a distinction that I can't make sense of — Banno

So much the worse for the ‘linguistic turn’ in analytic philosophy. Ontology concerns bigger questions, although like metaphysics it’s often regarded as obsolete in the academy.

Ontology is choosing between languages. It consist in no more than stipulating the domain, the nouns of the language. — Banno

Oh my God! Save this poor lost soul.

Ontology concerns bigger questions — Wayfarer

So you have said. But what they might be, apart from hand waving, remains obscure. And not so germane to this conversation.

Hand-waving to you might be sign language to someone else. ;-)

It brings out the conflict in my own arguments, between Midgley and Davidson, and provides something of a logical frame for that discussion. No small topic. — Banno

Have you got a reference to Midgley and Davidson? Is there an interesting professional discussion of these issues?

Davidson is just the ubiquitous On the very idea of a conceptual scheme. The argument presented there is that languages are translatable, an argument against relativism. Plenty of threads on that topic in the forum.

Midgley has it that there is a difference between various ways we talk about the world, especially between scientific and moral or intentional language. In various of her later books.

There's a prima facie disagreement here, but I think it is on the surface only, that Midgley is espousing something not too dissimilar to Davidson's anomalism of the mental.

This is mostly a problem for consistency in my own accounts, not something of direct relevance here.

But see the thread mentioned here:

I started a thread here a while back that might be of interest. — J

Davidson is just the ubiquitous On the very idea of a conceptual scheme. — Banno

Not ubiquitous to me, I'm a philosophical dummy. I'll Google around.

There's a prima facie disagreement here, but I think it is on the surface only, that Midgley is espousing something not too dissimilar to Davidson's anomalism of the mental. — Banno

I'm way out of my depth. I will do some surfing and maybe glean some clues.

A quick Google search yielded:

What is Davidson's summary of the very idea of a conceptual scheme?

Davidson attacks the intelligibility of conceptual relativism, i.e. of truth relative to a conceptual scheme. He defines the notion of a conceptual scheme as something ordering, organizing, and rendering intelligible empirical content, and calls the position that employs both notions scheme‐content dualism.

and my eyes glazed over. I'll check out the thread you linked. Thanks for the pointers.

Ok. See also 's other thread. And had one, too.

Ok. See also ↪J 's other thread. — Banno

Thanks much.

↪J Oh, that thread dropped off my list. I didn't see your last reply. Still the most annoying question on the forums. — Banno

Do I get a prize? :halo:

↪Wayfarer's is not just a "terminological question". It's (potentially) a choice between grammars, between languages. Which implies quantifier variance. Which I think we (you and I) are inclined here to deny. — Banno

You're right, the question expands beyond terminology to language itself. I was trying to keep it snappy. As for QV, I'm still plumbing the depths of the arguments. Though yes, at this point I'm inclined to deny it, or at least doubt it strongly, for Siderian reasons (see that other OP).

I red all the posts and as I am biologist I cannot say that I understand all the points you made but I have a question that I think is relevant. From the neuroscience point of view, what we describe as ideas or thoughts are specific structures of neuronic cells that fire consecutive action potentials. These active structures of neurons are the idea I have, the sensation I feel, the word I am thinking. Along the same line of thought, a number (and any other mathematical entity) is a set of neurons that form a specific structure in my brain. This structure consists of mater, exists in space and time and forms physical relations with other similar structures (corresponding to other mathematical entities in my brain) following the usual physical laws. We could assume that this material structure is all that is needed to produce all the properties of this mathematical entity.
If this description is accurate, could this result in a mathematical realism that is not platonic but physicalistic? (and in this way retaining the correspondence between mathematics and the physical world, without resorting to a weird abstract entity)

Do I get a prize? :halo: — J

Respect.

Along the same line of thought, a number (and any other mathematical entity) is a set of neurons that form a specific structure in my brain. — bioByron

There's a real problem with this view. If "seven" is a structure in your brain, then your "seven" is not the same as my "seven", which would be a distinct structure in my brain.

But when we each say seven is one more than six, we both mean the same thing.

Hence we must conclude that "seven" is not just a structure in your brain. Rather, it is in some way common to both you and I.

Plato answered this problem by positing a world of forms in which we both share. I think there are better answers, to do with how we use words.

