Response One

Response to Email One, below. Exceptional in its length and geekiness (email exchanges with "Dr. Math"??), but right up the alley to what was requested. Will certainly email again once he completes the paper on conscience in a few months. Let's hope the timeliness of all future respondents matches this precedent:

hello,

glad to hear that you enjoyed my paper. I am not surprised that you were arguing against a large opposition -the view that infinity is a number is almost always the minority opinion. Most sources you will find online (and I imagine you have already discovered this) argue that infinity is not a number. But, I believe they are all wrong. I don't know if I mentioned this in the essay, but Frege, who was the first to define number about a hundred years ago, found that infinity was obviously a number. In fact, he felt it was so obvious that he devoted no more than a paragraph to discussing the issue.

I don't know if you came across this in your studies of infinity, but mathematicians have been aware for some time (over a hundred years,) that there are different types of infinity. For example, the number of real numbers, while infinite, is in a very meaningful sense larger than the number of integers, which is also infinite. There is a way people use the term infinite, which is not a number, and that is to pick out the property shared by all these different infinities. This property is certainly not a number, just as 'finite' is not a number -it just picks out a property shared by all finite numbers. However, each entity within the set of things that can be described as finite is a number, and the same goes for infinity.

In answer to your question about the research for my paper, the paper was written for a class in analytic philosophy. I was studying the contributions of Frege to philosophy of mathematics, and chose the topic of infinity because of its immediate relation to Freges work, and because of the controversial nature of my thesis (which always makes writing a paper more interesting.) My research mainly involved discussions with various people, since I already had a good grasp of Freges view of numbers and the mathematics of infinity (having taken classes in discrete mathematics.) I discussed the issue with friends, people online (there were several e-mails sent between myself and "Dr.Math",) and professors at my university. In general, those trained in math were the ones to argue infinity was not a number. In fact, I don't remember a single mathematician who argued otherwise. This, despite of the fact that some of them subsequently identified the definition of number in terms of the cardinality of sets (a la frege.) I believe it is simply dogma of the mathematical institution that infinity is not a number -many of their arguments for their position are almost laughably bad. As I mentioned in the essay, it was at one time believed by mathematicians that zero was not a number, of course that position has fallen into disfavor. I am not entirely sure what it will take to change their minds about infinity, since it is precisely the same problem.

In a sense, it doesn't matter whether they call infinity a number or not, because their math will work either way. I might argue that if they don't call it a number then they haven't really understood it, and it might adversely affect their intuitions about theoretical mathematics. However, the real reason I would press them to change their view is that it is simply very irksome to me to have people claim with such
confidence a conclusion that has very little logical support.

if you are interested, I am currently working on a paper arguing that consciousness (in the sens of subjective experience -what it is like to be a sentient being) is a physical phenomenon. This is another controversial position (among the general population, but not, it seems, among philosophers.) I plan on being done within a month and a half or so, and putting it on my website.

http://www.johnath.com/~david/etc/

I also plan to create a very short work on the relation between religion and morality (I will argue that religion is largely detrimental to morality, contrary to popular opinion.)

Also in the works is a debate of sorts about global warming. I intend to put all the arguments and evidence provided by each side in a large chart, and each will correspond with a rebuttal from the other side. Once it is up, I will be encouraging people to provide other argument/evidence suggestions.

thanks again for your interest,