Recent Responses
In a democratic society, should felons retain the right to vote?
Allen Stairs
October 20, 2008
(changed October 20, 2008)
Permalink
In the United States, the answer varies from jurisdiction to jurisdiction. A few states allow felons to vote even while in prison; many allow felons who have served their sentences to vote. There is a chart in this essay from the Sentencing Project.
We might look at the issue from two points... Read more
When young children perform long division or multiplication, are they constructing a proof?
Richard Heck
October 18, 2008
(changed October 18, 2008)
Permalink
So I asked my brother about this, and he tells me that this kind of question is much discussed in the literature on mathematics education. Here's what he had to say:
"Good thing to think about. A related idea I've been considering for some time---and maybe the difference is just a matter of... Read more
When young children perform long division or multiplication, are they constructing a proof?
Richard Heck
October 18, 2008
(changed October 18, 2008)
Permalink
So I asked my brother about this, and he tells me that this kind of question is much discussed in the literature on mathematics education. Here's what he had to say:
"Good thing to think about. A related idea I've been considering for some time---and maybe the difference is just a matter of... Read more
What are numbers? Are they unquestionably EVERYTHING? Let's take 17 and 18 for example: Isn't there an infinite amount of numbers that exist between 17 and 18? There is no such thing as the smallest number, and there is no such thing as the largest number. WHY?!
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
Well, there are a lot of questions there. I won't try to answer the first one: That's a topic for a book, not an internet posting. And I'm not sure I understand the second one. But regarding the next two, yes, of course there are infinitely many numbers between 17 and 18. Here are some of th... Read more
We generally hold that a mathematical proposition such as "2 + 2 = 4" is necessarily true; it is difficult to imagine a possible world in which it is false. However, is it possible that "2 + 2 = 4" is not a statement that expresses a mathematical necessity (or an operation involving numeric values that must provide a certain result), but rather presents an inductive inference based on how people currently "define" the number "2", and the operator "+"? We could, for example, someday come to discover that "2" does not represent "2 things or ideas"; what we call 2 things may turn out to be 3 things, or 1 thing, etc. If this is possible then it would seem that "2 + 2 = 4" is an empirical, not a rational truth. Is this intelligible? I realize that this last statement, that we could discover 2 to refer to 3 things, etc., entails a theory of what a number is, i.e. a number "represents a quantity or amount of something". It seems, though, that in order to conclude that "2 + 2 = 4" is a necessary truth we must hold that a number is a "fixed" value; for example, a number is a (theoretical) quantity which is not grounded in any emprical relation (e.g. "2" represents a theoretical value that is "fixed"). Surely, though, the way we use numbers seems to indicate (as does applied mathematics) that we do not (always) mean that "2" is theoretical or rational; if this were true then we might (ironically) lose all meaning that mathematics provides in everday use. I realize there is more to this issue than what I present here; what, for example, does it mean for a number "to represent" to something or another. I think, however, there is enough here to make the question clear.
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
Perhaps the first thing to say here is that we need to distinguish the question whether it is necessary that 2+2=4 from the question whether the sentence "2+2=4" is necessarily true. It seems to me that no sentence is necessarily true. Any sentence might have been false, simply because that... Read more
Are the infinitely small and the infinitely large the same thing?
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
It would help to be told why one might think they were. But in mathematics, no, they are not. Something that is infinitely small---a so-called infinitesimal---is something that is smaller than anything of finite size. Something that is infinitely large is something that is larger than anythi... Read more
Could questions in the philosophy of language in principle be answered in terms of the structures of the human brain? Might we imagine, for instance, pointing at a certain lobe and saying "Well, this shows that Russell was wrong about denotation"?
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
Well, I don't know if it could be quite like that, but one dominant approach to contemporary linguistic theory holds that questions like, "How do descriptions work in natural language?" are ultimately questions about the psychology of competent speakers. Assuming that (cognitive) psychology... Read more
I am an American who has embraced the ideals of the Enlightenment, specifically the inherent value, perspective, and rights all humans on this planet. How do we reconcile these values with contemporary ideologies, specifically Zionism, that posits a racially, religiously unique group with "overriding" rights?
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
It's no doubt true that Zionism as such doesn't necessarily insist that Jews are "unique" and so deserve "overriding rights". That said, there's a case to be made that "national ideologies" are intrinsically racist, on the ground that the very notion of a "nation" that is being deployed here... Read more
I am an American who has embraced the ideals of the Enlightenment, specifically the inherent value, perspective, and rights all humans on this planet. How do we reconcile these values with contemporary ideologies, specifically Zionism, that posits a racially, religiously unique group with "overriding" rights?
Richard Heck
October 17, 2008
(changed October 17, 2008)
Permalink
It's no doubt true that Zionism as such doesn't necessarily insist that Jews are "unique" and so deserve "overriding rights". That said, there's a case to be made that "national ideologies" are intrinsically racist, on the ground that the very notion of a "nation" that is being deployed here... Read more
After discussing Socrates and his views on the state in Crito, a question came to mind. How would Socrates behave in 1930's Nazi Germany when the time came to join the military? Would his sense of right and wrong win out over his loyalty to the state? Or would he feel too great a responsibility to the state, as he clearly seems to in Crito, to put his personal choices and morality over it? Thanks, Jan-Erik
Nicholas D. Smith
October 16, 2008
(changed October 16, 2008)
Permalink
The question you pose continues to be debated by Socrates/Plato scholars, so you should probably regard the answer I will give as a controversial one. On the one hand, as scholars who wish to resist the "authoritarian" reading of the Crito insist, Socrates clearly says that it is unjus... Read more