I will take your word for it, but my understanding is that the precise nature of the relationship between Peirce's continuum and nonstandard analysis is still not fully settled. — aletheist
Does Peirce know his continuum has holes in it? It's logically necessary. — fishfry
If you read up on Peirce's synecheism - as his model of continuity - it gets clearer. The "continuity" then is of the systematic "constraints plus freedoms" kind that I employ. — apokrisis
Different point ... when you talk about points coming in and out of existence, that reminds me of the intuitionists. Which I regard as a somewhat mystical strain of thought. — fishfry
Where the standard real line has noncomputable numbers, the intuitionistic line has holes. — fishfry
* So my question is: Is Peirce a restrictionist, squeezing the noncomputables out of the standard reals and only creating reals when they pop into his intuition; or is he an expansionist, blowing wispy clouds of infinitesimals onto the real line? — fishfry
...the whole point of Peirce - as managing to resolve the tortuous dilemmas of Kant, Descartes and all the way back to the Miletians vs the Stoics - is that it is itself metaphysically fundamental that reality is organised by its own sign relations. — apokrisis
Just struggling a bit with how 'sign relations' come into the picture outside of biology..... — Wayfarer
Just struggling a bit with how 'sign relations' come into the picture outside of biology..... — Wayfarer
I thought sign relations were some kind of postmodern talk I don't know anything about other than that Searle thinks Derrida is full of sh*t. — fishfry
You can take my word for it that .999... = 1 is a theorem of nonstandard analysis. But actually you don't need to take my word, I provided a proof above. — fishfry
That is, either the judgement of "continuous" or "discrete" would be determinations imposed (counterfactually) on pure possibility. — apokrisis
The "continuity" then is of the systematic "constraints plus freedoms" kind that I employ. — apokrisis
In the beginning was the word, eh? — Wayfarer
The word plus the vagueness it could organise. — apokrisis
There was the vagueness that would be utterly patternless and directionless action. — apokrisis
And someone said that's a little boring. Let's tweak it with some contrast. Let's add some constraints to give it some light and dark. Let's create a little story about differentiated being. — apokrisis
And a better paper on the Peircean project is probably... http://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf — apokrisis
So at the moment I'm coming to Peirce by way of Zalamea's exposition of the mathematical philosophy of Grothendieck. — fishfry
In this context, do you basically see continuity as 3ns, discreteness as 2ns, and possibility as 1ns? — aletheist
Given that existence is 2ns, do you generally prefer to characterize 3ns as "constraints" and 1ns as "freedoms"? — aletheist
So that does conflict with some of Peirce's apparent definition of 1ns as brute quality (with its implications of already being concrete or substantial actuality). — apokrisis
So continuity or synechism itself is 3ns - but 3ns that incorporates 2ns and 1ns within itself. — apokrisis
So 1ns (in a misleadingly pure and reified sense) is vagueness (a certain unconstrained bruteness of possibility - as in unbounded fluctuations). — apokrisis
So 3ns is necessity, 2ns is actuality, and 1ns is possibility. — apokrisis
... see Menno Hulswit's excellent books and papers on this issue ... — apokrisis
But once you get used to it, it all makes sense. — apokrisis
And I expect you already get most of this. But just in case, that is a summary of why the answer is not so straightforward. — apokrisis
the irreducible triadicity of a sign relation. — apokrisis
From Googling around I think being triadic is what a mathematician would call ternary — fishfry
Again, Peirce did not use "bruteness" to refer to 1ns, only 2ns. — aletheist
I've had some exposure to category theory. Not much but enough to know that modern math is done very differently than anything you see as an undergrad math major. Equations are replaced by arrow diagrams. It's a very different point of view. — fishfry
I've always understood category theory to be loosely related to structuralism. We no longer care what things are made of, we care about their relationships to other things; and about very general patterns in those relationships that tie together previously unrelated areas of math. — fishfry
Why have I never heard of Peirce before? — fishfry
I still don't know what triadic Peircean phenomenology is. Can this be explained simply? — fishfry
Are your comments directed at any particular person or post? — aletheist
I wanted to mention that at one point Zalamea basically says that Peirce is doing category theory, or category theory is Peircean. — fishfry
Peirce acknowledged this - as soon as we talk or even think about a color or other quality, it is no longer 1ns in itself. — aletheist
Firstness is more or less indeterminate or determinate, not more or less vague or precise; only with Peirce's category of Thirdness can we speak of vagueness versus precision (and then there's also vagueness versus generality).
http://www.paulburgess.org/triadic.html
Hot damn! ;) — apokrisis
So category theory seeks an analytic foundations whereas semiosis seeks a synthetic one. — apokrisis
Possibility comes in two varieties - 1ns and 2ns. Firstness is unconstrained possibility and secondness is constrained possibility. So 1ns is more like the notion of pure potential, and 2ns more like the ordinary notion of statistical probabilty (or even a propensity). — apokrisis
Firstness is more or less indeterminate or determinate, not more or less vague or precise; only with Peirce's category of Thirdness can we speak of vagueness versus precision (and then there's also vagueness versus generality).
It seems you don't understand either category theory (at a philosophical level) or semiosis and are just seeking to nitpick with contradictory sounding quotes. — apokrisis
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.