I'm not sure I follow what you are suggesting here. Yes, sometimes folk make invalid inference, or fail make valid inference. But in order to recognise this, we must understand the distinction between valid and invalid inference.The challenge I see that presenting are that people can believe statements that block applications of inference rules, or otherwise not believe in appropriate inference rules. Even when two people share the theorems of the underlying logic... You just have to hope that every person innately believes every theorem. — fdrake
It might but I don't see that it does - those unbound variables make it hard to see what is going on here. But (Pa→Qa) does not allow (∀x (Px → Qx))... You've lost me.(P(x)=>Q(x) where x is arbitrary lets you derive (for all x P( x ) => Q( x ) ), and they can'd do that). — fdrake
It might but I don't see that it does - those unbound variables make it hard to see what is going on here. But (Pa→Qa) does not allow (∀x (Px → Qx))... You've lost me. — Banno
In order to recognise a failure of translation, you must understand what success would look like. — Banno
Hang on.You can introduce the quantifier onto (Pa->Qa) to get (for all x P(x)->Q(x) ) if you made no assumptions about a anywhere in your reasoning. — fdrake
Well, that's what I'm asking, by way of answering this:How does translation play into it here? — fdrake
I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation.The challenge I see that presenting is that people can believe statements that block applications of inference rules, or otherwise not believe in appropriate inference rules. Even when two people share the theorems of the underlying logic... You just have to hope that every person innately believes every theorem. If they don't use the quantifiers in the same way, they don't have the same intensions over people. — fdrake
And my answer remains, perhaps they are talking about different domains.How would you account for people's differences in use? — fdrake
"epistemology is like chess" (↪Janus). — Leontiskos
I think we can only know what experience, and reflection on the nature of experience tells us. We can also elaborate and extrapolate from formal rule-based systems like logic, mathematics, chess, Go etc. — Janus
I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation — Banno
I'm still wanting an example of where quantifier variation is not also domain variation. I don't think it can be done - quantifier variation just is domain variation — Banno
fdrake has been consistently talking about intensional differences in quantifiers, namely by way of introduction and elimination rules for quantifiers. — Leontiskos
If our domain is {a,b,c} then "U(x)fx" is just "fa & fb & fc"; and "∃(x)fx" is just "fa v fb v fc". — Banno
Seems to me that such equivocation is still about the domain. I think I showed that , above. Can you show otherwise? — Banno
Can you set out why or how the analogy does not work? In what salient way is logic not a game of stipulation? — Banno
Why doesn't it matter how you quantify or which logic you use? Isn't that of the utmost import? That there are multiple logics does not imply that they are all of equal utility or applicability. Propositional logic will be of little help with modal issues, and modal logic might be overkill for propositional problems. Some art is involved in the selection of a logic to use. — Banno
namely by way of differing introduction and elimination rules — Leontiskos
Is that bafflement gesturing toward incommensurability? — fdrake
I'm of the opinion that there is something substantive here to talk about. — fdrake
Their treatment of quantifiers is straightforwardly functionalist and unobjectionable — Srap Tasmaner
Particularly, in PI Wittgenstein is equivocal about use defining meaning in all cases. "For a large class of cases of the employment of the word ‘meaning’ — though not for all— this word can be explained in this way: the meaning of a word is its use in the language” (Philosophical Investigations 43, emphasis mine). — Count Timothy von Icarus
“If I had to say what is the main mistake made by philosophers of the present generation, including Moore, I would say that it is that when language is looked at, what is looked at is a form of words and not the use made of the form of words” (Wittgenstein)
Philosophical problems do not arise in ordinary life precisely because there we use language rather than stopping to study it. Besides Wittgenstein’s qualification (“for a large class of cases—though not for all”), G. E. M. rendering of the oft-quoted section 43 of the Investigations distorts his sentence by translating erklären as “define” rather than “explain” or “clarify.” Although a word’s meaning cannot be simply equated with its use, which would be the kind of debatable theory Wittgenstein says he isn’t proposing, we can only investigate its meaning from how it is used and what it is used for, just as we can only understand chess by watching it being played rather than staring at the queen under a microscope.(Lee Braver)
just as we can only understand chess by watching it being played rather than staring at the queen under a microscope
Sorry. Eli Hirsch and Jared Warren, Quantifier Variance. — Srap Tasmaner
But notice this: every serious theory of the world that anyone has ever considered employs a quantificational apparatus, from physics to mathematics to the social sciences to folk theories. Quantification is as indispensable as it gets. This is defeasible reason to think that we’re onto something, that quantificational structure is part of the objective structure of the world, just as the success of spacetime physics gives us reason to believe in objective spacetime structure.55 Questions framed in indispensable vocabulary are substantive; quantifiers are indispensable; ontology is framed using quantifiers; so ontology is substantive.
