Kirby, if something is mathematically possible, that does not imply that it is actually possible within the framework of real world. That is because number of objects that are available for us is limited. This is (common) fallacy in reasoning, because people do not distinguish mathematics from reality. This fallacy in reasoning goes back to Leibniz, Galilei and Platon.
Monadology wrote:Perfect play also takes the form of a logical conditional so it cannot be invalidated by a negation of the antecedent, which is all your argument against its existence could potentially manage.
I did refute the idea of logic as a product of your (false) experiences and imagination. Logic is empirically derived from experiences by induction. People have observed several occasions where Jackdaws (
Corvus monedula), have done something non-contradictory and thus they have generalized that contradictory events are logically impossible. And they have promoted the principle of contradictions as axiom of logic. And assumed that it is self-evident. But while observing quantum objects this axiom is not self-evident at all.
Go maybe defined as a abstract set of rules, but as soon as you are referring actual games (such as perfect game) it does exist as a natural, real world object. In the case of perfect play, reference is false. E.g. we can say that there is a unicorn, but statement is false.
Quantum phenomena are just as far away from having anything to do with the game of Go as the effectively indeterminable perfect line of play.
Of course it has all to do with the particular games that you have played. individual go games do exist, and you can view them with .sgf editor. That are visible due to quantum phenomena in liquid crystals and your retinal cells.
Monadology wrote:One of the problems, Liisa, is you're only considering the quantity of objects in the 'size' of the universe. This is not strictly accurate in terms of what it can contain computationally. Not only are there objects, there are relationships between and combinations of objects to count. And those possibilities easily exceed the size of Go as a game.
Problem is that if combinations are meaningful, it is required that we make changes to combinations (e.g. while reading output) and because speed of light limits individual particle's interaction. There is not gained significant increase in orders of magnitudes to the information content of the universe even if relations of particles has considered, because limiting factor will be time. E.g. Jackdaw does include way more information as a whole than it's constituents alone, but still for solving go this is irrelevant.
Liisa wrote:There are two interesting things what we get from quantum logic: A) logic is empirical science. B) mathematics as a science loses meaning.
In the case of A, Logic simply ceases to be anything like actual logic. B, I don't see how this follows at all.
I think that here your reason is that that you do not think that logic that you have learned can be questioned and you assume that logic is a priori truth. But logic is more or less derived from your experiences and therefore correspondence to the real world can be either true or false.
Mathematics loses meaning, because quantum logic (i.e. quantum physics) is inherently probabilistic theory of logic. That will imply that there cannot be anything that is called as truth in mathematical sense, but only highly probable events. Implication is that you can select any sets of mathematical axioms and make logical exercises with them, but they have little to do with real world. Correspondence between real world and mathematics will fail.
The thing that quantum mechanics is formulated using mathematics does not imply that mathematics is build into objects themselves, but they are only tools for humans to calculate probabilities, to make reasoning more simple.
Quantum logic is necessary concept from some reasons: a) it can show that logic is derived ultimately from experiences. b) contemporary logic is poor in handling probabilities and induction and QM is inherently probabilistic theory that has been derived by inductive method.
You are using contemporary logic in claiming (boldly) that empirical theories are not capable for verification. This is the reason why we need case b), because verification is possible within the framework of inherently probabilistic logic, because with probabilistic logic it is required for verification that we calculate only probabilities for the events that we can observe. And we can always calculate probabilities for the events.
Idea with this is that logic is based on assumption that it will generate a world that behaves like observed world. There is no inherent problems in describing flying jackdaw in contemporary logical terms. But there would be some inherent problems, if jackdaws would behave like quantum objects while flying through double slit. If that would be the case, we would have never developed a comtemporary logic, because that would not make any sense in describing observed world.
Quantum logic, however interesting subject by itself, is way off topic!
