Can you take another run at this? This says that to explain the relationship between tokens we will generally have recourse to something that does not itself explain the relationship. The only sense I can make of that is that objects don't talk, people do. — Srap Tasmaner
What would you say about the ontology of abstract objects? Why is math a valuable tool for describing the world? — frank
I strongly disagree with this statement. I actually think the opposite is true: by paying attention to the history of mathematical concepts, we see that they emerged not because we "made it just so", but were rather forced on us by the nature of the entities in question and the problems surrounding them. To my mind, mathematical entities form natural kinds, and the most fruitful mathematical definitions (such as continuity) capture the structure of those kinds.
But in the example at hand, you're grounding the type-token relation on the intention of the speaker/writer to use the relevant type. — Nagase
A more prosaic example may be the following: x is soluble iff if x is put into water, then x dissolves (this is a very rough characterization of solubility---a more exact approach would need to use counterfactuals and ceteris paribus clauses, but bear with me for the moment). The property of being soluble is not an atomic property, but a complex one, since it is structured. My point is: Jumblese cannot capture this internal structure of the property. — Nagase
But isn't this true of any property, even the simplest ones?
The 'internal structure' isn't really 'internal' - it's laid out in patterns of usage and webs of explication. — csalisbury
Another thought I had is substituting the idea of relation for the idea of predication. So, a red apple would be a particular relational complex comprising the apple, the light and the percipient. There would be no universal predicate redness unifying all the different red apples, but merely a set of "family resemblances" or relations.
You both may very well be right, I'm not sure, but I don't understand the connection between this statement and predication as relation. The way you formatted the post suggests they're related, but I'm missing something. If anything, your discussion of predication-qua-relation seems anti-universals.I agree with @Nagasse in that I don't believe any form of nominalism can provide an adequate solution.
I've been thinking about the difference between 'atomic' properties versus 'complex' ones. — csalisbury
The 'internal structure' isn't really 'internal' - it's laid out in patterns of usage and webs of explication. — csalisbury
An atom already has to explain why it endures in "uncuttable" forever fashion. — apo
My feeling is that when people naively resort to atomism, the whole maximally-located, maximally-durable thing is exactly what they mean by 'simple'. — csalisbury
I mean any term, right, has to include its opposite and differentiate itself from it. — csalisbury
The spirit driving the search for the simple, I think, is one that sees anything less-than-maximally located or less-than-maximally-enduring as relying on things that are maximally-located, maximally-enduring. It says this (everything) comes from that. — csalisbury
So, for instance, the whole Pierce triadic thing. Does it have to explain itself or not? and, if not, why not? It just is? — csalisbury
But what stops me from saying this procedure is as infected, at heart, as the atomist thing? — csalisbury
It wants to find the base of everything - then it thought a while and said, well, not the base, but the engine. — csalisbury
When we say 'the apple is red' we don't mean 'the apple is red to me.' If Tom, god bless him, were to see the apple, he'd see red as well. But we also don't mean by 'the apple is red' 'the apple is red to tom and me'. — csalisbury
Hmmm. You seem to me working your way up to "The apple is red to speakers of English,"... — Srap Tasmaner
The achievement of a Peircean approach is to do the most to minimise this aspect of the Cosmic mystery — apo
Not if you just assert that the apple is red to speakers with a shared neurology. No need to take things to the Whorfian extreme on colour perception. — apokrisis
The thing I really wanted to focus on was the "has to explain" part. As in "An atom already has to explain why it endures in "uncuttable" forever fashion." — csalisbury
So we can easily trip up the atomists by saying that their search for an explanation failed by their own lights - they stopped too soon, and without realizing that they were being false to their own, implicit, ontological/methodological directives. — csalisbury
When you talk about Peirce, it seems like you're talking about the terminal state of a certain way of looking at things. It seems quite refined, and finished. But why should I think this represents a core metaphysical truth rather than a completed way of thinking about the world? The final formalization of 'explanation' maybe. — csalisbury
That's a sad achievement though, isn't it? Why would that minimisation be an 'achievement'? What's left, after that achievement? But to trumpet the achievement? louder at first, then softer. But trumpeting nonetheless. because there's nothing left anymore, but to.... — csalisbury
So my reasonable sentence above ("This is red to speakers of English") turns out to be an explanation of how the word "red" is used, not an explanation of how perception works. — Srap Tasmaner
tldr: if you have a peircian hammer, everything looks like a perician nail — csalisbury
And the actual story is that both levels of semiosis are constraints on our habits of interpretance. — apokrisis
So if we say speakers of a shared language with a shared neurology — apokrisis
Isn't terminal the new foundational here? And the reason I see Peirce as metaphysically complete is the ontology is the epistemology. He started with the logic, the reasoning method, that makes the world intelligible to us. And then realised that the same logic was what made the Cosmos intelligible to itself - the way it developed its own rational state of being.
