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Having an almost three year old daughter leads me into deep philosophical questions about mathematics. :-) Really, I am concerned about the concept of "being able to count". People ask me if my daughter can count and I can't avoid giving long answers people were not expecting. Firstly, my daughter is very good in "how many" questions when the things to count are one, two or three, and sometimes gives that kind of information without being asked. But she doesn't really count them, she just "sees" that there are three, two or one of these things and she tells it. Once in a while she does the same in relation to four things, but that's rare. Secondly, she can reproduce the series of the names of numbers from 1 to 12. (Then she jumps to the word for "fourteen" in our language, and that's it.) But I don't think she can count to 12. Thirdly, she is usually very exact in counting to four, five or six, but she makes some surprising mistakes. Yesterday, she was counting the legs of a (plastic) donkey (in natural size), and she had to move around to see all of them: she managed to come to the conclusion that the donkey had six legs. Fourthly, she usually forgets one of the things or counts one of them twice when she is counting to seven, eight or nine. Finally, she never asked her parents what is the number "next" to some other number (say, the numbem "next" to twelve). Now, do you think that she can count? And to how many things can she count?
Richard Heck
August 15, 2012
(changed August 15, 2012)
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Most of these questions are not so much philosophical as empirical, and there has been a tremendous amount of extremely important work done in the last few decades on children's concepts of number. The locus classicus is The Child's Understanding of Number, by Rachel Gelman and Randy Galistel,... Read more
I just heard that, in the case of Hilary Putnam's "Twin Earth" experiment, Tyler Burge argued that Oscar and Twin Oscar had different concepts in mind when talking about "water". This seems bizarre, doubly so if neither Oscar nor Twin Oscar are familiar with the chemical composition of the stuff they call "water". If they don't know the chemical composition of the stuff, and the chemical composition is the only different between the two substances (all mesoscopic properties are identical), how can their mental concepts of the stuff possibly be different?
Andrew Pessin
August 14, 2012
(changed August 14, 2012)
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Suppose we individuate concepts by "reference," so two mental states/thoughts are identical if they are about the same things, otherwise different. If (arguably) one twin's thoughts 'refer to' H2O and the other's 'refer to' XYZ, then they would count as different thoughts or concepts. What yo... Read more
This might be a history question as much as a philosophy question but is there something profoundly distinct about the 20th and late 20th century that represents a distinct break from the past that is unlike any other break from the past in terms of its general significance? I honestly feel that is the case but then perhaps every century has felt that way.
Andrew Pessin
August 14, 2012
(changed August 14, 2012)
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No doubt many people feel, particularly around the turns of centuries, that something big/new/different is unfolding. But whether something big etc IS unfolding is probably only something that can be appreciated in retrospect, historically, long after the fact -- by historians, as you suggest... Read more
What do philosophers mean by "a philosophical move"?
Andrew Pessin
August 14, 2012
(changed August 14, 2012)
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Not sure this is a standard expression, and so it's not likely to have an particular definition ... However I could imagine using such an expression when I am complimenting a student, with stress on the 'philosophical' part -- it takes a certain kind of philosophical talent to appreciate cert... Read more
What is it about certain situations that makes anger, hate or rage morally justified (beyond merely being excusable)?
Bette Manter
August 12, 2012
(changed August 12, 2012)
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Anger is normal, but it is important to take responsibility for the effects of one's anger. Anger or rage can never justify actions that inflict harm on others. Why? Well, because we are not terribly aware of what triggers such destructive power, but often the real target is not the person... Read more
Hi there, I'm 17 years old and currently reading the Critique of Pure Reason in the German language (which happens to be my first language so that's no problem). While reading, one question has arised: How does Kant actually prove the existence of the thing in itself? He argues that the thing in itself stimulates the senses and thereby effects perception. This is an appliance of causality, which is -according to Kant himself- appropiate only in the realm of phenomena. Is this a mistake of Kant? Does he disprove idealism in another part of that book? Is it enough that the existence of the thing in itself is possible to think? Does this have something to do with existence being no predicate? I'm looking forward to an answer.
Thomas Pogge
August 10, 2012
(changed August 10, 2012)
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Kant's transcendental idealism explains the fact that experience presents us objects in a certain spatio-temporal order about which we can have some a priori knowledge by reference to a human capacity, our sensibility, through which alone we can become aware of objects. According to this expla... Read more
If a person pushes a fat man into an on coming trolley and in doing so prevents five people from being killing should that person be tried for murder? Is the law clear on whether this was murder? If it clear then wouldn't it be clear that switching tracks to avoid the death of five people but leading to the death of one person is also murder? Or does the law objectively determine that the "intent" in that instance is different than in the other instance?
Eddy Nahmias
August 10, 2012
(changed August 10, 2012)
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Good questions. The "fat man" and "switch" cases you described have been discussed ad nauseum in philosophy and more recently in psychology. These discussions have focused almost exclusively on the different intentions of the person deciding whether to act so as to kill one and save five. I... Read more
Have animals rights? If so, which ones?
Allen Stairs
August 10, 2012
(changed August 10, 2012)
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There's no clear reason why animals shouldn't have rights. After all, humans are animals and on our usual view, even infants and the severely mentally disabled have at least some rights. Certain rights – for example, the right to sign a contract – presuppose certain abilities and so non-human... Read more
Why do we attempt to avoid fallacies?
Nicholas D. Smith
August 9, 2012
(changed August 9, 2012)
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Fallacies are forms of reasoning that fail to provide support for the conclusions reached via that reasoning. In other words, the premises could all be true, but the conclusion still false. Just because something is a fallacy does not make the conclusion of such reasoning false, however.... Read more
Last week, I read a book called "Sophie's World" about a young woman who receives philosophy lessons in the mail from a secret source. Toward the end of the book, Sophie (the young woman) realizes that she is a character in a book, and her philosophy teacher proposes that her author might be a character in a book as well. Sophie's reality begins to change in preposterous ways, inviting characters from other books, sea monsters, etc., and we are introduced to a second girl who is reading about her, as we are reading about that girl. I "realized" with building panic that I, too, could be a character in a book, and felt sapped of free will. The fear evolved into a fear that nothing around me really existed, including (with intense regret) the minds and hearts of friends and family-- that it could all change or disappear against the "laws" of physics at any moment. How do we know that just because an experiment works once, it won't suddenly stop working? How do we know, for example, that a clock won't turn into an ice cream cone, just because it never has before? I decided that what I feared must be change or death, but that if change came I would deal with it then, and that if death came, that would be the end and I wouldn't have to worry about it... then I began to fear not just death, but the possibility of eternal damnation, independent of moral choices we make in life. I now find myself anxiously investing nothing but fragile, faltering faith in things I used to take for granted as fact, like gravity, my memory, and human consciousness, and cannot seem to banish the fear that everything will turn on me. I have written papers about "reality" and existentialism before, and have somehow never been bothered by these thoughts, because I've told myself that we make our own meaning, that meaning can derive from the examination of meaninglessness and the human will to create meaning from it... but I've never doubted the existence of other people or the predictability of the world around me. Is there a way of logically or philosophically thinking myself out of this hole so that I can give my heart a break? Thank you so much in advance for even considering this very weighty block of text. I hope that most minds are sounder than mine and won't be equally upset. Thank you, Samantha (19, college student)
Nicholas D. Smith
August 9, 2012
(changed August 9, 2012)
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Not sure you are going to feel much happier after you read my answer to your question, but let me try at least to tell you what philosophers generally do in response to this sort of question these days.
Your question raises the specter of what is called global skepticism--the idea that we... Read more