Recent Responses
I have a daughter that is 14 years young. As a mother I understand that teenagers in her age grow up and they want to have fun, most of them with the guys. But still I can't let her go out. I think it's wrong. But my question is, Is that really wrong? Because I remember myself in her age... I also see the friends around her, they don't go out... well she's the only one. But she suffers because of me not letting her to have a boy-friend. Do you think I should let her? Because I'm really confused...
Peter Smith
August 5, 2008
(changed August 5, 2008)
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Just three quick afterthoughts, to add to Nicholas Smith's and Jyl Gentzler's wise but perhaps slightly daunting words.
First, remember most teenagers do survive just fine (with a bit of a close shave here, and an emotional storm or two there): it is our burden as parents to worry far too much. S... Read more
Are necessary truths ultimately grounded in induction? For example truths of mathematics are said to be necessary, yet don't they make generalizations about an infinite set of numbers that are not verifiable; wouldn't this be considered induction? And if we ground our necessary truths on axioms, aren't these axioms theorems that a community has agreed to as being true and are not objectively true? Thanks for your answer, John
Allen Stairs
July 24, 2008
(changed July 24, 2008)
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First, we need to set an issue aside. The word "induction" is sometimes used to refer to a certain sort of mathematical argument in which we prove something for every case by showing it for a "base" case and then showing that if it holds in the first n cases, it holds in the n+1th case. But it's p... Read more
Does Rawls consider inborn abilities an important determinant of social status? I haven't read his entire text in A Theory of Justice, but when he mentions the veil of ignorance, is he considering social status more or less a matter of fate?
Alexander George
July 23, 2008
(changed July 23, 2008)
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If by "fate" you mean out of your control, then I think Rawls would have answered your first question: "Yes and no". Your social status is determined by elements out of your control such as the aptitudes you are born with, the lucky or unlucky breaks that come your way, and the manner in whic... Read more
Why is it that whenever I write something philosophical, I hate it? Do any other philosophers feel this way about their own writing? How do philosophers write?
Peter Smith
July 22, 2008
(changed July 22, 2008)
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Writing philosophy so very often involves uncomfortable compromises. If you put in all your own doubts and reservations, signal all the places where -- as you well realize -- objections might be raised, indicate all your silent assumptions, and so on, then your essay or paper or book would be prett... Read more
There have been many arguments that are offered in support of the proposition that God exists. So far, it seems that none of them have been compelling. Do you think that any possible argument offered as establishing a conclusion like 'God exists', could be compelling. That is, could there exist an argument such that it's conclusion is 'God exists' and the argument is compelling? If no such argument could possibly be compelling, can we not just infer that no argument offered as establishing the existence of God is compelling? Or, do you think one (an argument) exists that may be compelling when learned by us?
Allen Stairs
July 22, 2008
(changed July 22, 2008)
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If by "compelling" you mean something like "beyond reasonable doubt," then the answer is almost certainly no. But that hardly makes arguments about God's existence unique. The claim that God exists has at least this in common with philosophical claims in general: there's plenty of room to argue bo... Read more
Notation: Q : formal system (logical & nonlogical axioms, etc.) of Robinson's arithmetic; wff : well formed formula; |- : proves. G1IT is always stated in the form: If Q is consistent then exists wff x: ¬(Q |- x) & ¬(Q |- ¬x) but we cannot prove it within Q (simply because there is no deduction rule to say "Q doesn't prove" (there is only modus ponens and generalization)), so it's incomplete statement, I don't see WHERE (in which formal system) IS IT STATED. (Math logic is a formal system too.) In my opinion, some correct answer is to state the theorem within a copy of Q: Q |- Con(O) |- exists x ((x is wff of O) & ¬(O |- x) & ¬(O |- ¬x)) where O is a copy of Q inside Q, e.g. ¬(O |- x) is an arithmetic formula of Q, Con(O) means contradiction isn't provable...such formulas can be constructed (see Godel's proof). But I'm confused because I haven't found such statement (or explanation) anywhere. Thank You Very Much
Richard Heck
July 21, 2008
(changed July 21, 2008)
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One thing the questioner seems to want to know is in what kinds of theories the first incompleteness theorem can itself be proved. As Peter says, the proof of the theorem is fine given informally, as almost all actual mathematical results are. But still, one might want to know: Where is this theor... Read more
Can a guy REALLY love you if he comments on other girls saying that they're cute?
Peter Smith
July 21, 2008
(changed July 21, 2008)
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Well, of course he's going to notice cute girls. Love might make you blind, but not in that way. But it is, to say the very least, tactless to notice too obviously, let alone to point them out. I suppose his being an insensitive jerk might be compatible with his loving you ... in his way. But wheth... Read more
Notation: Q : formal system (logical & nonlogical axioms, etc.) of Robinson's arithmetic; wff : well formed formula; |- : proves. G1IT is always stated in the form: If Q is consistent then exists wff x: ¬(Q |- x) & ¬(Q |- ¬x) but we cannot prove it within Q (simply because there is no deduction rule to say "Q doesn't prove" (there is only modus ponens and generalization)), so it's incomplete statement, I don't see WHERE (in which formal system) IS IT STATED. (Math logic is a formal system too.) In my opinion, some correct answer is to state the theorem within a copy of Q: Q |- Con(O) |- exists x ((x is wff of O) & ¬(O |- x) & ¬(O |- ¬x)) where O is a copy of Q inside Q, e.g. ¬(O |- x) is an arithmetic formula of Q, Con(O) means contradiction isn't provable...such formulas can be constructed (see Godel's proof). But I'm confused because I haven't found such statement (or explanation) anywhere. Thank You Very Much
Richard Heck
July 21, 2008
(changed July 21, 2008)
Permalink
One thing the questioner seems to want to know is in what kinds of theories the first incompleteness theorem can itself be proved. As Peter says, the proof of the theorem is fine given informally, as almost all actual mathematical results are. But still, one might want to know: Where is this theor... Read more
What do we mean when we say that we think "in words"? When I think, I don't "hear" speech or "see" written words. So what is it, exactly, that we are aware of that indicates that thought is linguistic?
Peter Smith
July 17, 2008
(changed July 17, 2008)
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Indeed, not all thought is done 'in words'. Sitting in front of the chess board, I'm certainly thinking hard (and it's serious rational planning, not wool-gathering!). But I'm imagining sequences of moves on a board, not going in for inner speech. Likewise, when Roger Federer out-thinks his opponen... Read more
What do we mean when we say that we think "in words"? When I think, I don't "hear" speech or "see" written words. So what is it, exactly, that we are aware of that indicates that thought is linguistic?
Peter Smith
July 17, 2008
(changed July 17, 2008)
Permalink
Indeed, not all thought is done 'in words'. Sitting in front of the chess board, I'm certainly thinking hard (and it's serious rational planning, not wool-gathering!). But I'm imagining sequences of moves on a board, not going in for inner speech. Likewise, when Roger Federer out-thinks his opponen... Read more