Abstractions of the mind

Reply to Posty McPostface Can you find a use for them? Is there a meaning beyond that use?

The answer is the usual pragmatic one. Show that there is any actual mystery here. If we form a concept, it had some application. It was a constraint on possibility which served a purpose.

(Even if that purpose might seem really generic, or really minor.)

Quoting apokrisis

Can you find a use for them? Is there a meaning beyond that use?

Yes, I used the term in the context of numbers and/or God. What more do you want me to say?

Reply to Posty McPostface What was your purpose then?

(Pretty clearly, it was to suggest there might be a "dilemma" worth discussing. So given the familiarity of this debate, were you planning to offer anything new?)

Quoting apokrisis

What was your purpose then?

The purpose was to explore the meaning of the term "abstractions of the mind"? As in the OP, what are they, are they real or just metaphysical?

Quoting Posty McPostface

...are they real or just metaphysical?

...or demonstrably useful?

(Again, is there a good reason to debate realism vs idealism for the billionth time when you have pragmatism as the better choice?)

Quoting apokrisis

...or demonstrably useful?

(Again, is there a good reason to debate realism vs idealism for the billionth time when you have pragmatism as the better choice?)

Then how else would you phrase the issue instead of resorting to terms like "abstractions of the mind"?

Well "maths, numbers" are clearly a useful "abstraction of the mind" concept or universal. Whether numbers "exist" or are "actual" generally tends to be a word or language game.
The concept of God is found useful by many as a way to give higher meaning purpose and value not only to their own lives but to the universe in general.
So for many "abstractions of the mind" are just as real and valuable as physical material entities.

Quoting Posty McPostface

Then how else would you phrase the issue instead of resorting to terms like "abstractions of the mind"?

Conceptions. Habits of sign. "God" and "two" exist as words in a language. And as such, they mediate some pragmatic conceptual relation we might have with the real world.

Now of course you can go on from that to talk about whether they in fact relate us conceptually to the "real world" or just "metaphysically possible worlds", or whatever other kind of world you want to then name.

But that boils down to modality. Two-ness is being conceived of as completely generic - true of all possible worlds (where counting would work). And God is conceived of as completely fictional - not actually true of the actual world ... for the atheist at least.

So semiosis provides the larger encompassing framework already. It subsumes "material realities of the world" and "abstractions of the mind" into an over-arching semiotic relation. It cannot be a simple case of either/or - either God and two physically exists, or else mentally exists. It is already being said that for the words to exist, and be used within a language system, requires that both the mind and the world are "places" where they "exist". The existence is in fact the process which is a relation that works. Something about the world, and something about the mind, must be in fruitful co-ordination.

So God must be a useful fiction when the purpose was the regulation of traditional human societies. Two must be a useful generality once humans started to conceive of the world in terms of mathematical-strength signs.

Of course, there is aways something "out there" - that God-shaped hole to fill in a society seeking to be ruled by less earth-bound rules, that two-shaped identity to be discovered everywhere that counting appears to work.

But also there is always something "in here" - the participant in a language community capable of finding such a habit of interpretance a functional way to operate.

So your OP was setting things up for a false dilemma - something exists either in the world or in the mind. Pragmatism presumes that the existence of that something - the sign: some word that gets regularly used - must speak to a relationship that works. And for that to be the case, it exists as a unity bridging mind and world.

Of course - the next familiar Kantian difficulty - it is the "world" as it is for "us".

So it is the world as the phenomenal or an Umwelt, not the world as the noumenal. And it is us as an emergent modeller, not us as some Cartesian and unphysical res cogitans.

Quoting prothero

Well "maths, numbers" are clearly a useful "abstraction of the mind" concept or universal. Whether numbers "exist" or are "actual" generally tends to be a word or language game.

