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.

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.

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)

Hello everybody, first post in the forum! (Be kind :) ) Thinking about the top post, I believe there should be a distinction between what I think they call the minimal self, the sense of unity of the self of a single moment and the diachronic self, that persists through time and has some kind of identity.

From what I understand most people accept the unity of the minimal self as something that is real, that it is built on neurobiological processes and that it is embodied. These processes produce the experience of self (sense of agency, sense of ownership, the immunity principle of self and the non-conceptual first-person content of self). There are some who deny this unity (no-self theories) and I think they support that the sense of self is a set of symbols that appear and disappear in random ways. To be honest I do not find these no-self theories convincing, because, as the critics of these theories say, if it is random then it should not be always present in me (or maybe some moments I should have 2 or even more selves in me) and it should not be present in every person out there.

The continuity-identity of self on the other hand, is much more controversial and this is probably the one that is considered an illusion. Those that support this illusion claim, I think mainly say that a) there is no part of the mental states that constitute the minimal self that remains unchanged through time, so there is no core that is “saved” to form the identity of self (something that would remain constant, could be the physical manifestation of self) and b) any causal relation between changing states is not sufficient to form a diachronic identity (one way I understand it is that my last moment being alive is causing my first moment being dead, but the self is not there any more, so causality does not save the self. There are also the Parfit examples.)

But if the diachronic self is an illusion, there are two possibilities, that this illusion is constructed randomly or that there is a neuronal mechanism that produces it. If it is random, shouldn’t we get exceptions? Moments when I lose myself or find multiple “my selves”? How something random can be so catholic in the population? If on the other hand is based on a mechanism (neuronal process), why not say that this process (whatever might actually do) is the basis of self?

Finally, I would like to point out that we are talking about the illusion of self, then we are talking about the illusion of free will and then we are talking about the illusion of the subjectivity of consciousness. I would say, once it is luck, twice a coincidence, three times a patern. Three phenomena not completely unrelated that we are called to basically disregard them as fake and irrelevant. Maybe, the simplest answer could be to acknowledge that we simply don’t understand them yet.