Hi, If there are truly random events in the Universe like Quantum Mechancis seems to suggest then even if we had a computer that knew everything about the Universe at t1 then it would stil fail to preidct every event at t2. Then, why are there are not buildings collapsing randomly due to some atoms popping in and out of existence?

It is possible that a well constructed building could collapse. But the probability, from quantum mechanics, is exceedingly low. So low that you have never seen or heard about a well constructed building collapsing randomly. Perhaps it has, somewhere in the universe.

Cartesian dualism relies upon two substances, body and mind, which are totally distinguished by their properties. While the characteristic nature of body is Extendedness, the mind is known with its capability of thinking. So, Cartesian Dualism is founded on these two basic propositions: 1. All bodies are extended. And 2. All minds are thinkable. Abandoning the latter, the former (1) seems acceptable to all physicalists. But if so, then its contraposition might be true equally. In other words, physicalists should be agreed with this proposition too: 3. All non-extended are non-body The question is how physicalists justify this proposition? In other hand, the unavoidable consequence of this proposition (and its truth) is existence of a non-extended (entity) which isn't body, which isn't justifiable in reductive physicalism approach. So, considering this proposition that in reductive physicalism approach: 4. everything has identify with physics. But, isn’t paradoxical acceptance of (3) and (4)...

Dear Borhan, The answer to your question requires some deductive logic. Let's start with (1) all bodies are extended, which is Descartes' premise. It follows logically that if something is not extended, then it is not a body. Thus (3) follows logically from (1). You are worried because you think that (3) assumes that something is not extended. But it does not. It only claims that IF something is non extended then it is also not a body. So physicalists can agree with the claim.

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Do the developments in quantum mechanics (i.e. the best we can do on a very micro level is give probability distributions), really have anything to say about free will? It might mean that determinism isn't true (although there could be a weaker "probabilistic determinism" that gives the likelihood of different possible events), but introducing chance into the equation isn't helpful to free will either.

You are right; chance isn't what is meant by "free will." But freedom of the will may be consistent with determinism, anyway. (Compatibilists argue that free will may be determination by some processes--e.g. one's own character traits--and not others--e.g. external coercion.)

Is 20°C twice as hot as 10°C? Now, I know that the phenomenon (heat) described by 20°C is by no means twice as intense as is that described by 10°C. Yet 20 is also undoubtedly twice the size of 10, no more and no less. So we have two seemingly opposing ways of looking at the situation. Which one is correct, and what standards do we use to judge that correctness? Or is there no correct answer?

The Celsius scale of temperature places the zero at the freezing point of water, not at "absolute zero" which is conceptualized as the time when molecular motion ceases. So 20 degrees C is not twice the temperature of 10 degrees C. The zero for temperature is minus 273C.

Can something really be divided into an infinite number of parts? It seems like it's theoretically possible to infinitely continue dividing something, but that is in no way the same thing as saying that something can be infinitely divided at any point in temporality, since an infinite period of time must be reached before something has been infinitely divided (which is not even a theoretical possibility). It seems like vast claims and supposed paradoxes in physics and mathematics are founded on this dubious assumption that an object or shape can be theoretically divided into an infinite number of parts.

It may help to say that we only need "infinite divisibility"--we don't need the division to have actually taken place, only to be possible in principle. Also, what is your model of "dividing" here? Do you imagine scissors and paper and a lot of cutting? Perhaps there are other ways of conceptualizing infinite division that don't require time.