But, I highlighted the fact that we use "God" and "the number two" as abstractions of the mind. If they exist, then, they exist as abstractions of the mind, and nothing else. So, then what are abstractions of the mind if nothing else than a rigid designator of sorts? I'm sure in a possible world the same abstractions of the mind exist, maybe with different wording; but, that means it's not just generally speaking a language game of sorts.

Quoting apokrisis

"God" and "two" exist as words in a language. And as such, they mediate some pragmatic conceptual relation we might have with the real world.

Or again, they're just abstractions of the mind and nothing else. If they modally exist in other possible worlds, then that presupposes they have some function further than simply being abstractions of the mind. Again, rigid designators of sorts.

Quoting apokrisis

Now of course you can go on from that to talk about whether they in fact relate us conceptually to the "real world" or just "metaphysically possible worlds", or whatever other kind of world you want to then name.

But, that's an important distinction to make, surely?

Quoting apokrisis

But that boils down to modality. Two-ness is being conceived of as completely generic - true of all possible worlds (where counting would work). And God is conceived of as completely fictional - not actually true of the actual world ... for the atheist at least.

So, modally speaking, we have the number two and God being used interchangeably as abstractions of the mind. Hence, they appear real in any possible world.

Quoting apokrisis

So semiosis provides the larger encompassing framework already. It subsumes "material realities of the world" and "abstractions of the mind" into an over-arching semiotic relation. It cannot be a simple case of either/or - either God and two physically exists, or else mentally exists. It is already being said that for the words to exist, and be used within a language system, requires that both the mind and the world are "places" where they "exist". The existence is in fact the process which is a relation that works. Something about the world, and something about the mind, must be in fruitful co-ordination.

I'm not quite getting your gist here. Are you saying that pragmatically, they serve no further utility to use than using a different language game? Again, if they are modally independent of synthetic a priori judgments, then they exist universally.

Quoting apokrisis

Of course - the next familiar Kantian difficulty - it is the "world" as it is for "us".

So it is the world as the phenomenal or an Umwelt, not the world as the noumenal. And it is us as an emergent modeller, not us as some Cartesian and unphysical res cogitans.

You lost me here, care to expand?

Thanks for posting!

Just to harp on Kant. I think, that abstractions of the mind exist in a modal independent sense that makes possible synthetic a priori judgments. It would be the case that two exists as a rigid designator of these modally independent abstractions of the mind, that are possible in every possible world.

Just something to consider in regards to the topic.

My first forum post, way back, was about the reality of number. I argued that numbers are real on the basis that they are the same for anyone who can count, and also because they make actual predictions; to put it another way, because you can be wrong about them, then they are real. If I ask you to show me a number, you will point to a symbol - but that is what it is, a symbol. The number itself is a quantity which can only be grasped by a mind that is capable of counting. So on that basis, I argued that numbers are real but not existent - at least, not existent in the way that tables, chairs, and stars are existent, because they only exist in and for a rational intellect.

And indeed on that basis, I then went on to argue that God might also be ‘real but not existent’, but I’ll save that for later.

Quoting Wayfarer

My first forum post, way back, was about the reality of number. I argued that numbers are real on the basis that they are the same for anyone who can count, and also because they make actual predictions; to put it another way, because you can be wrong about them, then they are real. If I ask you to show me a number, you will point to a symbol - but that is what it is, a symbol. The number itself is a quantity which can only be grasped by a mind that is capable of counting. So on that basis, I argued that numbers are real but not existent - at least, not existent in the way that tables, chairs, and stars are existent, because they only exist in and for a rational intellect.

And indeed on that basis, I then went on to argue that God might also be ‘real but not existent’, but I’ll save that for later.

I do recall that you indeed posited that numbers are tantamount to affirming the concept of God. But, to ground what you have pondered over dutifully, I would assert that abstractions of the mind can be real in a Meinong's jungle of sorts. They can be abstractions of logical entities grounded in a non-modally dependant sense. What do you think about that?

Quoting Posty McPostface

So, modally speaking, we have the number two and God being used interchangeably as abstractions of the mind.

