March 28, 2012
The Word of the Week is: Modal Realism
Definition: Modal realism is the idea that all modal possibilities are actual.
More about the term: Anything that is possible actually happens. However, modal realism is, in a sense, modally limited. The state of affairs of the non-existence of anything cannot be true if something does exist so by definition modal realism must entail ~∃!W with W being the non-existence of anything—nothing, lest it suffer the consequence of being intrinsically incoherent (~∃!W = There does not exist just one W). In order to avoid an inherent incoherence perhaps there are logically antecedent reasons to affirm ~∃!W (i.e. actuality is logically prior to possibility, which makes possibility somewhat superfluous). Under certain multiverse scenarios different regions of space will exhibit different effective laws of physics (i.e. difference constants, dimensionality, particle content, relation of information, information propagation, etc.) corresponding to different local minima in a landscape of possibilities.
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January 25, 2012
The Word of the Week is: Existential Instantiation
Definition: A rule of inference that introduces existential quantifiers. The symbol for an existential quantifier is (∃x).
More about the term: The existential quantifier indicates that there is at least one thing in a categorical reference. Instantiation is an operation that removes a quantifier and replaces every variable bound by the quantifier with that same instantial letter. There are eight rules of inference to derive a conclusion of an argument via deduction:
- Modus Ponens: p ⊃ q … p… .:q
- Modus Tollens: p ⊃ q … ~q … .: ~p
- Pure Hypothetical Syllogism: p ⊃ q … q ⊃ r … .: p ⊃ r
- Disjunctive Syllogism: p v q … ~q … .:p
- Constructive Dilemma: (p ⊃ q) & (r ⊃ s) … p v r … .: q v s
- Simplification: p & q… .: p
- Conjunction: p … q … .: p & q
- Addition: p … .: p v q
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December 30, 2010
The question of whether or not one can prove a universal negative usually comes into question for the atheist in proving that God does not exist. (I’m using atheism in the sense that an atheist believes that God does not exist). The question is can an atheist prove the non-existence of a being (a universal negative)? Yes, he can. Usually you’ll hear arguments against atheism that suggest it’s untenable because it’s impossible to prove a universal negative (that’s really a bad argument, no one should ever use it).
What if I say that there are no tyrannosaurus rex living on earth today? There are certainly some questions like, “Are there any polka-dotted geese that exist?” Well, if that may be difficult to disprove universally since I would need exhaustive knowledge of the universe. So, okay, I cannot disprove that universal claim. So what now?
It’s actually quite simple to prove a universal negative or the non-existence of anything. All you would need to do is demonstrate a logical contradiction within the universal claim. So, for the atheist, I believe his best argument is to demonstrate the logical impossibility of God (to prove a universal negative). How would he do this? I don’t know, as a theist I don’t believe any atheist can prove an inherent contradiction in the existence of God, that’s his task, not mine.