If this description is accurate, could this result in a mathematical realism that is not platonic but physicalistic? — bioByron

Psychologism states that mathematical entities are constructions of the human mind. Under a physicalist reductive program for psychologism, I guess it could be defined as mathematical realism. Psychologism is typically classified as anti-realist, so it becomes a matter of semantics whether we want to classify this mathematical reductivism as realist or not.

The objection that the sevens are different between people is unproven and if proven, how exactly that is a problem is still unexplained.

For an actually physicalist ontology of mathematics, see immanent realism.

There's a real problem with this view. If "seven" is a structure in your brain, then your "seven" is not the same as my "seven", which would be a distinct structure in my brain. — Banno

You are right that it is impossible that the cells in my brain, that form “seven”, be identical with the cells in your brain that form your “seven”, but that is not necessary for the idea to work. “Seven” is what it is because of the relations that it has with the other mental states – numbers – mathematical entities. And even if every such entity is different as a neuronic structure in our different brains, the relations between them are the same. They are the same because we have taken a great effort through 12 or more years of education (involving exercises and tests and grades) to make sure that they are exactly the same.

For an actually physicalist ontology of mathematics, see immanent realism. — Lionino

What troubles me with immanent realism is that it suggests that universals are independent of the mind and my “seven” is a real object (from materials existing in space and time) inside my brain. The only difference between my “seven” and the table in front of my is that I have much more control over the entity inside my brain than the entity in front of me.

my “seven” is a real object (from materials existing in space and time) inside my brain — bioByron

In connection with numbers, one strategy is to take numbers to be universals of some sort — e.g., one might take them to be properties of piles of physical objects, so that, for instance, the number 3 would be a property of, e.g., a pile of three books — and to take an immanent realist view of universals. (This sort of view has been defended by Armstrong (1978).) But views of this kind have not been very influential in the philosophy of mathematics. A more prominent strategy for taking number talk to be about the physical world is to take it to be about actual piles of physical objects, rather than properties of piles. Thus, for instance, one might maintain that to say that 2 + 3 = 5 is not really to say something about specific entities (numbers); rather, it is to say that whenever we push a pile of two objects together with a pile of three objects, we will wind up with a pile of five objects — or something along these lines. Thus, on this view, arithmetic is just a very general natural science.

so that, for instance, the number 3 would be a property of, e.g., a pile of three books — and to take an immanent realist view of universals. (This sort of view has been defended by Armstrong (1978).)

Exactly here is my objection. My “seven” in not a property of some pile of seven objects (and hence something out of mind as the pile of odjects are what exists in my mind), it is an object in itself, with its own “properties” (= relations with other objects) for example it is the half of the object “14” or it is bigger that the object “three”.

to say that 2 + 3 = 5 is not really to say something about specific entities (numbers); rather, it is to say that whenever we push a pile of two objects together with a pile of three objects, we will wind up with a pile of five objects

This could perhaps be the way we start forming these odjects-numbers when we are children. We don’t think of seven independently, but we think of seven pencils or seven fingers. But eventually, I think the number becomes independent of piles, so that view fails to describe what a number is in the end.

(1) Formalism comes in variations, many of which are not the view that mathematics is only a symbol game. Indeed, Hilbert himself stressed that mathematics has a contentual part.

(2) Formalism is compatible with the method of models and its correspondence evaluation of truth. Indeed, consider Tarski himself. Moreover, consider mathematicians such as Abraham Robinson and Paul Cohen whose work is steeped in the method of models.

(3) Philosophy of mathematics includes a panoply of approaches and is not best characterized as a choice between between formalism and realism.

(4) Perhaps Hilbert denied that mathematical objects exist independently, but if he did, I would be interested to see a cite. Of course, Hilbert emphasized the difference between finitistic/contentual mathematics and infinitistic/ideal mathematics, but that does not, at least in and of itself, preclude that mathematical objects exist independently.

(5) This was addressed, but to stress: Using the method of models is not inconsistent with the symbol game view of mathematics, as models themselves may be taken per formalizations in the meta theories. Along with this, it is not required that the set of natural numbers be taken as existing independently of a formal theory that proves the theorems that there exist natural numbers and the set of them.

(6) This was addressed, but to stress: It is a salient result of model theory that PA does not define - not even within isomorphism, not even within equinumerousness - the system of natural numbers.