The modal distinctions I made were narratively different. Two would be general rather than particular. God would be fictional rather than factual.

Quoting Posty McPostface

Are you saying that pragmatically, they serve no further utility to use than using a different language game? Again, if they are modally independent of synthetic a priori judgments, then they exist universally.

I wouldn't focus on these two particular examples - two and God. My argument is that "abstractions of the mind" are only "conceptions of a world". So before we get into anything else, the first step is to avoid getting sucked into a Platonistic framing of the options. I would begin in the pragmatism of "language games" - though "form of life" would be the better term, if we must invoke Wittgenstein.

Pragmatism isn't just a game, but life itself. We are constrained by nature to make it work in the long run. And "we" are ultimately the product of the game more than its author. So again, it is about shifting away from the opposing extremes and telling the story from the balanced middle.

With two-ness and the divine, we can see them as important to our conceptions of ourselves, as we exist in a world. If we express it that way, we can see that both sides of the equation matter.

If we are talking about dogs and cats, or turnips and potatoes, there is no big deal. It seems we are talking about physical stuff that is just "out there" right now in relation to us and what we might think about those things "in here". The separation - and the regulative interaction that epistemic separation enables - feels direct and immediate. No mystery.

But talk about numbers and creators touch upon the kind of generalities that must now somehow incorporate "us" - our own being or existence as both physical and mental entities. So that alone is shifting the modal register. Two speaks to the greater generality that is entification itself - separability or countability. While God speaks to the desire for a causal explanation - a general reason for the particular individuations we might observe.

So on the one hand, there is a definite shift to a metaphysical register of reference. Pragmatism is about a conception of the world with us in it. It seems to be about the everyday human scale view of turnips and dogs. And then we find ourselves talking about "things" - like two and God - that must be classed as transcending that human scale view. That appears to break the spell of ordinary language. We feel we must be talking about either abstractions that actually also exist, or abstractions that are merely pure imaginative inventions.

But that is why - pragmatically - we have science (and maths). The appropriate thing to do, we have found through our adventures in philosophy, is to step up another level in semiotic scale and start describing reality from an "objective" rather than a "subjective" point of view.

So we resolve the Platonic dilemma not by deciding in favour of universals, generalities or abstracta being either "creations of the mind" or "facts of the world", but by establishing a systematically larger point of view that can achieve the level of pragmatic understanding we seek. The "world with us in it" becomes the world as a well-informed scientist or natural philosopher sees it - if that happens to be what you agree is the proper step up in viewpoint.

As I say, learning to see the world that way involves habits that then produce that form of selfhood. It is a form of life. And many would immediately leap forward to say the naturalistic image of nature is something they must hate and resist ... as it threatens their own habitual identity. :)

However setting that aside, the resolution of the paradox - abstracta: mental or real? - lies in seeing that everyday language is a pragmatic form of life. And then having formed a habit of conception that successfully presents the world with us in it, we are going to encounter the world as it currently seems much larger than just us. That then presents the next challenge we might want to answer. And the only actual tool to hand is the sign relation or semiosis.

This is the post in question.

Here I want to consider whether there is a difference between what is real and what exists.

'Exist' is derived from a root meaning to 'be apart', where 'ex' = apart from or outside, and 'ist' = be. Ex-ist then means to be a separable object, to be 'this thing' as distinct from 'that thing'. This applies to all the existing objects of perception - chairs, tables, stars, planets, and so on - everything which we would normally call 'a thing'. So we could say that 'things exist'. No surprises there, and I don't think anyone would disagree with that proposition.

Now to introduce a metaphysical concern. I was thinking about 'God', in the sense understood by classical metaphysics and theology. Whereas the things of perception are composed of parts and have a beginning and an end in time, 'God' is, according to classical theology, 'simple' - that is, not composed of parts- and 'eternal', that is, not beginning or ending in time.

