On a Philosophy Bites podcast I heard Daniel Dennett mention the following thought experiment, which he attributed to Galileo. Suppose that heavier objects fall faster than light ones. Take two objects, A and B, where A is lighter than B. Connect A and B with a string and drop them. Since A is lighter than B, A will act as a drag on B, and B will fall more slowly than it would have alone. Yet since A and B are jointly heavier than B, and heavier objects fall faster than light ones, B will fall faster than it would have alone. We have a contradiction. Therefore, heavier objects do not fall faster than light ones. I thought that this was really marvelous and also very surprising. I had been under the impression that one could not arrive at ostensibly substantive empirical claims like the one in question just by considering thought experiments. I was hoping that one of the panelists could explain exactly how Galileo's thought experiment works here.

One way of thinking of this kind of thing is that it uncovers a subtle contradiction between views we already hold. But it doesn't, by itself, prove anything positive. It's conceivable that one could deny, for example, that A and B are "connected" in the right way for them to fall faster together. The question how thought experiments work in science is an important one, and philosophers and historians of science have written on it extensively. One good place to start might be Thomas Kuhn's paper, "A Function for Thought Experiments", which discusses this one, and also Einstein's famous thought experiment involving the moving train. There's a nice You Tube version of that one here. Check out the SEP article on thought experiments , as well.

Theists often claim that it is impossible that the universe just randomly "sprang into existence" out of nothing, for no reason. M-theory posits a cosmological world-view in which an infinite number of universes are continually coming into and going out of existence within the framework of an eternal multiverse. If correct, does this disprove the theist argument?

I would have thought that the obvious theistic response would be that it is the existence of the eternal multiverse that is at issue. I.e., why are there any universes rather than none? From what I've read of Hawking's response to this, it does not seem to me to be very impressive. As usual with these things, it fails to take the motivations of its opponent at all seriously. None of that is of course to say that the theistic argument referenced is any good.

Are physical and logical truths distinct and, if so, how are they related? Is one more fundamental than the other? By ‘physical truth’ I mean something true in virtue of the laws of physics, such as ‘masses attract other masses’ (gravity) and by ‘logical truth’ I mean something true in virtue of logical or mathematical principles, like ‘2 + 2 = 4’. Could there be a world where some of the physical truths of our world were false but all of the logical truths of our world were true? That is, a world where masses always repelled other masses but 2 + 2 = 4? Conversely, could there be a world where some of the logical truths of our world were false but all of the physical truths of our world remained true? That is, a world where 2 + 2 = 5 but where, as in our world, masses attract other masses? [We’ve been discussing this hours and feel in desperate need of professional guidance - please help!]

One of the things usually taken to be distinctive of mathematical and logical truth is that such truths are in some very strong sense necessary , i.e., they could not have been false. Assuming that it is in fact true that 2 + 2 = 4, how could that have failed to be true? (Or, to take a logical example: How could it fail to be true that, if Goldbach's conjecture is true and the twin prime conjuecture is also true, then Goldbach's conjecture is true?) Presumably, the answer to this question depends upon what, precisely, one thinks "2 + 2 = 4" means, but it is hard to see how one could accept the statement that 2 + 2 = 4 as both meaningful and true and think that it might not have been true. It's important to be clear that this statement does not say anything about how actual objects behave, e.g., that if you put two oranges on a table with two apples and no other pieces of fruit, then you'll have four pieces of fruit. Weird things might happen in some worlds, but that would not make it false in...

Do computers defy the law of conservation of mass? Because, if a computer can copy a program there is twice the amount of space taken up. But how can you just duplicate an amount of space (MB, KB, GB,etc.) if you add nothing to it?

One way to think of why this might seem puzzling is in terms of the type-token distinction. To understand that distinction, consider the question how many words there are on the next line: The The The The You could answer "four" or you could answer "one", and both are correct. It's just that when you answer "four", you're talking about word- tokens , and when you answer "one", you're talking about word- types . This distinction applies to lots of different kinds of things: words, sentences, musical compositions, and, indeed, computer programs. As we normally talk of computer programs, they are types . You and I might install the very same program on our computers, just as we might write the very same word. But there are also program tokens , and our computers have different tokens of the program sitting on their hard drives, or in memory, or what have you. When you copy a program, you create a new token of it, and so you do "add something", as it were, even though, in another...

Hello. I wonder what you think about the following: About 13.7 billion years ago, there probably was a Big Bang. The astronomers start their counting of time from that. What do the philosophers think of what happened before the Big Bang? JB from Sweden

Well, I've answered other similar questions despite my not being terribly well-informed about science, so I'll take a stab at this one, too. The answer to this question depends partly upon whether the universe is "open" or "closed", that is, upon whether the expansion of matter will eventually cease, the universe will start contracting, and everything will end in a "Big Crunch". If so, then it is my understanding that the energy so generated would lead to another Big Bang, and the whole process would start again. If that's how things are, then, before the Big Bang, that may have been how things were. So suppose things weren't like that. Then I believe current physical theory implies that there wasn't any "before the Big Bang". Astronomers start counting time with the beginning of the Big Bang because time itself began with the Big Bang. If that seems bizarre, well, the theory of relativity does have a way of upsetting one's everyday assumptions about time. Someone who knows more about...