You can’t ask why the law of identity holds, or why elementary arithmetic proofs are valid. They are the basis on which judgements of validity are made. — Wayfarer

This is the view that logic is constitutively normative for thought. That is, the norms themselves make thinking possible, just as the rules of a game are constitutive for that game. They don't "regulate" how the game is played, they are part of what it is for the game to be the game that it is. Without the normative force of the logical laws, thinking is not possible. From the SEP:

Other philosophers have taken the normativity of logic to kick in at an even more fundamental level. According to them, the normative force of logic does not merely constrain reasoning, it applies to all thinking. The thesis deserves our attention both because of its historical interest—it has been attributed in various ways to Kant, Frege and Carnap[6]—and because of its connections to contemporary views in epistemology and the philosophy of mind (see Cherniak 1986: §2.5; Goldman 1986: Ch. 13; Milne 2009; as well as the references below).

To get a better handle on the thesis in question, let us agree to understand “thought” broadly as conceptual activity.[7] Judging, believing, inferring, for example, are all instances of thinking in this sense. It may seem puzzling at first how logic is to get a normative grip on thinking: Why merely by engaging in conceptual activity should one automatically be answerable to the strictures of logic?[8] After all, at least on the picture of thought we are currently considering, any disconnected stream-of-consciousness of imaginings qualifies as thinking. One answer is that logic is thought to put forth norms that are constitutive for thinking. That is, in order for a mental episode to count as an episode of thinking at all, it must, in a sense to be made precise, be “assessable in light of the laws of logic” (MacFarlane 2002: 37). Underlying this thesis is a distinction between two types of rules or norms: constitutive ones and regulative ones.

The distinction between regulative and constitutive norms is Kantian at root (KRV A179/B222). Here, however, I refer primarily to a related distinction due to John Searle. According to Searle, regulative norms “regulate antecedently or independently existing forms of behavior”, such as rules of etiquette or traffic laws. Constitutive norms, by contrast

"create or define new forms of behavior. The rules of football or chess, for example, do not merely regulate playing football or chess but as it were they create the very possibility of playing such games". (Searle 1969: 33–34; see also Searle 2010: 97)

This is the view that logic is constitutively normative for thought. That is, the norms themselves make thinking possible, just as the rules of a game are constitutive for that game. — Kornelius

Right! Hence my remark in the other thread that numbers (etc) are constitutive of thought. That is exactly what I meant! And as I can see you are learned and competent, I greatly appreciate the opportunity to try and explain this point further.

I agree with the gist of the SEP passage above, where it says that 'the normative force of logic does not merely constrain reasoning, it applies to all thinking.' And I think you could argue that this applies even at the level of language itself. Why? Because language is grounded in abstraction, in judgements that 'this' is 'like that', and 'that' means 'this'. These judgements are likewise constitutive of reason and rational inference, and they are being made whenever we assert or describe or argue anything whatever. They are the 'fabric of reason', so to speak. (For further elaboration on Freger's view of the 'laws of thought' in particular, see Frege on knowing the Third Realm, Tyler Burge.)

But I should take some steps back. The idea that first got me interested in philosophy forums was exactly about the reality of abstract objects (such as, but not only, number.) Now, in the other thread, I said I was dubious about the usage of the term 'objects ' in this context. I think that in effect describing 'concepts' as ‘objects’ is a reification. I accept the usage of the term ‘object’ as a linguistic convention, but I think this usage leads to a basic misunderstanding of the nature of what is being discussed. And the reason for that, is that modern thinking is overwhelmingly oriented towards the 'domain of objects' - the domain presumed fundamental and exclusively real by natural science . That's why in many such debates, the issue of the reality of abstract objects nearly always comes down to the dismissive question 'where could this "ghostly domain" of abstract objects exist?" There's literally no conceptual space for it in modern naturalism, as what is real is regarded as existent, 'out there somewhere', as the saying has it (see the remark on 'animal extroversion' in the quotation below.)

In earlier philosophies - such as scholastic realism and the various forms of Platonism from which it descended - abstract objects are understood to be real in their own right, i.e. to be ontologically distinct from material or phenomenal objects or to possess or indicate another level or kind of reality. (Hence in Platonic epistemology, knowledge of arithmetical forms is categorised as "dianoia" - which appears in modern philosophy mainly in the guise of Galileo's mathematisation of physics.)

One of the profound consequences of the transition to modernity was the 'flattening' of ontology, such that there is said to be only one real substance (ouisia, bearer of attributes), those being the primary objects of the natural sciences specified in mathematical terminology. Western culture is now so steeped in that, that the ability to think in (scholastic) realist terms is forgotten. Whereas, if we admit the reality of conceptual and intellectual "objects", then

There are a whole range of other realities whose reality we can now affirm: interest rates, mortgages, contracts, vows, national constitutions, penal codes and so on. Where do interest rates "exist"? Not in banks, or financial institutions. Are they real when we cannot touch them or see them? We all spend so much time worrying about them - are we worrying about nothing? In fact, I'm sure we all worry much more about interest rates than about the existence or non-existence of the Higgs boson! Similarly, a contract is not just the piece of paper, but the meaning the paper embodies; likewise a national constitution or a penal code.