So it is an epistemology that works as that is how the ontology itself works. And we "know" that because modelling the reality that way is what works.
Isn't terminal the new foundational here?
If I say - as part of my univocal metaphysics - that certainty only asymptotically approaches its limits - then you say, well, that ain't good enough for you. The glass that is 99.999...% full is, gulp, sad.
Your view. My view was formed by encountering the fundamental problems of neurocognition and philosophy of mind, then finding Peirce sorted out the epistemology/ontology for life and mind in general. And for 20 years, biosemiosis has been roaring away.
So if we must do battle by cheap metaphor, why not say Peirce is the key that unlocks every door, or the language that expresses every thought? Who said rhetoric was dead.
The full version is: "If you don't know that's red, either you don't speak English or there's something wrong with you." — Srap Tasmaner
There's a difference, though, between works-because-it-establishes-some-relation-with-the-outside and works-because-it-totally-captures-the-outside. — csalisbury
Does he or does he not edge the fragments of the world he experiences toward this or that aspect of his solitude-won system? — csalisbury
It was more like: its sad to drink alone, at the end of the world. — csalisbury
I don't want to drag you into tawdry battles you'd normally avoid, but these kinds of metaphors....How do we fold peirce upon himself, in order to talk about unlocking everything or expressing everything through reference to one thing? — csalisbury
Are transfinite cardinals or ordinals natural kinds? Are categories natural kinds? What about partially ordered sets or finite fields? — fdrake
I prefer to read it as the evolution of a concept whose boundaries are fuzzy - something like a composite of continuity/differentiability/IVP - becoming more demarcated when the level of mathematical precision was elevated through the emphasis on axiomatisation. I don't see what insisting that mathematical objects are real does to help someone actually doing/teaching maths (the community thereof + history is where mathematics comes from). — fdrake
If the questions is 'what makes the tokens stick together in the type' - why isn't 'they're used together with some commonalities between them' a sufficient answer? Something like 'I see red' and 'I see red', if there's an underlying redness it better also reference anger; 'red' is a lot more complicated than 'redness' in the colour. Where do you get the ontological or epistemic resources to glue tokens together relationally? Also, how's this furnished through there being an abstract object or natural kind to save us and instantiate itself? — fdrake
Another aside, I'd be quite surprised if there wasn't an equivalence relation approach to tokens and types here, in terms of exemplifications. Like in the construction of fractions. 2=1+1=4/2=...(every other possible expression for 2), then the number 2 is defined as [2], that set of expressions which evaluate to 2. And arithmetic is defined in terms of operations on equivalence classes rather than on their constituent terms (this is why algebraic substitution works). Thus simultaneously every object exemplifies the type. — fdrake
Not the intention, the fact of it being asserted to be so (and not: 'the fact of it being asserted to be so'). — StreetlightX
I need to respond to this in more depth in a bit, but I don't see why this would pose any problem, in principle, to a treatment in terms of metalinguistic illustration: there is a way of speaking about an x, such that, when the thing so designated an x dissolves in water, we call x soluble. And to learn this way of speaking, is to understand just that language game involving certain rule-governed correlations between linguistic and non-linguistic objects. — StreetlightX
In other words: Any property is susceptible of being indicated through a simple notation, and any property also harbors a complexity which comes out in explication and usage (I think that's the significance of the 'myth of the given' - things aren't simply 'given' because to know what something is requires having some minimal ability to explicate) — csalisbury
I'd say that yes, those are examples of natural kinds. As Frege would say, they have all passed the "acid test" of concepts, namely their fruitfulness.
I have the opposite idea. I think the semantics of mathematical kind terms is very similar to the semantics Kripke-Putnam sketched for scientific natural kind terms, in the sense that mathematical kind terms are (primarily) non-descriptive, i.e. their semantic value is their reference. That is why we can say that Euler and Cauchy were mistaken in (e.g.) treating convergence as uniform convergence (yes, I'm aware that the historical debate here is controversial). So, according to my story, it's not that we started with fuzzy, open-texture concepts and proceeded to precisify them; rather, we started with a collection of examples and proceeded to unveil their structure. Of course, this story needs to fleshed out, and fleshing it out is one of the projects on which I'm currently working
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