Therefore, 'God' does not 'exist', being of a different nature to anything we normally perceive. Theologians would say 'God' was superior to or beyond existence (for example, Pseudo-Dionysius; Eckhardt; Tillich.) I don't think this is a controversial statement either, when the terms are defined this way (and leaving aside whether you believe in God or not, although if you don't the discussion might be irrelevant or meaningless.)

But this made me wonder whether 'what exists' and 'what is real' might, in fact, be different. For example, consider number. Obviously we all concur on what a number is, and mathematics is lawful; in other words, we can't just make up our own laws of numbers. But numbers don't 'exist' in the same sense that objects of perception do; there is no object called 'seven'. You might point at the numeral, 7, but that is just a symbol. What we concur on is a number of objects, but the number cannot be said to exist independent of its apprehension, at least, not in the same way objects apparently do. In what realm or sphere do numbers exist? 'Where' are numbers? Surely in the intellectual realm, of which perception is an irreducible part. So numbers are not 'objective' in the same way that 'things' are. Sure, mathematical laws are there to be discovered; but no-one could argue that maths existed before humans discovered it.

However this line of argument might indicate that what is real might be different to what exists.

I started wondering, this is perhaps related to the Platonic distinction between 'intelligible objects' and 'objects of perception'. Objects of perception - ordinary things - only exist, in the Platonic view, because they conform to, and are instances of, laws. Particular things are simply ephemeral instances of the eternal forms, but in themselves, they have no actual being. Their actual being is conferred by the fact that they conform to laws (logos?). So 'existence' in this sense, and I think this is the sense it was intended by the Platonic and neo-Platonic schools, is illusory. Earthly objects of perception exist, but only in a transitory and imperfect way. They are 'mortal' - perishable, never perfect, and always transient. Whereas the archetypal forms exist in the One Mind and are apprehended by Nous: while they do not exist they provide the basis for all existing things by creating the pattern, the ratio, whereby things are formed. They are real, above and beyond the existence of wordly things; but they don't actually exist. They don't need to exist; things do the hard work of existence.

So the ordinary worldly person is caught up in 'his or her particular things', and thus is ensnared in illusory and ephemeral concerns. Whereas the Philosopher, by realising the transitory nature of ordinary objects of perception, learns to contemplate within him or herself, the eternal Law whereby things become manifest according to their ratio, and by being Disinterested, in the original sense of that word.

Do you think this is a valid interpretation of neo-platonism? Do you think it makes the case that what is real, and what exists, might be different? And if this is so, is this a restatement of the main theme of classical metaphysics? Or is it a novel idea?

Actually the first response to that OP was from 180 Proof, who responded quite positively. (Indeed I think it was the only positive interaction I was to have with him.)

Reply to Wayfarer

That's a phenomenal breakdown of the issue. Yet, it still stands that 'abstractions of the mind' can be conferred with 'intelligible objects'. My noesis is increasing as I go along reading this.

Modally speaking, intelligible objects are tantamount to saying that they exist independently of particular. They form the substance of the world in a neo-Platonic fashion.

Quoting apokrisis

So we resolve the Platonic dilemma not by deciding in favour of universals, generalities or abstracta being either "creations of the mind" or "facts of the world", but by establishing a systematically larger point of view that can achieve the level of pragmatic understanding we seek. The "world with us in it" becomes the world as a well-informed scientist or natural philosopher sees it - if that happens to be what you agree is the proper step up in viewpoint.

Well, yes. We can submit to a collectivism of solipsistic manners of language games; but, intelligible objects persist after we are gone into some void of spirituality.

Quoting Posty McPostface

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

They exist independently of particular minds, but are nevertheless only perceptible to a rational intellect. Hence, ‘real ideas’ - which is close to the meaning of ‘objective idealism’. And actually I’m totally onboard with the paragraph that you have snipped from Apokrisis above; not a coincidence, I suspect, because if you google ‘objective idealism’, one of the primary exponents is Pierce.

