..and that involves two minds.

In any case, ‘mind’ is kind of a collective noun; when we say ‘the mind’ we’re assuming were saying something that is applicable to all minds, the ‘law of identity’ being one of those.

SO the concept two involves multiple minds?

Does it also involve multiple things?

SO the concept two involves multiple minds? — Banno

Certainly not. The whole point of the example of number, is that numbers are indeed the same for any mind capable of counting. That is why quantification is at the heart of objective science - there's no room for equivocation, it's not a matter of 'more or less' or 'like or dislike'.

Anyway the remark you commented on 'the number two exists as an abstraction of the mind' is perfectly normal English, as it is commonplace to speak of what the mind does. The mind boggles! The mind shrinks from such a conclusion. And so on.

"the mind"? Singular?

That strikes me as odd. — Banno

How so, I'm not following you here.

Certainly not. The whole point of the example of number, is that numbers are indeed the same for any mind capable of counting. — Wayfarer

Hang on - numbers need to be the same for any mind, but the concept does not require multiple minds?

You know where I'm headed: the concept is the application.

I just something off about the conception of 'multiplicity of minds'. Compare it to water - there are many bodies of water, and different forms of water - ice, liquid and vapour - but there are not 'many waters'.

I do get the 'concept is the application' but really that's just a way for your modern 'plain English' philosophers to avoid the whole can of worms of the ontology of abstracts. As soon as you open that can, then you're doing metaphysics, which is the one thing they are most keen on avoiding.

the ontology of abstracts. — Wayfarer

A can of worms, alright. The notion of an ontology of abstracts is oxymoronic. Wanting to avoid absurdity is worthy.

But what if it only appears absurd, because philosophers have lost the ability to make sense of it. And that goes right back to the debates between realism and nominalism in the middle ages. Because the nominalists were the antecedents of much of today's empiricism, which is hugely influential, then sure, from their point of view, then the notion of the reality of abstracta is absurd. It's a case of 'history being written by the victors'. But that inability is a deficiency on their part, in my opinion.

Like Macbeth, Western man made an evil decision, which has become the efficient and final cause of other evil decisions. Have we forgotten our encounter with the witches on the heath? It occurred in the late fourteenth century, and what the witches said to the protagonist of this drama was that man could realize himself more fully if he would only abandon his belief in the existence of transcendentals. The powers of darkness were working subtly, as always, and they couched this proposition in the seemingly innocent form of an attack upon universals. The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.

Richard Weaver, Ideas Have Consequences

C. S. Peirce understood nominalism in the broad anti-realist sense usually attributed to William of Ockham, as the view that reality consists exclusively of concrete particulars and that universality and generality have to do only with names and their significations. This view relegates properties, abstract entities, kinds, relations, laws of nature, and so on, to a conceptual existence at most. Peirce believed nominalism (including what he referred to as "the daughters of nominalism": sensationalism, phenomenalism, individualism, and materialism) to be seriously flawed and a great threat to the advancement of science and civilization.

Review of Pierce and the Threat of Nominalism. His warning, however, fell mainly on deaf ears.

Yep, nominalism is one of those absurd metaphysical extravagances beloved of those who like to warn against absurd metaphysical extravagances.

Broad sweeps make for an interesting narrative, but at the expense of accuracy.

Which comes first - even for us pragmatists. The big ideas or the nit-picking?

One can say that the number two exists as an abstraction of the mind. — Posty McPostface

Two is a part of the activity of counting, and thence maths. But is it correct to say it exists?

Perhaps it would be better to think of numbers as a grammar. We can (perhaps) see that it is unclear what it might mean to say that "the", "and", "is" and so on - the connectives of some language - exist.

TO be sure there are uses for these words, so it's not that they do not exist - but they are not the sort of thing that can be placed in a straight forward fashion into an existential quantifier.

That is, it is not clear what we might mean by saying that the number exists as such-and-such.

So,

intelligible objects are tantamount to saying that they exist independently of particular.
— Posty McPostface

They exist independently of particular minds, but are nevertheless only perceptible to a rational intellect. — Wayfarer

might be taking existence further than we ought.

Yeah, I don't subscribe to nominalaism, either in pure form or that of the TLP. It doesn't jive with how we use language in reality.

It might be taking existence further than we ought. — Banno

Exactly the kind of point I’m trying to make. Many things - using the word 'things' a bit loosely - such as numbers, grammatical rules, and so on, are indubitably real, but they don't exist in the sense that phenomena do.

In other words, they're real as the constituents of thought and reason. But as rational and language-using beings, they're the means by which we make the world navigable. We do this instinctively from a young age - in fact a large part of learning, is learning to do just that - but we also do it collectively, as the net sum of knowledge of the world expands.

