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Logic textbooks which offer a system of natural deduction containing a so called "rule of replacement" restrict this rule to logically equivalent formulae. Only these can replace each other wherever they occur. I have often wondered why this is so. It seems to me that, having e.g. p<=>q and p&r as lines in a proof (as premisses, say), would allow one to soundly infer q&r directly from them by replacement of p by q in p&r, without requiring that p and r be logically equivalent. In less formal situations, for example, when solving a math problem, I find myself (and others) doing this all the time. I've searched the internet for this, but couldn't find any answer so far. Most grateful in advance for a reply.
Richard Heck
August 14, 2008
(changed August 14, 2008)
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There's a need for some care here. In classical logic, one certainly does have the rule: From A <==> B and ...A..., infer ...B..., in the sense that the former things will always imply the latter thing, and also in the sense that, in any complete system, applications of this rule could a... Read more
Most people believe that a belief is true if it corresponds to a fact. But facts and ideas are very different things. They exist in completely separate realms. How can they "correspond" to each other?
Jonathan Westphal
August 15, 2008
(changed August 15, 2008)
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You write that facts and ideas are very different things. (You also contrast beliefs and facts to make the same point, so perhaps you believe that beliefs are ideas.) From this you infer a difficulty about the possibility of ideas and facts corresponding to one another. 'Facts and ideas a... Read more
No art exists but what man calls art, and man is partial. If this is true, and if it means that art is only valuable to men, and is thus immaterial outside of that context (the Human Context), then what is the true value of art-—the objective value? I would presume that it is valueless. Further, if an artist knows this, how can he still appreciate art, knowing it to be esoterically meaningful? …*Why* should he continue to appreciate art? --Darwin K.
Allen Stairs
August 12, 2008
(changed August 12, 2008)
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Suppose I happen to get great pleasure from something that more or less no one else cares about. Maybe I really enjoy writing poems that avoid using the letter "p." I know that there's no cosmic importance to poems of this sort, and I know that it's just a quirk of my psychology that I enjoy w... Read more
Look at this inference: Premise 1: All desks have the same color. Premise 2: That desk is brown. Conclusion: All desks are brown. Now, I understand that this is a deduction. However, the conclusion is a generalization of one of the premises, and generalizations of premises are what one would expect in induction. Where did I go wrong?
Peter Smith
August 12, 2008
(changed August 12, 2008)
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True: In any situation in which both premisses are true, the conclusion has to be true too. So the displayed inference is deductively valid. [There are possible wrinkles here, but let's ignore them.]
Also true: Inferring the conclusion from the second proposition alone would be be an inductive... Read more
Would Immanuel Kant oppose alternative rock? If we were to universalize the maxim "It is permissible to listen to alternative rock" then "alternative" rock would become mainstream, since everyone would listen to it. This of course creates a contradiction, implying we have a perfect duty not to listen to alternative rock. (I'm not trying to be silly. I think I've wildly misinterpreted Kant, and I was wondering if you could clear it up.) You might say that just because alt. rock was permitted, that doesn't mean everyone would listen to it. But if stealing was permitted, it doesn't logically follow that everyone would steal. (Same goes for lying.)
Douglas Burnham
August 11, 2008
(changed August 11, 2008)
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Very clever question. Maxims can fail to live up to the moral law in (at least) two ways. Either they are themselves impossible as universal laws; or they are impossible for us to consistently will to be moral laws. An example of the first type would be a rule such as ‘lie when it is in you... Read more
During discussions with one of my friends (who is an undergraduate biologist) we often enter into the empiricism vs. rationalism debate. In support of empiricism as the best route to true knowledge my friend often cites the many practical achievements made throughout history resulting from a scientific/empirical approach. In response to this I find it difficult to cite any significant advancements or examples of knowledge which can be credited to the side of rationalism. Indeed it seems to me the invocation of science's great 'utility' is often used as a defence of its (sometimes questionable) actions as well as its assumed superiority as a means to true knowledge. Therefore my question is how can one most effectively challenge science's monopoly on truth and knowledge (particularly in today's 'science worshipping society') in the face of its great practical achievements?
Allen Stairs
August 6, 2008
(changed August 6, 2008)
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Perhaps we need to ask a prior question: why would we make such a challenge? And living in a country where large numbers of people are suspicious of evolution and think that people who worry about global warming or nutty or part of a conspiracy, I'm not so sure that society really is "science wo... Read more
Many great thinkers are pessimists and often reach the conclusion that everything is pointless. Tolstoy even said that life is just a "sick joke". I started to read a lot of philosophy and I reach the same conclusion, that there is no absolute meaning and life is pretty pointless. And please don't reply that we should live in the now or we make our own happiness, etc.
Peter Smith
August 6, 2008
(changed August 6, 2008)
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The implication in the question, that Tolstoy was straightforwardly among the pessimists and thought that life is a sick joke, should perhaps not be let pass without comment.
In A Confession, Tolstoy looks back at the period of his greatest worldly success. War and Peace and Anna Karenina had bee... Read more
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
Many great thinkers are pessimists and often reach the conclusion that everything is pointless. Tolstoy even said that life is just a "sick joke". I started to read a lot of philosophy and I reach the same conclusion, that there is no absolute meaning and life is pretty pointless. And please don't reply that we should live in the now or we make our own happiness, etc.
Peter Smith
August 6, 2008
(changed August 6, 2008)
Permalink
The implication in the question, that Tolstoy was straightforwardly among the pessimists and thought that life is a sick joke, should perhaps not be let pass without comment.
In A Confession, Tolstoy looks back at the period of his greatest worldly success. War and Peace and Anna Karenina had bee... Read more
Is consciousness a byproduct or “add-on” of our evolution or is it something that is intrinsic and inseparable from the skills we humans have? I know this question sounds strange but it's something that has bugged me for quite some time.
Amy Kind
August 5, 2008
(changed August 5, 2008)
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I don't think your question is strange at all. In fact, many philosophers of mind have been pre-occupied with just this very question for quite some time. Then again, perhaps that just makes us strange!
It might help to start by being clear about what exactly you mean by consciousness. Sometimes... Read more