*are*physical objects is advocated. I am truly baffled when I hear such beliefs. Here are the some questions:

Is the number $0$ aFor example, what is the mass of $(\omega, <)$? Can you find it somewhere, perhaps at Tesco's?physicalobject?

Is the number $2^{2^{2^{2^{2^{2^{2^{2}}}}}}}$ aphysicalobject?

Is the wellorder $(\omega, <)$ aphysicalobject?

Is the topological space $\mathbb{R}^4$ aphysicalobject?

Is the Lie group $SU(3)$ aphysicalobject?

Is the rank $V_{\omega + 57}$ aphysicalobject?

I would believe this only if this was advocated by abstract objects.

ReplyDeleteSeriously, where has this been advocated?

Hi AJ JA

ReplyDeleteUltrafinitists make this claim. E.g.,

http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Ultrafinitism.html

They insist, e.g., that because a physical computer, say, is finite, there aren't numbers beyond what it represents. But this philosophical conclusion requires the further assumption that numbers *are* physical objects. This assumption is the one that is not justified.

Cheers,

Jeff

Hi again AJ JA,

ReplyDeleteIt is advocated by E.B. Davies (see E.B. Davies, 2005: "Some Remarks on the Foundations of Quantum Theory", Brit. J. Phil. Sci. 56, p. 530.)

See

http://m-phi.blogspot.co.uk/2011/04/2-become-1.html

Cheers,

Jeff

Hi AJ JA,

ReplyDeleteAnother example - the physicality of mathematical objects is advocated by Doron Zeilberger:

"(ii) the traditional real line is a meaningless concept. Instead the real REAL ‘line’, is neither real, nor a line. It is a discrete necklace! In other words R = hZp, where p is a huge and unknowable (but fixed!) prime number, and h is a tiny, but not infinitesimal , ‘mesh size’. Hence even the potential infinity is a meaningless concept."

http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf

Zeilberger's philosophical view here simply assumes that mathematical objects (such as $\mathbb{R}$) must be *physical*. Otherwise, the relevant concept is, he says, "meaningless".

But the reasonable view is that $\mathbb{R}$ is an abstract object, and its connection, if any, to the physical world is something to be investigated empirically.

Cheers,

Jeff

Thanks, Jeff!

ReplyDeleteCheers,

A