Once we break the stranglehold on our thinking by our "animal extroversion", we can affirm the reality of our whole world of human meanings and values, of institutions, nations, finance and law, of human relationships and so on, without the necessity of seeing them as "just" something else lower down the chain of being yet to be determined. ¹ — Neil Ormerod

So that is the drift. It is not exactly what I set out to say when I sat down to write, but I hope it conveys something of what I'm getting at.

Right! Hence my remark in the other thread that numbers (etc) are constitutive of thought. — Wayfarer

I think that in effect describing 'concepts' as ‘objects’ is a reification. — Wayfarer

Typically, we say that rules or, rather, norms are constitutive. If we think that mathematics is logic (logicist position), then we still have the problem of explaining logical objects.

Logic can be constitutive of thought while logical objects exist. That's no problem at all (rather, it presents no more issues that what realists about abstract objects face in any case).

These judgements are likewise constitutive of reason and rational inference, and they are being made whenever we assert or describe or argue anything whatever. They are the 'fabric of reason', so to speak. (For further elaboration on Freger's view of the 'laws of thought' in particular, see Frege on knowing the Third Realm, Tyler Burge.) — Wayfarer

Careful quoting Frege's view on this. While Frege likely held the constitutive thesis, he definitely was a realist about mathematical objects :) He would be a great example of holding both that logic's normativity is constitutive of thought, as well as the view that mathematical (logical) objects exist (and not in a metaphorical sense). Also, thanks for the reference. I am familiar with Burge's paper :)

I think that in effect describing 'concepts' as ‘objects’ is a reification — Wayfarer

I never did that, and the realist position does not endorse this. In fact, Frege wrote a whole paper on distinguishing concepts from objects.

Numbers, for Frege, are not concepts, however. They are objects. If you think that numbers are concepts, then you need to give an account of mathematics in which number terms occurs as predicate terms in the logical language, or as quantificational statements (whether they be first-order or second-order concepts).



The point is that realists think this is not possible, and so numbers have to be full-fledged objects.

What I mean to say here is that the position does not use the term 'object' in a loose, metaphorical sense, or in a sense that "reifies concepts'. It doesn't treat numbers as concepts. We know this because concepts have formal analogues in a precise logical language. Indeed, Frege's insistence that concepts and objects are not the same is reflected in the very syntax of first-order logic (and Frege's logic has a complete first-order fragment).

I accept the usage of the term ‘object’ as a linguistic convention, but I think this usage leads to a basic misunderstanding of the nature of what is being discussed. And the reason for that, is that modern thinking is overwhelmingly oriented towards the 'domain of objects' - the domain presumed fundamental and exclusively real by natural science . — Wayfarer

So I think your position is this: we make syntactic distinctions in our formal languages differentiating concepts (predicate expressions) from objects (terms). But the syntactic distinctions do not map onto any metaphysical distinctions between concepts and objects at all.

Ok, but the issue I see is this: empirical objects occur as terms in our formal languages. They are undoubtedly objects. Properties occur as predicate expressions in our formal languages, and properties are undoubtedly concepts (or the referents of concepts, though I take it you mean to use properties and concepts somewhat interchangeable. In any case that doesn't affect the discussion). But then why should terms that refer to abstract objects be taken to be "reification" of what are in fact concepts? Why not take it as evidence that we may have been doing the reverse, i.e., referring to abstract objects as mere concepts, when in fact they were not?

There's literally no conceptual space for it in modern naturalism, as what is real is regarded as existent, 'out there somewhere', as the saying has it (see the remark on 'animal extroversion' in the quotation below.) — Wayfarer

Correct: metaphysical naturalism is incompatible with mathematical/logical realism (in the ontological sense). Still, mathematics remains the most significant challenge to naturalism and one which the naturalists have yet to solve.

So that is the drift. It is not exactly what I set out to say when I sat down to write, but I hope it conveys something of what I'm getting at. — Wayfarer

It did, and I hope I have a better sense of your view so that my objections to it may seem more convincing! (or can be more easily dismantled :P)

That being said: I think we should dig out Frege's paper on Concepts and Objects.

But then why should terms that refer to abstract objects be taken to be "reification" of what are in fact concepts? Why not take it as evidence that we may have been doing the reverse, i.e., referring to abstract objects as mere concepts, when in fact they were not? — Kornelius

Someone would just say that numbers are objects like leprechauns are objects- made up ones. What would it matter if objects are objects if objects can be imaginary? Numbers can be useful, made up objects. So being an object in Frege's own conception would not make something real. It can be useful though.

