| Response posted on September 1, 2010 by Peter Smith |
| On the standard account, given two finitely long lines, even of different lengths, their points
can indeed be matched up one-to-one, e.g. by the kind of projection the
teacher indicated. And the possibility of that kind of one-to-one matching
is just what we... |
| Mathematics |
|
| Response posted on August 22, 2010 by Peter Smith |
| Shame on your school! :-)After a basic logic you can either go deeper (more of the same, but pursued to greater depth), or go wider (look at logics that deal with more than do sentential and predicate logic -- modal... |
| Education, Logic |
|
| Response posted on August 13, 2010 by Peter Smith |
| Of course we might expect religions to take issues about sexual life and conduct seriously (though with some due sense of proportion, compared with other matters, like issues of social justice -- and it is the seemingly too prevalent lack... |
| Religion, Sex |
|
| Response posted on August 12, 2010 by Peter Smith |
| My maternal grandmother was the youngest but one of a Victorian family of ten; her oldest brothers were about twenty years older than her. It doesn't seem at all morally inappropriate that she should have cared about her nearest siblings... |
| Children, Ethics |
|
| Response posted on August 10, 2010 by Peter Smith |
| My colleagues raise a number of points, some rather puzzling, which deserve more that there is space for here. But some quick reflections:1. Love of the good, to take Charles's example, may be a fine and noble thing. But something... |
| Beauty |
|
| Response posted on August 6, 2010 by Peter Smith |
| You ask a grad student ...Well, I semi-jest, but a good way of making a start on some new topic is indeed to ask someone what the two or three recent "must read" items are. And reading these will firstly... |
| Education, Ethics |
|
| Response posted on August 3, 2010 by Peter Smith |
| Isn't that simply a false dichotomy? You need the good questions and the right spirit of enquiry. If you've no clear, well-formulated, questions then you'll just produce an ill-directed ramble. If you aren't driven by curiosity actually to explore the... |
| Education, Philosophy |
|
| Response posted on August 2, 2010 by Peter Smith |
| Of course it isn't true! Just walk down the street with your eyes open ... Most of us just don't make it in the beauty stakes. Most of us are just very ordinary -- not even quirkily striking. Tough,... |
| Beauty |
|
| Response posted on July 30, 2010 by Peter Smith |
| I agree with Richard's and Alex's general remarks about "logicism" and what counts as "logical". It would indeed be far too quick to reject every form of logicism just because it makes the existence of an infinite number of objects... |
| Logic, Mathematics |
|
| Response posted on July 29, 2010 by Peter Smith |
|
In the Principles of Mathematics, Russell boldly asserts"All mathematics deals exclusively with concepts definable in terms of a very small number of logical concepts, and ... all its propositions are deducible from a very small number of fundamental logical principles."Principia,... |
| Logic, Mathematics |
|
| Response posted on July 29, 2010 by Peter Smith |
| When it comes to moving from the BA to beginning graduate studies, the only thing (in my experience) that grad schools really care about is just how smart you are at philosophy. So they will take note of how well... |
| Education, Philosophy |
|
| Response posted on July 22, 2010 by Peter Smith |
| Neither.Assuming by "philosophy paper" you mean student essay, then what you need to be doing is evaluating arguments, as carefully and as honestly and as rigorously as you can. You must aim for maximum explicitness, maximum clarity, maximum organization of... |
| Philosophy, Profession |
|
| Response posted on July 22, 2010 by Peter Smith |
| There's no right answer.Zermelo's original set theory allowed "urelements", i.e. entities in the universe which are members of sets but not themselves sets. Some modern writers use "ZFC" to refer to a descendant of Zermelo's theory allowing urelements. George Tourlakis... |
| Mathematics |
|
| Response posted on July 22, 2010 by Peter Smith |
| I agree that philosophers should engage with relevant science. But of course, what science (if any) is relevant depends very much on what philosophical questions you are tangling with.If you are concerned with the metaphysics of time, for example, then... |
| Philosophy, Science |
|
| Response posted on July 20, 2010 by Peter Smith |
| Perhaps it is worth taking continuing the conversation just a bit further.The idea that a proposition (statement, belief) is true if and only if it "corresponds to reality" is -- as I'm sure William would agree -- not entirely transparent.... |
| Truth |
|
| Response posted on July 13, 2010 by Peter Smith |
| A few comments on Hilbert's Hotel (since Charles Taliaferro has brought that up) and "actual infinities":If you want a standard presentation of the usual Hilbert's Hotel "paradox", which has nothing to do with money, then check out Wikipedia's good entry.... |
| Physics |
|
| Response posted on July 4, 2010 by Peter Smith |
| You might well enjoy reading the wonderful Philosophers without Gods (edited by Louise Antony, one of the contributors to this site). Some of the essays in that book might help you see that belief need not be "equivalent to superstition... |
| Ethics, Religion |
|
| Response posted on July 3, 2010 by Peter Smith |
| Here's a somewhat differently slanted view -- in favour, perhaps, of being a bit "daft"! :-)No matter how many times I read three-year old Daisy her favourite book, no matter how well she knows it by heart, she hasn't read... |
| Literature |
|
| Response posted on July 3, 2010 by Peter Smith |
| Jack says "The next train to London is at 11.15"; Jill adds "That's true".Jill's remark in effect just repeats Jack's message. To say it is true that the next train to London is at 11.15 tells us no more about... |
| Truth |
|
| Response posted on June 28, 2010 by Peter Smith |
| A formal system (of the kind to which Gödel's incompleteness theorem applies) is a consistent axiomatized theory which contains a modicum of arithmetic and is such that it is mechanically decidable whether a given sentence is or isn't an... |
| Logic |
|