jas0n
191
So, if we're to avoid the pitfall of talking past each other, we must come to an agreement as to what the words we use mean,
— Agent Smith
To do so would require that we use words, yes? Hence the hopelessness of starting from scratch. And what works in math won't work in philosophy. 'Language is received like the law,' and meaning evolves historically. — jas0n
I wouldnt say agenda. I’d say the eternal transformation of agendas. Is that still an agenda? — Joshs
So freedom is play within an overarching frame? Free variations on a theme? — Joshs
History as pre-assigned boundary conditions of behavior, within which there is freedom to excel or screw up. — Joshs
A Romantic free-thinking and feeling individual implies more oppressively severe fundamental constraints than an entropy dissipating system. — Joshs
So the I that espouses my freedom is not the same I that overthrows my current values. — Joshs
The world of maximum social pluralism and the world of maximum social conformity (authoritarianism) are two poles of a binary, — Joshs
And then there is the overthrow of the system of values: — Joshs
An even bigger picture begins with the overthrow of a value system which depicts a cosmos structured by specific objective laws, and a history that can be probabilistically calculated. It proceeds from this overthrow to what Nietzsche called a revaluation of all values, not a tolerant pluralism or celebration of subjective freedom but a yoking of current self and value system to a non-calculable other history and other self-to-be, an eternal return of the same , always different self, history and values. — Joshs
I like the battle over the continuum. — jas0n
Wildberger on infinities and continuums
The basic division in mathematics is between the discrete and the continuous. A largely unquestioning uniformity has settled on the discipline, with most students now only dimly aware of the logical problems with “uncomputable numbers”, “non-measurable functions”, the “Axiom of choice”, “hierarchies of cardinals and ordinals”, and various anomalies and paradoxes that supposedly arise in topology, set theory and measure theory.
While engineers and scientists work primarily with finite decimal numbers in an approximate sense, “real numbers” as infinite decimals are idealized objects which attempt to extend the explicit finite but approximate numbers of engineers into a domain where infinite processes can be ostensibly be exactly evaluated. To make this magic work, mathematicians invoke a notion of “equivalence classes of Cauchy sequences of rational numbers”, or as “Dedekind cuts”.
Each view has different difficulties, but always there is the crucial problem of discussing infinite objects without sufficient regard to how to specify them. I have discussed the serious logical difficulties at length around video 80-105 in the Math Foundations series. For example the video Inconvenient truths with sqrt(2) has generated a lot of discussion.
The idea of “infinity” as an unattainable ideal that can only be approached by an endless sequence of better and better finite approximations is both humble and ancient, and one I would strongly advocate to those wishing to understand mathematics more deeply. This is the position that Archimedes, Newton, Euler and Gauss would have taken, and it is a view that ought to be seriously reconsidered. I believe it is also closer to the view of modern giants such as H. Poincare and H. Weyl, both of whom were skeptical about our uses of “infinity”.
- https://njwildberger.com/2021/10/07/finite-versus-infinite-real-numbers/
Let’s consider here the situation with “infinity”. Most modern pure mathematicians believe, following Bolzano, Cantor and Dedekind, that this is a well-defined concept. By what rules of logic is someone going to convince me of the errors of my ways?
Perhaps they could invoke the Axiom of Infinity from the ZFC axiomfest! As a counter to such nonsense, I would like to propose my own new logical principle. It is simple and sweet: Don’t pretend that you can do something that you can’t.
According to this principle, the following questions are invalid logically:
If you could jump to the moon, then would it hurt when you landed?
If you could live forever, what would be your greatest hope?
If you could add up all the natural numbers 1+2+3+4+…, what would you get?
- https://njwildberger.com/2015/11/27/a-new-logical-principle/
In any case, the tension between intuitions of the discrete and the continuous has fascinated me for quite a while. — jas0n
I can't understand where the 'camera' is positioned when the Cosmos looks at itself, since the inside/outside framing seems to no longer apply, unless it is some kind of Hegelian thing where the stuff on the other side of the concept is itself just more concept and the mental/physical distinction breaks down. What's the relation of this idea to indirect realism? — jas0n
Grand statements are delivered which contain important insights and yet the implicit self-subversion of such insights is ignored. Concrete details are mostly omitted. Examples are sparse. Purple haze. — jas0n
In so doing, sociologists incorrectly attribute to Saussure (1) the postulate that meaning is arbitrary; (2) the idea that signs gain meaning only through relations of opposition to other signs; (3) the view that there is an isomorphic correspondence between linguistic signs and all cultural units of analysis, ergo culture is fundamentally arbitrary; and finally (4) the idea that he offers a Durkheimian theory of culture (i.e. Saussure was a follower of Durkheim).
But then let's not get all AP about it and just dismiss the dichotomy out of hand as (ugh) metaphysics. Let's dance around the corpse of logic in a mad jig of delight, proclaiming now the victory of ... the irrational, the pluralistic, the absurd!!! — apokrisis
Have you come across Norman Wildberger's dissident maths? — apokrisis
Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that need to be done, let him do it himself.
The discrete = 1/continuous, and the continuous = 1/discrete. Each exists as the limit of the other. And both exist only to the degree that it is pragmatically useful to keep forcing the issue.
