Recent Responses
I've heard that 2 to the power of 2, to the power of 2, etc... 6 times is a number so huge that we could never figure it out. Would that qualify as being infinite? And how would we be able to intelligibly come to that conclusion, or is it a "rough estimate" that we could never figure it out? Thank you for your time. ~Kris S.
Richard Heck
February 25, 2006
(changed February 25, 2006)
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This question concerns, in effect, number-theoretic functions that grow very fast. We can say a lot about them.
The operation in play here is called "superexponentiation", and is also known as "tetration". We can define it as follows:
superexp(0) = 1
superexp(n+1) = 2^(superexp(n))
So supe... Read more
In response to question 26 [http://www.amherst.edu/askphilosophers/question/26], should it not be possible for an omnipotent being to create the possibility for a contradictory object to exist?
Richard Heck
February 25, 2006
(changed February 25, 2006)
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I'm not sure why that should be possible. Indeed, suppose we accept that it is not possible for an omnipotent being to make some contradiction true. Then—if we assume that anything possibly possible is possible (this is the modal axiom known as "4")—it follows immediately that such a being... Read more
A question about logic. When symbolizing and making inferences in natural languages that contain such terms as "it is necessary that", "A ought to do X", "A knows X", and "it is always the case that", there are extensions of classical logic, respectively, modal, deontic, epistemic, and tense logic that attempt to deal with such natural language analogues. My question is: What about propositions that contain a mixture of all the above terms? For example, there are sentences in natural language of the form “It is necessary that John ought to always know that 2+2=4." Is there a logic that can effectively handle (i.e. symbolize and correctly infer) such propositions? If so, is this logic both sound and complete? If there is no such logic, what is a logician to do with such propositions? My intuition is that things get tricky when you mix these operators together and/or the classical quantifiers. Thanks kindly for your reply, A Concerned Thinker
Richard Heck
February 25, 2006
(changed February 25, 2006)
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Things get tricky anyway when you mix modal operators and the quantifiers, so it's best if we just leave it to the propositional case. And I'll add, just by the way, that it is quite controversial whether such "operator" treatments are correct for any of these cases, more so for tense, per... Read more
Is the physical world proportional? What I mean is: is it possible, for instance, that we find a solar system exactly like ours except for the fact that every object (planets, stones, animals, trees, etc.) is one thousand times longer or less long? What if only twice longer? And what about a different universe where even atoms (and elementary particles, if they have any length at all) were one thousand times "longer"? Is this meaningless?
Thomas Pogge
February 24, 2006
(changed February 24, 2006)
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With regard to both questions, I understand you as imagining that objects are longer or shorter in all dimensions (not merely in one dimension). So spheres would still be spheres, except larger or smaller ones. Right?
On your first question, this is not possible if we hold fixed the laws o... Read more
Do men need speech in order to think? In other words, can we do the act of thinking without "speaking" to ourselves consciously or unconsciously? For myself, I use colloquial English, the language I am most fluent in, when I think in my mind. Does it have to be the case that one would use his or her most developed language to think?
Louise Antony
February 24, 2006
(changed February 24, 2006)
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There are two competing views on this. The first view -- possibly the more popular view among philosophers -- is that thought and language are essentially tied together, so that there cannot be one without the other. (Leave aside all the evidence from casual observation that it's all t... Read more
Why do people want to know so much about life if in the end we're all going to die anyways?
Rachana Kamtekar
February 24, 2006
(changed February 24, 2006)
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Your question seems to assume that things can't have value if they're temporary. But we care what happens today even though today will end in a few hours. This is because one important source of value is what we experience: it matters to us to avoid pain, to enjoy the lives we live.... Read more
Who was the Greek philosopher who was condemned to slavery, why so, how he got freed and by whom? thanks and thanks
Rachana Kamtekar
February 24, 2006
(changed February 24, 2006)
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Epictetus (c. 55-135) was born a slave and was freed by his master in later life; it's not really known why, but such a thing was not uncommon. In the ancient Greek world, people became slaves if they were captured in war or were born of a slave (rather than being 'condemned' to slave... Read more
Is the "theory" of the Matrix, or something along those lines, possible? We perceive the world with little signals sent to our brain, so couldn't those signals he rigged to, say, a machine? And everything happening around us is just in our heads? If you dissagree with this, what could you use to prove me wrong? ~Kris S.
Matthew Silverstein
February 24, 2006
(changed February 24, 2006)
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I do not disagree with this, nor (I suspect) would most philosophers. The story of The Matrix is possible.But as long as we're talking about possibility, your situation might beeven worse than the one depicted in the movie. At least in the filmwe're all sharing the same, collective... Read more
Believing that once all factors have weighed in the construction of any individual (genetic disposition, cultural programming, the expectations of family and friends, the influences of the magazines on your coffee table...) that free will and freedom of choice are nothing but a comforting delusion, could anyone point me to a philosopher I might study who shares this thought?
Matthew Silverstein
February 24, 2006
(changed February 24, 2006)
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The view you're expressing--that everything about us is caused byexternal factors, and that this rules out the possibility of free willand moral responsibility--is often referred to as hard determinism. One classic defense of this view can be found in The System of Natureby Baron d'... Read more
Could a newly discovered law of physics ever change/affect a law of logic?
Marc Lange
February 24, 2006
(changed February 24, 2006)
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Very good question!
Let's begin by drawing an important distinction. By "changing a law of logic", you might mean (i) our changing our minds about what the laws of logic are, or (ii) the actual laws of logic changing -- one set of laws was in force at one time and another set is in force at... Read more