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Predicate Logic Help!

  1. Apr 29, 2008 #1
    I have been asked to translate an argument from english into PL and show deductive validity through constructing a PL derivation. I have no problem constructing the derivation but this is the first time I have had to translate from English into PL. I am stuck and any help would be greatly appreciated. The only clue that I have is that there is somehow a hidden premise, what it is I don't know but I dont think that the statement will be deductively valid without this 'hidden' premise. Here is the English statement:

    There are two main philosophical schools about the nature of mathematical objects:1
    realism and antirealism. Although adherents of each school subscribe to a variety of
    positions, they share a common core. Mathematical realists are unified in their conviction that it is rational (for us) to believe in the (literal) truth of at least some existential assertions about mathematical objects.2 Antirealists, on the other hand, do not accept the (literal) truth of such assertions. Perhaps, the most prominent argument for mathematical realism is called the indispensability argument. Here is a simplified version of this argument. There are two principles of rationality that seem self-evident. First, it is rational to believe in the truth of any assertion that forms an indispensable component of a highly confirmed theory. Second, it is rational to believe in the truth of a theory only if it is rational to believe in the truth of any assertion implied by the theory. Now, it is clear that each of our best scientific theories (such as general relativity and quantum mechanics) incorporates at least one mathematical theory as an indispensable part of it. It is also clear that all mathematical theories imply existential assertions about mathematical objects. Given the obvious fact that our best scientific theories are highly confirmed, it follows that it is rational to believe in the truth of at least some existential assertions about mathematical objects.
     
  2. jcsd
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