Something being useful is a good start.

I think that pragmatism would a good philosophical school. I wonder why Americans aren't so much into it, even if it is genuinely of American origin (Pierce and Dewey).

Thank you very much for your comments. Informed criticism such as yours is invaluable and hard to come by. (Although I will also acknowledge that what follows might be categorised as "counter-cultural/alternative", and not the kind of view that is typically endorsed in the secular academy. I will mention that I majored in comparative religion, not philosophy proper.)

Frege wrote a whole paper on distinguishing concepts from objects. — Kornelius

I have looked very briefly into that. What I responded to in the Tyler Burge paper was Frege's sense that 'arithmetical primitives' (etc) are self-evidently true, i.e. can't be explained at any lower level, and also the fact that Frege simply assumes this to be the case, and doesn't feel the need to justify it further. This I saw as a residue of Platonism in Frege's philosophy (which Burge acknowledges). Also the fact that the conceptual domain does indeed comprise 'a realm' (specifically, the third realm) i.e. a domain of concepts that really exist, which again is close in meaning to Platonic realism:

...thought content exists independently of thinking "in the same way", Frege said "that a pencil exists independently of grasping it. Thought contents 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." — Tyler Burge

So, indeed, a 'realist' view - but I think nearer to a scholastic, than a modern scientific, realist!

But please let me explain my approach to the terminology of 'concepts and objects', as I think it is internally consistent, even if it is different to Frege's.

My initial insight about mathematical realism was a sudden realisation about numbers. This was that (1) they do not come into or go out of existence, and (2) they're not composed of constituent parts (although I later came to realise that this last was only true of prime numbers.)

But in this respect, at least, the nature of number is ontologically distinguishable from the nature of phenomenal entities, all of which are limited in time and are composed of constituents. Accordingly, when the mind sees a mathematical or arithmetical truth, it does so in a different manner to seeing an object of sense; it does so apodictically and on the basis of reason alone, rather than mediated by sense - a distinction which is at the basis of what later comes to be called 'hylomorphic dualism'.

When I had that insight into number - an 'aha' moment! - I thought I had grasped that this was why classical philosophy esteemed mathematical knowledge above 'mere sense impression'. And this insight didn't arrive as a consequence of my having studied Platonism or classical philosophy, it was an unexpected epiphany, although in the long period since I haven't found anything to disconfirm the idea and the more I study, the more likely it seems to be true.

So that is why in my particular (and I readily admit, probably idiosyncratic) heuristic, numbers are not 'objects' - because I use the term 'object' to designate 'phenomenal' or 'corporeal objects'. Furthermore, that the domain of phenomenal objects is, properly speaking, 'the realm of existents' or 'the phenomenal domain' - which I also assume to be the domain of the natural sciences.

I have argued this point specifically with reference to an article called The Indispensability Argument in the Philosophy of Mathematics (an article which I find abounds in unintentional irony).

It begins by saying 'Standard readings of mathematical claims entail the existence of mathematical objects. But, our best epistemic theories seem to debar any knowledge of mathematical objects.' The 'best theory' is described as given by Quine, and comprising the 'abandoning of the goal of a "first philosophy" (i.e. metaphysics). Furthermore, says the article, 'Instead of starting with sense data and reconstructing a world of trees and persons, Quine assumes that ordinary objects exist', which is indeed the basic stance of naturalist philosophy.

Later we read that

Some philosophers, called "rationalists" claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought (//which I would describe as "reason"//). 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.'

But rather than dismissing physicalism on that account, the article then goes on to argue as to why we have to accept the efficacy of mathematics on the grounds of its 'indispensability' - even though its nature seems irreconcilable with 'our best theories'! (Talk about inconvenient truths!)

Whereas, I would rather argue that the capacity for reason is, just as the Greeks said, precisely that which differentiates humans from other animals, and, therefore, difficult to accommodate within philosophical naturalism (which you acknowledge, and which is what makes it highly unfashionable in the current academy.)

why should terms that refer to abstract objects be taken to be "reification" of what are in fact concepts? Why not take it as evidence that we may have been doing the reverse, i.e., referring to abstract objects as mere concepts, when in fact they were not? — Kornelius

Well, coming back to Frege, that Burge paper says that:

Frege held that both the thought-contents that constitute the proof-structure of mathematics and the subject-matter of these thought-contents (extensions, functions) exist.

(Emphasis added.) Now, my heuristic around this point is that such things don't actually exist in the sense that 'phenomenal objects' exist. But they are real, nonetheless: hence, real but not existent! It's not that they're non-existent in the sense that unicorns and square circles are non-existent; rather that their reality is purely intelligible or noetic (this is very close in meaning to the word 'noumenal' which is derived from the root 'nous', i.e. 'an object of thought'.)

