Posts by Cassius

Martin K. posted:

Hartry Field is the best modern exponent of the fictional nature of maths. He has written extensively on it. The monograph Science Without Numbers [Oxford University Press: 2016] being the best.

I'd also politely point out Aristotle was the first person in human recorded history to expressly adopt this position. He is the original anti-Platonist. Another talking point between the Epicurean and Aristotelian we have in common.

“The next point to consider is how the mathematician differs from the student of nature. For natural bodies contain surfaces, volumes, lines and points, and these are the subject-matter of mathematics. Now the mathematician, though they too treat of these things, do not treat them as the limits of a natural body. Nor do they consider the attributes indicated as the attributes of such bodies. That is why they separate them. For in thought they are separable from change and it makes no difference nor does any falsity result if they are separated. The holders of the theory of the forms do the same, though they are not aware of it.”

[Natural Puzzles 2:2, 193b 23-36]

Maths is abstracting real qualities from physical items “by supposing separate what is not separate.”

[After the Of Nature, 13:3 couched in an extended discussion at 1077b21-1078a31]

It is an interpretative tool helpful for solving problems — not the study of a distinct realm of real non-physical phenomena.

Full Derek Abbott paper here: https://ieeexplore.ieee.org/document/6600840

Lots of good stuff in it:

"Hamming's paper marvels on how complex numbers so naturally crop up in many areas of physics and engineering, urging him to feel that “God made the universe out of complex numbers” [3]. However, for the engineer, the complex number is simply a convenience for describing rotations [7], and, of course, rotations are seen everywhere in our physical world. Thus, the ubiquity of complex numbers is not magical at all. As pointed out by Chappell et al. [8], Euler's remarkable formula e−jπ=−1 is somewhat demystified once one realizes it merely states that a rotation by π radians is simply a reflection or multiplication by −1."

Yep that's him! It's worth watching the video because it's fairly well put together - it's just that it's put together as a call to minimalism for the sake of minimalism, or something very similar. If you check out the guy's other videos on his channel you can detect a pattern that has very little to do with Epicurus.

This video encapsulates just about every modern popular notion of Epicurus that exists. Everyone has to make up their own mind about each one, but I've made up my mind and I label virtually every major point of this video "WRONG""

"In Epicureanism desire itself was considered to be a form of pain...." WHAT?????

And of course where does this line of thought end up? MINIMALISM!!!

And one of Epicurus' key thoughts was to "live an analyzed life"????????

OK I finished it. This is seven minutes of the most densely-packed set of errors about Epicurus I have ever seen. From that point of view it serves an excellent purpose. Only by confronting issues and explaining a better alternative can the discussion advance.

What an absolutely awful presentation!

Starting from the very first words (that Epicurus spend his life focused on what makes us happy) to the immediate jump to "pleasure = the absence of pain" and continuing to the very end with the three alleged key ideas.

The ancient definition of pleasure did not mean the presence of enjoyment...." ARGH!

I've now read the full physics . org article and think it is good. I want to track down the full Abbott article to which it refers. But as I read this, the logical conclusion is:

There's no real difference in kind between (1) the most complicated 2019 NASA formulas that calculate the size and movement and composition of the sun and (2) a Roman centurion pointing at the sky and saying 'the sun is a ball of fire that rises and sets on the horizon every day."

Both are simply human expressions / symbolic mental summaries of our own observations and they have no direct connection whatsoever to the reality of the sun and its workings. Unless we are astronauts the Roman centurion's observation were as useful to him as a NASA equation is to most of us. And if we happen to be among those NASA scientists (if there are any) who think that our formulas have some kind of mystical divine connection to some external ultimate reality, then we've actually regressed in 2000 years. If we think our math is the key to the meaning of life we're **less** intelligent than the Roman centurion who considered his description of the sun as all he needed to plan the campaigns of his legion.

Martin would you agree?

Which is opposed to THIS, which is what Epicurus was fighting against:

From the look of this excellent graphic, this article describes the position taken by Epicurus on the issue of Math vs Reality. It ends with something that sounds consistent with Epicurus to me: "For Abbott, these points and many others that he makes in his paper show that mathematics is not a miraculous discovery that fits reality with incomprehensible regularity. In the end, mathematics is a human invention that is useful, limited, and works about as well as expected."

I am posting this not only for discussion of this article but to ask that if you know of other well-stated articles which take a similar position, that you drop us a link so we can compile a list of reference cites. So if you are aware of others, please post here, and we'll work on more material about this issue in the future.

https://phys.org/news/2013-09-m…tive-world.html

Wow that is quite a video! I have never seen that!

Yep. That remark of his rang a bell with me from the moment I read it some years ago.

Wow - great photos! Thank you Joshua!

Outstanding example, Joshua, thank you!!! And you are channeling DeWitt - who makes almost exactly this same point in his book:

"But this involves a logical sleight-of-hand; it employs an argument by analogy, but argument by analogy only works if things really ARE analogous."

There must be books / articles / citations which help explain this point. Over time I would like to try to find some and this will be a good place to post them.

Sedley is suggesting that in attitude toward logic/dialetic we may have another deviation (watering-down) by later Epicureans. The first two areas were (1) thinking that pleasure has to be defended logically (Torquatus in On ends) and (2) coming up with four criteria of truth instead of Epicurus' three (Diogenes Laertius description of the canon). Sedley is suggesting that Epicurus himself didn't just reject logic/dialectic, he SCORNED it, and that later Epicureans (and therefore presumably us) should not make peace with logic/dialectic at all.......

It gets old to keep saying that everything is "important" - but here is another important passage, confirming how BOTH the Platonists and the Aristotelians were against Epicurus' position.

Here is the section from Lucretius to which Sedley refers in that last quote --

It is hard to overstate the importance of this observation on the Epicurean view of "truth," from the same source:

I see that Sedley would dispute Bailey's word "misleading" in the sentence I quoted above "Logic they reject as misleading...." Sedley thinks the better translation is "Logic they reject as redundant..."