Qualia Logic Let p be a statement of classical propositional calculus. We want to add cases for which p is a statement about qualia. Classically, if p is a statement it can have truth values T or F. But if p contains qualia it contains ineffable information. One way to allow for this is to let p take on the truth values (T), (F), (T, i) or (F, i) for 'true', 'false', 'true and ineffable' or 'false and ineffable' [2]. For example I would give the sentence 'one way that green appears to me is ██' the truth-value (T, i). If p is true and q is true then pq is true. Some reflection shows that if p is true and q is true and ineffable, then the proposition pq is ineffable... One can go through the truth value alternatives for pq systematically and construct a truth table for pq: Truth Table (matrix) for pq q (T) (F) (T, i) (F, i) p (T) (T) (F) (T, i) (F, i) (F) (F) (F) (F, i) (F, i) (T, i) (T, i) (F, i) (T, i) (F, i) (F, i) (F, i) (F, i) (F, i) (F, i) If p has truth value (T, i), then ¬p could have either truth value (F, i) or (F). The first case happens when, for example, I assert that I'm seeing green when I'm really seeing purple. The second happens if I'm a zombie. In that case I would not be experiencing color at all, so ¬p gets the value (F). A first attempt at a truth table for pq is q (T) (F) (T, i) (F, i) p (T) (T) (T) (T, i) (T) (F) (T) (F) (T, i) (F, i) (T, i) (T, i) (T, i) (T, i) (T, i) (F, i) (T) (F, i) (T, i) (F, i) Apparently truth tables could be given for other operators too. These give a 4-valued logic that one might call Qualia Logic (QL). Notice in the above tables the and-over-or distributive law fails. A first guess at a truth table for p->q is q (T) (F) (T, i) (F, i) p (T) (T) (F) (F) (T) (F) (T) (T) (F, i) (F, i) (T, i) (F) (F) (T, i) (F, i) (F, i) (F, i) (F, i) (T, i) (T, i) Notice that if p is going to answer the Hard Problem(s) (how and why qualia?), it must imply some proposition q that has a truth value (T, i). But in the (tentative) truth table above, this is not possible if p has truth value (T). Therefore the truth value of p must be (T, i). Therefore the answer to the Hard Problem will itself be constituted at least partially by ineffable qualia. Questions: What's the difference in the logic (metaphysical or epistemic) of a zombie and the logic of those of us who do experience (or have) qualia? (I suppose a zombie cannot assign a truth value (T, i) metaphysically...) If we consider our experiences related to time as the 'input' qualia, can we apply QL and derive a temporal logic? Can QL be construed as an enlargement of the scope of the logic of physical laws? References [1] Merriam, Full Variables, 8/9/11 blog ReflectionsOnTime, http://reflectionsontimepmer.blogspot.com/search?updated-max=2011-08-28T19:58:00-07:00&maxresults=100&start=47&by-date=false [2] Priest, Graham, Beyond true and false, aeon Magazine, http://aeon.co/magazine/world-views/logicof-buddhist-philosophy/