[quote]Dr.Matt581 wrote:<<< All of my posts have regarded misconceptions people have regarding number theory >>>[/quote] I hod NO conception of “number theory” at all. Mis or otherwise Not the point. Try this post I wrote to Groo which would have been a PM if they worked. Maybe you missed it maybe not. Numbers ARE NOT the point. They are a tool that illustrates the point, which is logical certainty.
This is the PM to Groo that I cannot send. Not the way I wanted to do it, but here it is.
[quote]groo wrote: I am not certain he understands what you are driving at. >>>[/quote]I am certain he does not understand, which I hasten to add says literally nothing about his intelligence or lack thereof. [quote]groo wrote: You are asking for something like this correct? Introduction to Mathematical Philosophy >>>[/quote] What I am asking for, neither he nor you nor any other man can give me though we all use it every second of every day. [quote]groo wrote:
Especially bits like this?
In seeking a definition of number, the first thing to be clear about is what we may call the grammar of our inquiry. Many philosophers, when attempting to define number, are really setting to work to define plurality, which is quite a different thing. Number is what is characteristic of numbers, as man is what is characteristic of men. A plurality is not an instance of number, but of some particular number. A trio of men, for example, is an instance of the number 3, and the number 3 is an instance of number; but the trio is not an instance of number. This point may seem elementary and scarcely worth mentioning; yet it has proved too subtle for the philosophers, with few exceptions.[/quote] Plurality is an expression and symptom of number, but not number itself. I agree. What I’m saying is subtler (more foundational) still than this man’s assertion that “trio is not an instance of number” which I also agree with, but which also still does not get to what I’m asking for.
On page 2 this guy says, before he goes on to give a bunch of different illustrations of the point he’s trying to make.:[quote]These remarks are relevant, when we are seeking the definition of number, in three different ways. In the first place, numbers themselves form an infinite collection, and cannot therefore be defined by enumeration. In the second place, the collections having a given number of terms themselves presumably form an infinite collection: it is to be presumed, for example, that there are an infinite collection of trios in the world, for if this were not the case the total number of things in the world would be finite, which, though possible, seems unlikely. In the third place, we wish to define â??numberâ?? in such a way that infinite numbers may be possible; thus we must be able to speak of the number of terms in an infinite collection, and such a collection must be defined by intension, i.e. by a property common to all its members and peculiar to them.[/quote]
This is where he is stabbing around for my point, but winds up with a bunch of gobbledygook. Things in the world are infinite? Really? I’d like to know how he defines “world”. If Kamui reads this he is going to quite rightly see the problem of the one and the many reasserting itself right here. (another story).
Just as when you and I met a year ago now Groo, I am after logical certainty. I use simple mathematics as a vehicle because nobody will ever deny that 2+2=4 in our pragmatic day to day life where it matters. We all live and breathe in certainty every second. You said so yourself. On this page: Documented Cases of Evolution - Politics and World Issues - Forums - T Nation When you said:“Yes I think we can know some things for certain. Or at the very least I act as if I believe this. Pragmatically everyone does.” A statement for which I awarded you my highly coveted (yeah right =D ) “Hallelujah Worthy Bullseye” award here: http://tnation.T-Nation.com/free_online_forum/world_news_war/free_will?id=4523136&pageNo=11
The bottom line here is this. DrMAtt has been telling me about every related thing except why 2+2 is CERTAINLY 4. Everything he has said to me thus far can be summed up in the purely tautological statement of “that’s just the way it is”. We’re right back where we started. I, you, DrMatt, we are pickled in pragmatic logical certainty without which not one single syllable of intelligible thought word or deed, mathematical or otherwise is possible, yet almost none of us has ever questioned why at that level.
