Hi, I've been reading about transfinite cardinal numbers and was wondering if you could answer this question. Supposedly the set of integers has the same cardinality as the set of even integers (both are countably infinite) since there exists a bijection between the two sets. But at the same time, doesn't there also exist a function between the set of even integers and the set of integers that is injective while NOT bijective (g(x) = x), since the image of f does not compose all of the integers (only the even ones)? To clarify, let f and g be functions from the set of EVEN integers to the set of ALL integers. Let f(x) = 1/2 x, and g(x) = x. Both are injective functions, but f is onto while g is not. So f is a bijection, while g is merely 1-to-1. Why, then, can I not say that the set of even integers and the set of all integers do NOT have the same cardinality since there exists some 1-1 function that is not onto? It seems like I should be able to draw this intuitive conclusion since g is 1-1, so for...

Well, I am a math major. I am about to graduate, and I wish to attend graduate school in philosophy. I took one class in the philosophy of science. I know it is not enough, but I really have a deep passion for philosophy. I read alot on metaphysics, philosophy of mathematics and science by myself. It is to the point that I can understand much of the material in professional philosophical papers. I have a deep interest on the issue of ontological commitment to abstract objects, and the nature of the laws of nature. I really want to be a philosopher. What can I do?

How do you determine the panel? How do you determine who is and who is not a philosopher, more importantly? Isn't there such thing as a philosopher without a PhD and tenure, or whatever else holds this group of panelists together?

If we can neither prove nor disprove the existence of a 'God', is it rational to even consider the possibility that he/she exists? Without the dedication of the few who preach from the worlds' religious houses, the notion of a 'God' surely wouldn't cross the mind of even the most imaginative of thinkers?

Why is the use of police force justifiable to stop the attempted murder of a neighbor, but military force unjustifiable when used to stop the attempted murders of civilians in other countries who peacefully advocate for human rights (speech, assembly, voting, etc.)?

My question has to do with why we attribute differing levels of blame for equivalent actions that produce different outcomes. For example, why does attempted murder go along with a much lesser sentence than actual murder. If I try my hardest to kill you and you get away, how is that action less punishable than if I was sucessful? Another example would be drunk driving. Consider three drivers driving home after one too many drinks: One arrives home safely. Although there is a spectrum on this issue, most will consider this a minor offense. The next driver was pulled over and arrested. He goes to jail and is considered by most to be a criminal. The last driver hits and kills a pedestrian and is charged with Vehicular Homicide. When he eventually gets out of jail, this person is a pariah. Given that these three drivers had the same number of drinks in the same amount of time, how are any of these three situations different? From a judicial standpoint I can see an argument for the differing levels...

Do numbers exist?

Occam's razor seems to be a devestating weapon when it comes to the atheist's argument to why God doesn't exist, or more precisely it is more likely that he doesn't exist. It seems the scientific community has the consensus that they will never rely on "God" for the answer to any problem. Will there ever be a scenario in which God might prove simpler than the scientific or mathmatical explanation, and Occam's razor can be used to justify a belief in God?

What sort of logical arguments might be used to support metaphysical naturalism? Is it simply an assumption based on the lack of evidence for the supernatural? Also, do the majority of philosophers today advocate this view? Thanks for your answers.

After reading Douglas Burnham's response where he mentioned Deleuze, I tried reading the Stanford Encyclopedia's entry on Deleuze, with little understanding. Could someone please explain what "difference" is in Deleuze and what preeminence of "identity" he is trying to undermine?? And/or recommend further (comprehensible) reading on the matter? Much appreciated.