true propositions (called the premises) that we will through a series of steps wind up with another true proposition and not a false one (i.e. how can we be sure that the relationship between the premise set and the conclusion is, in fact, a valid one). Put differently, we want to make sure that the logic we are using will never take us from truths to falsity. We have been using our rules to show that if we start with a set of (assumed to be) true propositions we can derive another proposition that must be true if the premises are. But we have only studied a finite number of arguments. There is an infinite number of arguments. So, how can we be sure that there i...
Read more