There is a new book out about the Greek philosopher Parmenides, the central figure of the Eleatic school. Well, it is listed as a 2025 publication. I, for one, will call that "new" given the antiquity of the subject matter. It is an anthology titled simply, Parmenides: New Perspectives , edited by A.G. Long and Barbara M. Sattler. The Eleatics may have made their greatest impact on subsequent philosophy through Parmenides' disciple Zeno. The simplistic view (my view) is that Parmenides took a position that seemed, simply, nuts. There is no change, no motion, and no division in the word, there is only Being. Zeno provided arguments for that position that made it seem less nutso, by making the common sensical world of change, gaps, and differences itself seem oddly paradoxical. That conventional understanding makes Zeno seem the more interesting figure in that dyad. But the Long/Sattler book offers "new perspectives". One of them is that Parmenid...
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Continuing a thought from last week ... Aristotle is our main source for Zeno's paradoxes. As a side note, there is no mention of a turtle in Aristotle's account of the paradox of Achilles' race with a slower runner. The slower runner is just that. The paradox began to turn on Achilles against a turtle when Simplicius wrote up his paraphrase. Simplicius didn't come along and write his commentaries on Aristotle until the early 6th century AD -- three centuries after the flourishing of Diogenes of Laertius. I am still puzzled that D of L is so scattershot about Zeno and that when he does get around to the argument about motion, gives only one version of it, the idea that something is either at motion in a particular moment or at rest, and that a moving object can't really be either of those. But let us not go there. Let us go back to Simplicius. I wonder: was he simply paraphrasing Aristotle and adding some zoological pizzazz to it by throwing in the...
I'm going to try to make some connections. Parmenides to Zeno to Democritus to Newton and Leibniz. Parmenides: everything is one. And the One that is all is unchanging. Division, motion, change, are impossible. Accordingly, they must be illusions. Why did Parmenides come to these conclusions? Generally, he had a simple line of thought that puns on negative words such as "nothing." If there is nothing between A and B, then A and B must be in the same place. Thus, if they are some distance from each other, then they must actually be one. If you don't get that, don't worry about it. Zeno came up with a cleverer way of arguing for Parmenidean monism. He argued that the common-sense notions of the world we live in are rife with paradox. In order to get rid of paradox, we must run to the the shelter of the Parmenidean One. I've written of such things before, usually in comedic form. https://jamesian58.blogspot.com/2020/07/the-two-zenos.html The only point ...
The Nobel Prize winning economist Kenneth Arrow died recently (February 21). Let us give his work some thought on his way out of this world. Arrow was best known for the "Arrow Impossibility Theorem," a powerful and very influential argument that given certain assumptions and five (quite reasonable sounding) goals, there is no actual or possible system of voting that will work every time -- that will avoid violating one or more of those goals -- because the conditions themselves are incompatible. Arrow accomplished this result, one regarded every since as foundational to social choice theory and welfare economics, in his Ph.D dissertation in 1950, when he was 31. It might have been tempting to spend the rest of his scholarly career defending and expanding on the terrain of that theorem. But he left that work for others, and many others have stepped in, including Amartya Sen. Arrow moved on, and among much else helped Gerard Debreu develop a rigorous proof of the exist...