Daniel Barnes Posted July 4, 2007 Share Posted July 4, 2007 (edited) Greg:>Some time ago Daniel asked me to present my own summary of Peikoff's argument in the ASD.Hi Greg,I recall, perhaps incorrectly, that I was suggesting a formalisation of Peikoff's argument - as you were going to do it for something else less relevant - rather than a summary of it. But thank you for doing it anyway. I have read Peikoff's essay previously. It seems you have a formalisation in mind at some point. That would be useful if you get round to it.> This should serve to remind us of the empirical origin of even our mathematical concepts. Let's look at this issue from a slightly different angle: namely, origin from is, rather obviously, not the same as equivalent to.To wit: even if it could be easily decided one way or the other, what does the genesis of the concept "triangle" matter? This is rather like saying there is no "dichotomy" between a bison and a jellyfish as we might speculate they all originated in some simple organism at the dawn of time. The cutting edge of the issue is, as you state generally (but then seem to take back in a rather ad hoc formulation which we will look at in a moment), that "perfect triangles" do exist in our heads but do not exist in the physical world. Thus there is a clear dichotomy, or at the very least a highly useful distinction. If all you want to argue is that there is some kind of original connection between the abstraction and the real world, well so does Plato. But this seems to me to be beside the point. Incidentally, I do not get into debates over the meanings of words, but I would suggest a minor terminological clarification that might save confusion. When you write:Greg: "...these beings do not exist in the physical world we should say that they don't exist at all, but we have thoughts of them..."...it might be better to say these "beings" - such as perfect triangles - exist, but abstractly, and not physically.Now, with that minor distinction made, what appears to me to be a rather ad hoc formulation is as follows:Greg:"...there are surfaces that look perfectly triangular to the unaided eye, and from these we formed the concept of perfect triangles, without even needing to idealize, and then only later, when we measured carefully, did we find that the triangles were not composed of perfectly straight lines." (italics DB)This seems simply confused, and merely verbalist, because when we "formed the concept of perfect triangles", we could have hardly done anything else but "idealised" them - obviously because the perfect triangle did not physically exist in the first place! Your theory becomes even weaker as you don't mention exactly what objects "look perfectly triangular" - in reality no object does, although there are objects that resemble perfect triangularity to a greater or lesser extent. However, to even make such a judgement seems to presume an abstract standard in the first place.These are pretty straightforward criticisms of your position. FYI, I am a Popperian, and find Popper's "3 World" cosmology provides a fruitful hypothesis for some of these and other perennial problems. Edited July 4, 2007 by Daniel Barnes Link to comment Share on other sites More sharing options...
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!Register a new account
Already have an account? Sign in here.Sign In Now