tag:blogger.com,1999:blog-2631035637795172582.post7854839407464162431..comments2023-01-24T10:06:57.212-08:00Comments on (Blog&~Blog): Truth-Values For Quantum Logic?Benhttp://www.blogger.com/profile/06702722560438833244noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2631035637795172582.post-12414765167461258302010-01-27T21:34:24.600-08:002010-01-27T21:34:24.600-08:00In case it is not clear, that was simply supposed ...In case it is not clear, that was simply supposed to be a demonstration of how you can get a truth value for a given complex expression without assigning truth-values to its components.<br /><br />To extend the point to the case you have in mind: I assume that Q and R are contrary assessments of some feature of the subatomic particle. For simplicity, let's suppose that there is some S (the remainder of the rival properties) such that:<br />1) Q entails ~S&~R, ~Q entails (S v R)<br />2) R entails ~S&~Q, ~R entails (S v Q)<br />3) S entails ~Q&~R, ~S entails (Q v R)<br />(If these suppositions are taken to constrain admissible p-assignments for L, then this will result in "is true" applying to (Q v R v S) on any admissible p-assignment ).<br /><br />Now, suppose we have learned P and ~S. We are then in a position to infer P&(Q v R), (even on p-assignments that are silent with respect to Q and R).<br /><br />What I am realizing now is that, even if this approach works (w/r/t the concerns you raise in the later portion of the blog post) it would not undermine (as far as I can tell) the inference from P&(Q v R) to (P&Q)v(P&R), since "is true" would apply to that relative to permissible p-assignments.Anonymoushttps://www.blogger.com/profile/01332656312627191207noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-27769956972876764562010-01-27T21:13:25.172-08:002010-01-27T21:13:25.172-08:00Suppose I adopt some version of the "refusal ...Suppose I adopt some version of the "refusal to assign truth values" approach (rather than the "assigning non-standard truth values" approach).<br /><br />Let a p-assignment A- be any properly partial function from atomic sentence letters of L to truth-values (that is, let a p-assignment be the assignment of truth-values to some, but not all, of the atomic sentences of the language).<br /><br />Call an assignment A a completion of the p-assignment A- just in case i) A is a total function from atomic sentence letters of L to truth values and ii) for every atomic sentence letter S, if A- assigns V to S, then A assigns V to S.<br /><br />Now, consider the following rule(s) governing the application of "is true"/"is not true" relative to a p-assignment A-: <br />1) For any sentence S, if every completion of A- is such that "is true" applies to S, "is true" applies to S relative to A-.<br />2) For any sentence S, if every completion of A- is such that "is not true" applies to S, "is not true" applies to S relative to A-.<br /><br />These rules for "is true"/"is not true" would render "Q v ~Q" true relative to every p-assignment (even those that are silent with respect to Q). This seems like a non-arbitrary way to extend "is true" beyond the assignments of the weak Kleene scheme without running afoul of the charge of "meaning shift".Anonymoushttps://www.blogger.com/profile/01332656312627191207noreply@blogger.com