But what does that mean? Is "different" a property an object can have?
Yes, I'm being a little cagey, but you can do better than a shrug. — Srap Tasmaner
Do you mean numbers as abstracted from any particular instantiation if them? — Count Timothy von Icarus
What do you think of the claim that discrete entities only exist as a product of minds? That is, "physics shows us a world that is just a single continuous process, with no truly isolated systems, where everything interacts with everything else, and so discrete things like apples, cars, etc. would exist solely as 'products of the mind/social practices.'" — Count Timothy von Icarus
Yes, and this is an important way that the logic reflects the commitments or intentions of its creators. It is not logic qua logic; it is logic qua mathematics. — Leontiskos
I actually think ↪fdrake's post may be most instructive and fruitful. — Leontiskos
Now if quantifier variance is occurring—superable or insuperable—then the existential quantifier is doing more than presupposing a univocal notion of existence. Or, if you like, the two secretly competing meanings of existential quantification are each “presupposing” a different notion of existence, and this is the cause of the disagreement. Thus arises the very difficult question of how to adjudicate two different notions of existence, and this is the point of mine to which you initially objected. — Leontiskos
What do you think of the claim that discrete entities only exist as a product of minds? That is, "physics shows us a world that is just a single continuous process, with no truly isolated systems, where everything interacts with everything else, and so discrete things like apples, cars, etc. would exist solely as 'products of the mind/social practices.'" — Count Timothy von Icarus
We don't see individual objects in isolation, but as embedded in and different from their surroundings, so difference if not a property of some putative completely isolated object, but a property it displays in its situatedness. — Janus
What do you think of the claim that discrete entities only exist as a product of minds? That is, "physics shows us a world that is just a single continuous process, with no truly isolated systems, where everything interacts with everything else, and so discrete things like apples, cars, etc. would exist solely as 'products of the mind/social practices.'" — Count Timothy von Icarus
Are you not arguing for two kinds of reality—the reality of the body and the different reality of the mind? — Janus
each object is an instantiation of one — Janus
Wouldn't be the first time, but he was addressing the topic, and I have yet to develop an interest in doing that. — Srap Tasmaner
Still agree? — Srap Tasmaner
Do as you like, I just don't see the point. We can talk about existence all we like without dragging quantifiers into it, — Srap Tasmaner
It's a funny thing. This is all Quine's fault, as I noted. "To be is to be the value of a bound variable" comes out as a deflationary slogan, but what we was really arguing for was a particular version of univocity: the idea was that if you quantify over it, you're committed to it existing, and he meant "existing" with the ordinary everyday meaning; what he was arguing against was giving some special twilight status to "theoretical entities". If your model quantifies over quarks, say, then your model says quarks are real things, and it's no good saying they're just artifacts of the model or something. --- The reason this is amusing is that all these decades later the consensus of neuroscientists and cognitive psychologists, so far as I can tell, is that absolutely everything we attribute existence to in the ordinary everyday sense -- medium-sized dry goods included -- is an "artifact of the model" or a "theoretical entity", so the threat to univocity Quine was addressing never actually existed, if only because the everyday meaning of "exist", the one Quine wanted to stick with, is in fact the "twilight" meaning he wanted to tamp down. And so it goes. — Srap Tasmaner
That's the gist, or part of a gist, of my view. — Srap Tasmaner
It is a common view these days — Leontiskos
I don't think logic is inherently mathematical, I don't think "mathematics is good at treating of [everything]," and I don't think mathematical logic is necessarily the epitome of logic. In fact at my university mathematical logic was very much acknowledged to be but one kind of logic, and I think this is correct. — Leontiskos
Aristotle was more interested in representing the way the human mind draws conclusions than adhering to an a priori mathematical paradigm — Leontiskos
this seems to prove the point insofar as Quine's notion of existence (and quantification) differs from the approach of neuroscience — Leontiskos
Is this a property it acquires naturally, along with its chemical composition, its mass, etc?
Or do we deem each object to be an instantiation of One? — Srap Tasmaner
And you don't see any circularity here?
Remember the issue was whether number could be a property of an object, and it just obviously can't unless sets count as objects. It's really straightforward and it pissed Quine off considerably. — Srap Tasmaner
Are you not arguing for two kinds of reality—the reality of the body and the different reality of the mind?
— Janus
Not two kinds but two levels, phenomenal and noumenal - and the role of the mind in synthesizing them to produce a unity. — Wayfarer
By 'existent' I refer to manifest or phenomenal existence. Broadly speaking, this refers to sensable objects (I prefer that spelling as it avoids the equivocation with the other meaning of 'sensible') - tables and chairs, stars and planets, oceans and continents. They're phenomenal in the sense of appearing to subjects as sensable objects or conglomerates.
I am differentiating this from what used to be called 'intelligible objects' - logical principles, numbers, conventions, qualifiers and so on. For example, if I were to say to you, 'show me the law of the excluded middle', you would have to explain it to me. It's not really an 'object' at all in the same sense as the proverbial chair or apple. — Wayfarer
Glad to hear you say that. I'm not innovating here, I think, just trying to connect the dots. — Srap Tasmaner
I get that. I'm using "mathematics" pretty broadly. What I have in mind is the mathematical impulse, the attempt to understand things by schematizing them, abstracting, simplifying, modeling. A musical scale is such an abstraction, for example, and "mathematical" in the sense I mean.