Maths and logic traditionally come from the other metaphysical angle. Reduction to a monism must rule. Mathematical reality can only admit the one grounding choice. Pick your poison. — apokrisis
Don't get caught up in nonsense talk about departed Cheshire cats and their still lingering grins. — apokrisis
I don't get how Wittgensteinian philosophers can be so certain of their claims when they simultaneously also assert that the very thing they're making the claims with - language - is inadequate for this purpose. — Agent Smith
How does one measure certainty ? — jas0n
Language is received like the law' is something that it obvious once noticed. — jas0n
Then you go on to ask me how we measure uncertainty. — Agent Smith
Every PoMo argument ever boils down to saying this thesis leads dialectially to its own antithesis. — apokrisis
I don't mean to offend you. Maybe the metaphor is obscure. The point is simple. You didn't choose the sounds you chew when you have to talk to strangers and deal with the business of life. You didn't....invent the English language....or do I need to prove that? Am I so bold to be quite sure that neither of us forged their code we are currently employing? — jas0n
Saussure does imagine signs as cutting into an otherwise undifferentiated continuum of thoughtstuff. — jas0n
Psychologically our thought — apart from its expression in words — is only a shapeless and indistinct mass. — Saussure
There are no pre-existing ideas, and nothing is distinct before the appearance of language. — Saussure
It is widely known by Saussure scholars that Bally and Sechehaye took many liberties when organizing the student’s notes, by relying mostly on Constanin’s notes, reordering the topics, and coloring Saussure as much more settled on difficult issues.
Thought, chaotic by nature, has to become ordered in the process of its decomposition. Neither are thoughts given material form nor are sounds transformed into mental entities; the somewhat mysterious fact is rather that "thought-sound" implies division, and that language works out its units while taking shape between two shapeless masses. Visualize the air in contact with a sheet of water; if the atmospheric pressure changes, the surface of the water will be broken up into a series of divisions, waves; the waves resemble the union or coupling of thought with phonic substance. — Saussure
Language can also be compared with a sheet of paper: thought is the front and the sound the back; one cannot cut the front without cutting the back at the same time; likewise in language, one can neither divide sound from thought nor thought from sound. — Saussure
The bond between the signifier and the signified is arbitrary. Since I mean by sign the whole that results from the associating of the signifier with the signified, I can simply say: the linguistic sign is arbitrary.
The signifier, though to all appearances freely chosen with respect to the idea that it represents, is fixed, not free, with respect to the linguistic community that uses it. The masses have no voice in the matter, and the signifier chosen by language could be replaced by no other. This fact, which seems to embody a contradiction, might be called colloquially "the stacked deck." We say to language: "Choose!" but we add: "It must be this sign and no other." No individual, even if he willed it, could modify in any way at all the choice that has been made; and what is more, the community itself cannot control so much as a single word; it is bound to the existing language.
No longer can language be identified with a contract pure and simple, and it is precisely from this viewpoint that the linguistic sign is a particularly interesting object of study; for language furnishes the best proof that a law accepted by a community is a thing that is tolerated and not a rule to which all freely consent. — Saussure
(it's not all wordsalad to me, albeit at the limit of intelligibility a little too often) — jas0n
Not sure how to translate that. But from my Vygotskian/social constructionist perspective, language was the new medium that structured the "undifferentiated continuum" of the language-less animal mind.
So to actually characterise the difference language made to animal consciousness, we have to also be able to accurately characterise what kind of consciousness that was. — apokrisis
Ok. So you are quoting from the text that Stotlz points out is problematic as a representation of Saussure's views.... — apokrisis
So yes, this is Janus faced. The switch has a foot in both worlds. But the thought is the logical model - which in the Bayesian brain view, sets the switch in advance as best it can, then discovers the degree to which reality has tripped it the other way, spelling some error in the prediction.
So what can't be divided is the three way deal of the model, the switch or sign as the interface, and the world. The mind predicts, the world corrects, the switch mediates this triadic interaction. — apokrisis
One might argue that mathematics is biased toward the discrete in the pursuit of an ideal if not actual machine checkability. You end up using a finite alphabet of symbols when talking about towers of differing uncountable infinities. — jas0n
Group theory comes to mind. Its theorems apply to any system which satisfies certain criteria (intuitively I like to think of finite groups as sets of permutations.) — jas0n
Thus you can see that if this is the Saussure that informs Derrida's own further rewriting of what Saussureanism ought to mean, then yeah, just give it the flick. Start again with Peircean semiosis. — apokrisis
Peirce and other systems thinkers protest that reality at the fine grain is naked fluctuation. There is no certainty as a base, just the continuous blur that is the vagueness of an uncertainty. — apokrisis
Saussure had different priorities ? Shows his age? Note that he thought in terms of 'form not substance' on both sides.. The phonic 'image' is something like an equivalence class of actual pronunciations. It's not sound. — jas0n
All that matters is the difference between them. This difference is unheard. Each signifier is 'essentially' the negation of all the others. — jas0n
Yep. That is how I would argue it. — apokrisis
the switch is the Procrustean bed that forces such a division on the world. — apokrisis
Language - verbal or numerical - reduces the analog reality to a digital recording. But hey, digital recordings can be as good as the real thing for all practical purposes. And they can be better if you don't like the scratching and hissing of vinyl, or you want the most compressed recording possible. — apokrisis
But recall that Derrida criticized Saussure in his own terms, praised Peirce, and showed how the dyadic sign broke down, connecting Saussure's 'phonocentrism' to one of the oldest prejudices of philosophy. — jas0n
I understand Derrida to call out the play/ambiguity of our signs. Since they primarily refer to one another (describe the blur of reality with a set of finite switch-positions like mind/matter or male/female), they aren't grounded in anything but our flexible reapplication of an old sign in a new context. This allows for drift. I read him with Wittgenstein, as a linguistic philosopher I suppose. — jas0n
You are managing to make Derrida seem like a reasonable guy. The question is what kind of sociology would encourage the torture of the accepted PoMo academic style? — apokrisis
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