Anyway, to try and drive the point a bit further - one of my [many] scrap-book quotes is from Einstein, who said, in dialogue with Hindu mystical poet, Tagore, that ‘I cannot prove scientifically that Truth must be conceived as a Truth that is valid independent of humanity; but I believe it firmly. I believe, for instance, that the Pythagorean theorem in geometry states something that is approximately true, independent of the existence of man.’ But what I think even Einstein overlooks in saying this, is the fact that the Pythagorean theorem is something that can only be seen by a rational intellect. So even though it is ‘mind-independent’ in the sense of independent of your or my mind, it is also mind-dependent in that it can only be grasped by a mind. It is, I think, what Augustine intended by the term ‘an intelligible object’ [and probably literally, as the Pythagorean theorem is one of the kinds of principles that even an Augustine would have been aware of.]

So I think it is a huge, unstated assumption that we understand what exactly the status of such principles is; we seem to think that evolutionary theory ‘explains’ these kinds of ideas. Whereas I am of the view that when h.sapiens evolved to the point of being able to grasp such principles, then we ‘transcended the biological’. That is why Platonists felt that there was a link between geometry, mathematics, and ‘higher truth’ - because you’re actually seeing into the ‘domain of forms’, the underlying ideas which give rise to, or even underwrite, the ‘phenomenal domain’. That is what scientists are actually seeing, but I don’t know if they always appreciate the philosophical significance of their insights. Instead they are always trying to seek ‘the cause’ in ‘the effect’ from the Platonic point of view, due to the influence of empiricism, as the ‘vertical dimension’ of Platonic epistemology is precisely what was lost in the transition to modernity.

Quoting Wayfarer

Anyway, to try and drive the point a bit further - one of my [many] scrap-book quotes is from Einstein, who said, in dialogue with Hindu mystical poet, Tagore, that ‘I cannot prove scientifically that Truth must be conceived as a Truth that is valid independent of humanity; but I believe it firmly.

I believe this was answered by Kant in his Prolegomena. We can have synthetic a priori judgments made and in this view, intelligible objects are a feature of the world, not our way of thinking or us or language games or forms of life as @apokrisis suggests.

Reply to Posty McPostface Your second sentence contradicts the first; because the precise import of Kant’s ‘Copernican revolution in philosophy’ is that things conform to thoughts, not thoughts to things.

Quoting Wayfarer

Your second sentence contradicts the first; because the precise import of Kant’s ‘Copernican revolution in philosophy’ is that things conform to thoughts, not thoughts to things.

That can be interpreted as just a proof by inversion, I think.

Reply to Posty McPostface Good luck with that in a Kant tute. :wink:

Reply to Wayfarer

But, you do get the significance of viewing things this way, don't you? I mean, if mental abstractions are a feature of the world and not only the mind, then it's almost a spiritual revelation of sorts.

All this makes me want to take a community college class in mathematics, heh. I think I will.

Reply to Posty McPostface Indeed. Now you’re getting it. :ok:

Quoting Posty McPostface

But, I highlighted the fact that we use "God" and "the number two" as abstractions of the mind. If they exist, then, they exist as abstractions of the mind, and nothing else

Except any mathematical realist or devoted theist would take exception with the notion that God and Numbers are just "abstractions of the mind" as would any neo Platonist. Any good idealist would grant you your premise, but go on to state all of our experiences are "abstractions of the mind". So I am not sure where your premise gets you. You seem to wish to say you can somehow tell "abstractions of the mind" from other things which apparently have some other type of existence or reality. I do not think it is that easy, clear cut or agreed upon.

Reply to prothero ‘Real but immaterial’ suits me. There are ornate arguments deployed against the reality of number, because if it is true that they’re real but incorporeal, then it mitigates against materialism and even some forms of naturalism; which is, at the same time, embarrassing, considering how important maths is to science. It’s my favorite theme. :wink:

Quoting Posty McPostface

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

"the mind"? Singular?

That strikes me as odd.

Reply to Banno If I ask you for two bananas, do I know what to expect?