You're right, of course, that as commonly used the phrase "mathematical logic" is just a branch of mathematics, but to me logic is very much a product of the mathematical impulse, as when Aristotle abstracts away the content of arguments and looks only at their form -- and then follows up by classifying those forms! And we end up with the square of opposition, which is a blatantly mathematical structure. You see what I mean, I'm sure. — Srap Tasmaner
But I still say the foundation here is mathematical because with the brain we're really talking about prediction, and thus probability. The brain is a prediction engine that is constantly recalibrating. It instantiates a machine for calculating probabilities. The "following from" here is neural activity, which is messy and complicated, but has effects that are in principle measurable, and whose functioning itself is parametrized (concentration of ions and neurotransmitters, number of incoming connections and their level of excitation, distance to be covered by transmission, and so on). — Srap Tasmaner
But his just thinking that doesn't get you there, to my mind. He was mistaken -- only because he was too early, really... — Srap Tasmaner
You seem to be dragging me into the actual topic... — Srap Tasmaner
Frege was trying to reduce mathematics to logic . . . this isn't necessarily a deformation of logic by focusing on a limited domain, so much as an idealization of logic by focusing on the domain that most cleanly, we might say, represents human thought. And as it happens, I think Frege thought so as well. I think he was mostly of the opinion that natural languages are too much of a mess to do sound work in. — Srap Tasmaner
What's asserted in an existentially quantified formula is not really, say, "Rabbits exist," but the more mundane "Some of the things (at least one) that exist are rabbits." Or "Not all of the things that exist aren't rabbits," etc. — Srap Tasmaner
To take the example of the OP: quantifier meaning is not unconditioned by ontological commitments — Leontiskos
Does QV amount to a claim that no one can be mistaken? — Srap Tasmaner
basic logic is the fundamental tool of everything done in mathematics, absolutely everything -- it's just taken as given at lower levels of learning, without any suggestion that you're actually borrowing from some rarefied advanced field of mathematics. — Srap Tasmaner
Yep An incipient notion. It probably relates to Austin's treatment of abstracts in Are There A Priori ConceptsWith all respect to Banno, the formula "Numbers are something we do" could use some clarification. — J
Austin carefully dismantles this argument, and in the process other transcendental arguments. He points out first that universals are not "something we stumble across", and that they are defined by their relation to particulars. He continues by pointing out that, from the observation that we use "grey" and "circular" as if they were the names of things, it simply does not follow that there is something that is named. In the process he dismisses the notion that "words are essentially proper names", asking "...why, if 'one identical' word is used, must there be 'one identical object' present which it denotes". — Wiki article
I'm going to maintain that the domain, and hence the ontology, one way or another, is stipulated. And see where that leads.So on to ontological pluralism? — J
Knowing what mathematics is seems like one of the biggest philosophical questions out there. Not to mention that a number of major breakthroughs in mathematics have been made while focusing on foundations, so it hardly seems like a useless question to answer either. — Count Timothy von Icarus
Good questions. The property analogy will only go as far as "counts as..." or "as if...". And as I've said, we do treat numbers to quantification, equivalence and predication - all nice neat uses of "is". Numbers are in many ways not like property.Why this huge difference? — Count Timothy von Icarus
Kant's phenomenal/ noumenal distinction as I understand it is not between sense objects and abstracta, but between what we can know and what we cannot. — Janus
The Greek word νοούμενoν, nooúmenon (plural νοούμενα, nooúmena) is the neuter middle-passive present participle of νοεῖν, noeîn, 'to think, to mean', which in turn originates from the word νοῦς, noûs, an Attic contracted form of νόος, nóos, 'perception, understanding, mind'. A rough equivalent in English would be "that which is thought", or "the object of an act of thought".
"in the same way", Frege says "that a pencil exists independently of grasping it. Thought contents (e.g. numerical value) are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." — Frege on Knowing the Third Realm, Tyler Burge
Vedānta (specifically Advaita)... talks of the ātman (self) in similar terms as the noumenon.
and
Regarding the equivalent concepts in Plato, Ted Honderich writes: "Platonic Ideas and Forms are noumena, and phenomena are things displaying themselves to the senses... This dichotomy is the most characteristic feature of Plato's dualism; that noumena and the noumenal world are objects of the highest knowledge, truths, and values is Plato's principal legacy to philosophy."
Kant -- damn his eyes -- was right: we only understand of the world what we put into it.
We distinguish one bit from another, sort those bits and classify them, even paint them different colors to make it easier to keep track of them.
Mathematics is, first of all, our analysis of what we're doing when we do all that. More than that, it's a simplification and idealization of the process, to make it faster and more efficient.