If you remain unconvinced and skeptical of ontology, what are your options?
First, you could reject the notion of objective structure altogether. I regard that as unthinkable.
Second, you could reject the idea of structure as applied to logic. I regard that as unmotivated.
Third, and more plausibly, you could accept the idea of structure as applied to logic, but deny that there is distinguished quantificational structure in particular. This is in effect quantifier variance, but there are some interesting subcases. . . — Sider, Ontological Realism, pp. 37-8
You haven't interacted with any of this. — Leontiskos
I think this is the first time that paper has been quoted in this thread. — Leontiskos
and logic...In what salient way is logic like chess? Why would we assume such a thing? Chess is just a made-up game we created to have some fun and amusement. — Leontiskos
I think this it he first time that paper has been quoted in this thread. — Leontiskos
I seriously doubt it. QV seems to be the love-child of incommensurability and a bizarre over-promotion of the principle of charity. I don't know why I'm even posting, it's so stupid. — Srap Tasmaner
FWIW, here first, which happens to be a post of mine you responded to, but I quoted it in the section responding to Banno, so understandable that you missed it. — Srap Tasmaner
So you haven't been reading my posts. Fine. — Banno
It is a fact that not everyone in every context means the same thing by "all" or by "some". But this is nowhere near the sort of variance our heroes are promoting, in my limited understanding. — Srap Tasmaner
that is, "...for arbitrary a..." just is "for any a you might pick", or "for any a" - it's introducing a quantifier. — Banno
How would you account for people's differences in use? — fdrake
Although a word’s meaning cannot be simply equated with its use, which would be the kind of debatable theory Wittgenstein says he isn’t proposing, we can only investigate its meaning from how it is used and what it is used for, just as we can only understand chess by watching it being played rather than staring at the queen under a microscope.
Do you mean this?
Pressing the chess analogy further, the third is as if a child marvelled at the fact that one bishop always stayed on the red, and one on the white, and supposed this to be "a principle at work in the world" or perhaps posited some transcendent force that makes it so, rather than seeing a consequence of the rules.
Can we list them? We have the is of predication: the cat is black; the is of quantification: there is a black cat; and the is of equality: The cat named Tiddles is the cat named Jack.
There might be more. First order logic at least allows us to differentiate these three.
Yeah, I like it, it's a bit divergent, but on topic. "Any particular man is mortal" introduces a quantifier almost obliquely. In first order logic it would be parsed "For all x, if x is a man then x is mortal", but now I am wondering if there might be an alternate parsing in some alternate logic. — Banno
At least in other games, in order to avoiding even implicit metagaming in group play, there can sometimes be requirements for draws too so that players don't accept draws easily due to both being sure to advance on a draw. — Count Timothy von Icarus
Now, the "examination of the queen," might actually have a role in the explanation of language. Here we might substitute the queen for "the human sensory system, psychology, neuronal structures/signaling, etc." That is, the properties of our "pieces," will tend to explain part of how language emerges and has the structure it does. But you can't focus just on this. This is what I was talking about before when I said it would be strange if information theory didn't shed some light on language, or human communication in general, but it also doesn't seem like it could possibly adequately explain everything. — Count Timothy von Icarus
I think the formalisations are thus red herrings in the discussion regarding quantifier variance. Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology! — fdrake
Quantier variance: There is a class, C , containing many inferentially adequate candidate meanings, including two that we may call existencePVI and existenceDKL. PVI’s claims are true when ‘exists’ means existencePVI and DKL’s claims are true when ‘exists’ means existenceDKL. (Similarly, other views about composite material objects come out true under other members of C .) Further, no member of C carves the world at the joints better than the rest, and no other candidate meaning carves the world at the joints as well as any member of C —either because there is no such notion of carving at the joints that applies to candidate meanings, or because there is such a notion and C is maximal with respect to it. — Sider, Ontological Realism, p. 11
After thinking on it, it seems not to be a possibility.Never seen one. — fdrake
Indeed, since Universal Generalisation is taken as granted in first order logic. The formalisation is trivial.But you do so in natural language. So you don't care about the underlying formal logic. — fdrake
Formal logic can serve to clarify usage in natural languages. The primary case being how first order logic sets out and separates the three uses of "is" - predication, quantification and equivalence.Since if even mathematical reasoning has both ambiguity and commonality regarding the underlying logic and its quantifier introduction rules, why would we expect logic to behave as more than a prop, crutch or model of quantification in natural language? Never mind ontology! — fdrake
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