Reply to Wayfarer ..and that involves two minds.

Reply to Banno 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.

Reply to Wayfarer SO the concept two involves multiple minds?

Does it also involve multiple things?

Quoting Banno

SO the concept two involves multiple minds?

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.

Quoting Banno

"the mind"? Singular?

That strikes me as odd.

How so, I'm not following you here.

Quoting Wayfarer

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

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.

Reply to Banno 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.

Quoting Wayfarer

the ontology of abstracts.

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

Reply to Banno 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.

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

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

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

Quoting Posty McPostface

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

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,

Quoting Wayfarer

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.

might be taking existence further than we ought.

Reply to Banno

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.

Quoting Banno

It might be taking existence further than we ought.

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.

Quoting Wayfarer

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.

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.

Quoting Wayfarer

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

Here we agree.

Quoting Wayfarer

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'.

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.

Quoting Posty McPostface

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

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

Quoting Banno

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.

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.

Quoting Banno

So what is a real 2 being contrasted against?

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.

Quoting Wayfarer

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

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.

Reply to Wayfarer 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.

Quoting Relativist

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.

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

Quoting Banno

What colour is seven?

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

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

Reply to Posty McPostface Hmph. If they agreed as to the colour of seven.

Quoting Banno

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

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.

Reply to Posty McPostface Others have already done that and found pretty much no correlation.

Reply to Banno

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

Reply to Posty McPostface They (usually) persist over time for an individual.

Quoting Banno

They persist over time for an individual.

Fascinating stuff, don't you think?

Reply to Posty McPostface
'Where's the referent in the sentence, "I like this place."'

It is the specific place that the speaker of the sentence has in mind, and has presumably referenced in another way.

Quoting Relativist

It is the specific place that the speaker of the sentence has in mind, and has presumably referenced in another way.

I mean, this place, the TPF? Right here?

Reply to Posty McPostface If you have to ask, you need to get a better grasp on the English language.

Reply to Posty McPostface You just answered your own question, but is TPF a place?

Quoting StreetlightX

If you have to ask, you need to get a better grasp on the English language.

:fear:

What do you mean by that?

Quoting Relativist

You just answered your own question, but is TPF a place?

I don't know, is it?

Reply to Posty McPostface
No.

Reply to Posty McPostface I mean that the question is inappropriate, and that you're not paying close enough attention to the context of the use of 'here' in your statement. There's no 'philosophical conundrum' here - just a false problem caused by an inattention to grammar. A linguistic triviality confused for philosophical profundity. As with the whole issue of math, which is not an abstraction of the 'mind', but an abstraction of the sign.

Quoting StreetlightX

As with the whole issue of math, which is not an abstraction of the 'mind', but an abstraction of the sign.

So, the sign exists independently of the mind, and the mind only makes it intelligible?

https://en.wikipedia.org/wiki/Nous

https://en.wikipedia.org/wiki/Noetics

Relevant seemingly.

Quoting Relativist

No.

How so?

Reply to Posty McPostface Forget minds. Minds are overrated and largely uninteresting. Think in terms of behaviour, action, practice. Math is a practice.

Quoting StreetlightX

Forget minds. Minds are overrated and largely uninteresting. Think in terms of behaviour, action, practice. Math is a practice.

So, you're a nominalist or instrumentalist of math? I'm not sure we can throw 'minds' out of the window...

Reply to Posty McPostface Off a cliff, preferably. Along with the rest of Greek philosophy. But those labels I think obfuscate more than they clarify. As Banno relates, asking if numbers are 'real' or 'nominal' seems to be a bad question to begin with. One should refuse the question, not pick an answer.

Quoting StreetlightX

Off a cliff, preferably.

Is this some Spinozian turn? I'm attentively listening if so.

Reply to Posty McPostface
Do you have a point? I don't care to semantics.

Quoting Relativist

Do you have a point? I don't care to semantics.

No, I just thought this was a place, that's all.