So my basic argument is that these kinds of things (or entities or whatever) are as real as the objects of perception, but of a different order or 'domain'. There have been several recent philosophers who hold such a view: Frege ('the third realm'), Popper, Godel, and several others. But the issue is that this attitude is generally speaking identified with platonism (lower case) and so is inimical to philosophical materialism:

Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects.

SEP. There's another article on Internet Encyclopedia of Philosophy that contains this gem:

Some philosophers, called "rationalists", claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

In other words, the reality of abstracta, if established, undermines materialism. And that's why most of your plain-language philosophers won't have a bar of it, although they won't necessarily put it in those terms. Instead, they'll talk about 'language as use', thereby hoping to sidestep the whole issue.

In other words, the reality of abstracta, if established, undermines materialism. And that's why most of your plain-language philosophers won't have a bar of it, although they won't necessarily put it in those terms. Instead, they'll talk about 'language as use', thereby hoping to sidestep the whole issue. — Wayfarer

Don't you think the appearance of this forum or this very place, is a metaphysical construct enabled by the very logically of computers? This gives me the impression that the simulated reality hypothesis isn't as farfetched as it sounds or that we could simulate reality some day.

But as rational and language-using beings, they're the means by which we make the world navigable. — Wayfarer

Here we agree.

So my basic argument is that these kinds of things (or entities or whatever) are as real as the objects of perception, but of a different order or 'domain'. — Wayfarer

And this is were we might differ. When we say there are connectives and numbers and universals, we are saying no more than that this sort of language is used - this game is played. That is, phrase "...as real as..." does nothing.

The way to understand a thing's being real is to look for what that reality is contrasted against. A real coin is not counterfeit. The real Gaddafi is not the imposter. The real mat is not an hallucination.

So what is a real 2 being contrasted against?

Nothing, so far as I can see.

And my conclusion is that the word "real" is being misused here.

Don't you think the appearance of this forum or this very place, is a metaphysical construct enabled by the very logically of computers? — Posty McPostface

I do! I think people overlook this all the time.

And this is where we might differ. When we say there are connectives and numbers and universals, we are saying no more than that this sort of language is used - this game is played. That is, phrase "...as real as..." does nothing. — Banno

But this doesn't allow for the fact that we can discover genuinely new and previously-unknown things through reasoning and mathematics. Those who know maths, know something real that those who don't, don't. There are entire domains like that. And taking that seriously changes your view of what is real - because 'what is real' is no longer just 'what is out there' - the physical cosmos. What is real also includes the reality of transcendentals. That's the thin end of a big wedge. And that's why those articles I mentioned got written - like, some actual philosopher has found it necessary to try and explain away the apparent reality of mathematical objects, because it doesn't fit in to the procrustean bed of 20th century materialism. And because there's a big investment in that view, nobody will argue; look at the way philosophers who argue against materialism are treated.

So what is a real 2 being contrasted against? — Banno

And the contrast is actually between the existence of phenomena and the existence of numbers, laws, and so on. So phenomena, generally speaking, are composed of parts, and have a beginning and end in time; in other words, they're compound and temporal. Whereas numbers, while real, do not come into or go out of existence - hence, not temporal - and prime numbers, for example, are not divisible.

Consider how we form abstractions in our mind: it entails a partial consideration of actual objects - contemplating one or more of their properties.

Square objects in the world have squareness (and other properties, including spatio-temporal locations). "Square" has no real world referrent, so squares do not exist in the world.

If God exists, there is a real world referrent for the abstracted properties of God-ness.

I do! I think people overlook this all the time. — Wayfarer

Glad there are other's out there that recognize this fact. I'm using "fact" loosely here, and I don't even know why, heh.

What colour is seven?

I suspect you might agree that this question is not helpful.

I suspect that "Seven is real" is not unlike "Seven is pink". Saying seven is pink is an inappropriate use of words. So is saying seven is real.

But notice that it is not true that seven is not pink - it is not, after all, some other colour. And it is not true that seven is not real.

Square objects in the world have squareness (and other properties, including spatio-temporal lications). "Square" (qua square) has no real world referrent, so squares do not exist in the world. — Relativist

Where's the referent in the sentence, "I like this place."

What colour is seven?

I suspect you might agree that this question is not helpful. — Banno

Not to someone with Grapheme-color synaesthesia! An interesting phenomenon that I think offers a glimpse into the Platonic realm.

Hmph. If they agreed as to the colour of seven.

Hmph. If they agreed as to the colour of seven. — Banno

If I could conduct a survey of people with Grapheme-color synaesthesia, that would be the first question I would ask, if they perceive each color the same.

Others have already done that and found pretty much no correlation.

Hmm, interesting. Do the colors persist over time for each individual or change also depending on the context?

They (usually) persist over time for an individual.

They persist over time for an individual. — Banno

Fascinating stuff, don't you think?