It's all signal processing. The brain is not fundamentally interested in the world, but in the maintenance of the body it's responsible for, and the signals the brain deals with are about that body: they have an origin and and a type and a strength, and so on. Some of this is instrumented, so there's a reflective capacity to see how all these signals come together, and that's the beginning of mathematics. — Srap Tasmaner
In ...Engagement and Metaphysical dissatisfaction, Barry Stroud argues that the project (of metaphysics) cannot be carried out, because we are too immersed in the system of concepts that we hope to subject to metaphysical assessment. This "prevents us from finding enought distance between our conception of the world and the world it is meant to be a conception of to allow for an appropriately impartial metaphysical verdict on the relation between the two."
Stroud believes that we cannot succeed in reaching either a positive (often called realist), or a negative (anti-realist) metaphysical verdict about a number of basic conceptions – that we cannot show either that they succeed in describing the way the world is independent of our responses, or that they fail to do so. He argues for this claim in detail with respect to three of the most fundamental and philosophically contested concepts: causality, essentially, and value. The argument has a general and powerful form. Stroud contends that the use of the very concepts being assessed, and judgements of the very kind being questioned play an indispensable part in the metaphysical reasoning that is supposed to lead to our conclusions about these concepts and beliefs. — Analytical Philosophy and Human Life, Thomas Nagel, p 218
And the conclusion to that section,What all of this illustrates, is that in tying quantification to existence, two distinct roles are ultimately conflated:
(a) The quantificational role specifies whether all objects in the domain of quantification are being quantified over or whether only some objects are.
(b) The ontological role specifies that the objects quantified over exist.
These are fundamentally different roles, which are best kept apart. By distinguishing them and letting quantifiers only implement the quantificational role, one obtains an ontologically neutral quantification. Ontological neutrality applies to both the universal and the particular quantifier (that is, the existential quantifier without any existential, ontological import). — Quantifier Variance Dissolved
However, once again, no variance in any quantifier is involved.
I am planning to take a hiatus from TPF. — Leontiskos
"in the same way", Frege says "that a pencil exists independently of grasping it. Thought contents (e.g. numerical value) are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." — Frege on Knowing the Third Realm, Tyler Burge
Unfortunately I don't have the rhetorical skills to fend of such exalted polemics. And, as always, you declare what you yourself don't understand as the limits to what anyone else would consider. — Wayfarer
Responding to the messiness of natural language, he/we’ve gone on to develop the quantificational apparatus and the ability to speak Logicalese, which really does clear up some of the mess, quite often. But it leaves us with puzzles too, like this one about whether quantifier variance is a coherent idea. — J
This would be the pro-QV position... — J
That is what you see in practice though. There are no modal operators in propositional logic. But both modal and propositional logic are great. Their semantics also differ considerably. When you write the possibility and necessity symbols in a modal logic, you quantify over possible worlds. When you write them in a quantified modal logic, you quantify over worlds, and there's also quantification within worlds in the usual logic way.
Those quantifiers are introduced differently, and as the paper "Quantifier Variance Dissolved" notes that provides a strong argument for a form quantifier variance without a reduction of quantifier meaning to underlying entity type it quantifies over, and without committing yourself to the claim that there's a whole bunch of equally correct logics for the purposes of ontology. — fdrake
I've noticed that if anyone disagrees with you or questions your ideas you fall back on the claim that they don't understand. — Janus
I deal with every interaction on its merits, or lack thereof. — Wayfarer
If you don't want to try, then I'll conclude that you don't have such an argument. — Janus
By 'existent' I refer to manifest or phenomenal existence. Broadly speaking, this refers to sensable objects (I prefer that spelling as it avoids the equivocation with the other meaning of 'sensible') - tables and chairs, stars and planets, oceans and continents. They're phenomenal in the sense of appearing to subjects as sensable objects or conglomerates.
I am differentiating this from what used to be called 'intelligible objects' - logical principles, numbers, conventions, qualifiers and so on. For example, if I were to say to you, 'show me the law of the excluded middle', you would have to explain it to me. It's not really an 'object' at all in the same sense as the proverbial chair or apple. You might point to a glossary entry, but that too comprises the explanation of a concept. The same with all kinds of arithmetical proofs and principles. Even natural laws - the laws of motion, for example. All of these can only be grasped by a rational intelligence. I could not demonstrate or explain them to a cow or a dog. They are what could be described as 'noumenal' in the general (not Kantian) sense, being 'objects of intellect' (nous) - only graspable by a rational mind.
As I said at the outset, in regular speech it is quite clear to say 'the number 7 exists'. But when you ask what it is, then you are not pointing to a sensable object - that is the symbol - but a rational act. (That's the sense in which I mean that 'counting is an act', but it doesn't mean that the demonstrations of rudimentary reasoning in higher animals amounts to reason per se.)
In Plato these levels or kinds of knowledge were distinguished per the Analogy of the Divided Line . Those distinctions are what have been forgotten, abandoned or lost in the intervening millenia due to the dominance of nominalism and empiricism. But In reality, thought itself, the rational mind, operates through a process of synthesis which blends and binds the phenomenal and noumenal into synthetic judgements (per Kant). — Wayfarer
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