Sell also Question 406 .

In trying to understand why Quine or others would not countenance antinomies, or real paradoxes, perhaps it would help to add that the conception of paradox in play here is that of an argument , a collection of premises that entails a conclusion. The arguments that appear to be paradoxes are ones whose premises seem obviously true, whose reasoning seems impeccable, and whose conclusion seems obviously false. So, on this conception what would a real paradox be? An argument that leads from true premises via correct reasoning to a false conclusion. Now, why be confident that there couldn't be such a thing? Because what we mean by "correct reasoning" is just reasoning that leads from true premises to a true conclusion. To judge something to be a real paradox would then be akin to judging something both to be an apple and not to be an apple. That is not a possible judgment. So, the judgment that there are no real paradoxes doesn't stem from an optimistic confidence in the powers of the human...

One says "The value of the function f( x ) = x 2 changes with the value of x ", but nothing is actually changing. Perhaps you can compare it to our saying that the landscape changes as one drives along the road. (One difference though: trees and hills can change over time, but numbers and other mathematical entities cannot.) Mathematicians often look at functions as you suggest: as a collection of ordered pairs of objects <a, b> that satisfies the condition that if <a, b> and <a, c> are both in the collection, then b=c. These pairings are what you've called assignments. Functions are then just particular kinds of sets: sets that contain instructions about what is assigned to what. You could define a function f( t ) = the color of the ball at time t . It too could be viewed as a set of ordered pairs. But what such unchanging functions help us to describe is a physical object, the ball, that is changing. I wonder whether at the root of your question is the thought...

Each true claim can be paired with a unique false one, namely its negation (i.e., the result of prefixing the original claim with "It is not the case that ..."). And each false claim can be paired with a unique true one (again, its negation). So, there are exactly as many true claims as there are false ones.

See also Question 997 .

The Law of Identity states that each object is identical to itself -- hard to deny. "Daniel is identical to Daniel" is a particular instance of that Law. Your clone is not identical to you: if you and your clone we're alone in a room and we counted the number of objects in the room, we'd get two , not one. "Daniel is identical to Daniel" does not express that the word to the left of "is identical to" is the same word as the word to the right of it: it expresses that the object the first word refers to is the same as the object the second one refers to. This can be made plainer by considering, for instance, this claim: "Daniel Defoe is identical to the author of Robinson Crusoe ." This is a true identity claim, even though the words "Daniel Defoe" and "the author of Robinson Crusoe " are not themselves identical. It would be difficult to say why the Law of Identity is true. Any defense of it would either involve using words like "equals," "same as," etc. all over again, or would...

Metaphysics is indeed a central area of philosophy: you will rarely find a philosophy department that doesn't have a course (or many) in metaphysics. We've chosen not to use the name here because it probably doesn't mean anything to someone who doesn't know much about philosophy. If you'll notice, the category names at left are all everyday terms that have some significance even to those who've never encountered philosophy. There are plenty of questions/responses about metaphysics on the site: you'll find them in categories like Color, Existence, Identity, Science, Space, and Time.

In his Confessions (Book XI), St. Augustine turned his attention to those who kept asking "What was God doing before he created heaven and the earth?" and he answered them that "He was preparing Hell for people who pry into mysteries"!!! But he realized himself that "it is one thing to make fun of the questioner and another to find the answer." Eventually, he seemed to settle on the view that God brought the whole temporal order itself into being, and that before the existence of the temporal order notions like "before", "after", "then", "now" made no sense. He said that "if there was no time before heaven and earth were created, how can anyone ask what you [God] were doing 'then'? If there was no time, there was no 'then'." (For a more extended quotation from Augustine, see Question 249 .) For a similar kind of response to a question about the intelligibility of talking about what happened before the Big Bang, see Question 577 .

If someone asks me what's in the refrigerator and I answer "Absolutely nothing", what am I saying? I'm not saying that there's something in the refrigerator after all, namely absolutely-nothing. What I'm doing is denying that there is something in the refrigerator. Although the sentences "The milk is in the refrigerator" and "Absolutely nothing is in the refrigerator" are grammatically comparable, their logical structures are different. In order for the first claim to be true, there must be something that "The milk" refers to and that something needs to be in the refrigerator. But that's not the case for the second claim. In order for the second to be true, the claim that there is at least one thing in the refrigerator needs to be false. It is not the case that in order for the second to be true "Absolutely nothing" must refer to something and that something is in the refrigerator. People have, for thousands of years, been misled by the superficial grammatical similarities of these two...

In connection with Professor Stairs' last two paragraphs, you might also read Question 997 and some of the further entries referred to there.