But this is an ontological distinction which has been forgotten, lost or abandoned in modern thought (although the distinction of 'existence' and 'reality' is still recognised by Peirce.)

That's the sense in which 'intelligible objects' comprise a domain or a realm; but, because of our encultured naturalism, it's impossible for us to conceive of a realm that is not located in time or space. Hence the invariable question 'where is this realm'?

There's a passage in the Cambridge Companion to Augustine on intelligible objects, which says:

By focusing on objects perceptible by the mind alone and by observing their nature, in particular their eternity and immutability, Augustine came to see that certain things that clearly exist, namely, the objects of the intelligible realm, cannot be corporeal. When he cries out in the midst of his vision of the divine nature, "Is truth nothing just because it is not diffused through space, neither finite nor infinite?", he is acknowledging that it was the discovery of intelligible truth that first freed him to comprehend incorporeal reality.

Note here again the use of 'object' in the context of 'object of thought'. I suppose my objection comes down to the fact that this suggests that the criterion of the reality of something is it's "objectivity", but that I take "objectivity" to be a naturalistic criterion, as it invariably has to be correlated with something in the empirical domain. Whereas the 'incorporeal' realm is not at all 'objective' in the naturalistic sense. So here we are actually dealing with metaphysics proper - precisely in that sense that Quine, et. al., has rejected. This is where, I think, that Western philosophy lost its connection to metaphysics proper.

Anyway - enough already! Or probably too much.

Someone would just say that numbers are objects like leprechauns are objects- made up ones. — schopenhauer1

This person ought to immediately cease and desist from using computers, which only operate by virtue of the fact that numbers are not simply 'made up objects'. It would be more consistent with such a view if they eschewed technology altogether and returned to subsistence farming.

Then they would just say it's the physical output of an electrical circuit opening and closing other circuits. This would be a physical act.

:rofl:

Indeed, meaning presupposes identity. — jorndoe

Not all meaning. Linguistic meaning... as it pertains to logic... sure.

Why laughing? I am just saying, Frege seems to think anything is an object as long as it is not a predicate statement. Thus, any old imaginary thing can be an object. That does not seem to be a great definition of an object. In a way, I agree with your interpretation of an object as material.

Why laughing? — schopenhauer1

Well, first of all I was reacting to:

Someone would just say that numbers are objects like leprechauns are objects - made up ones. — schopenhauer1

What I tried to get at is that almost everything about the technology we're using every day (or minute!) relies on the 'unreasonable efficacy of mathematics'. We can't "make up" fundamental arithmetic and geometry, or the science behind computers - it is something that has had to have been discovered. Now, I know this then segues into the whole 'is math discovered or invented' conundrum, but I'm of the 'discovered' view - hence my initial (and admittedly sarcastic) response.

But then there was:

Then they would just say it (the computer) is the physical output of an electrical circuit opening and closing other circuits. This would be a physical act. — schopenhauer1

Yes, a computer is physically existent, but its physical form is simply the means of interfacing with intellectual or intelligible objects. I argue that logic itself is not a physical phenomenon - it can be expressed or realised or instantiated physically, but in essence, it's the relationship of ideas, not of physical entities. That's why humans can build calculating devices, and Caledonian crows, despite their cleverness, cannot - because humans can 'see reason', so to speak.

Frege seems to think anything is an object as long as it is not a predicate statement. Thus, any old imaginary thing can be an object. — schopenhauer1

No, I don't think he says that at all, but must confess to not having read his 'concepts and objects' paper.

No, I don't think he says that at all, but must confess to not having read his 'concepts and objects' paper. — Wayfarer

I'm not sure. @Kornelius what would be the difference between numbers and leprechauns in Frege's conception of objects? I realize that question is funny as I write it :).

Something being useful is a good start.

I think that pragmatism would a good philosophical school. I wonder why Americans aren't so much into it, even if it is genuinely of American origin (Pierce and Dewey). — ssu

I think many Americans don't engage in much philosophy at all if you are to characterize it as a whole. I'm guessing that is most societies though, except perhaps France who may put more stock in philosophy as more a political-cultural statement? If you are talking about academics and professors, I honestly don't know what is most popular. My sense is that Pragmatism as well as analytic philosophy in the tradition of Russell, Wittgenstein, Kripke, Quine, Austin, etc. rates pretty high in academic citations.

The populace as a whole I would say values use over other considerations. Technological innovation is a huge part of American industry. However, I suspect use-value is prized in almost all countries. Philosophical abstractions would not rank high as a value for most people anywhere.

Also, being such a pluralistic society, by de facto, Americans assent to a sort of pragmatism whereby if it is useful to you, and it does not interfere with what someone else finds useful, then they all should be considered legally equal. There is a pragmatism with dealing with people from so many backgrounds that have to "get stuff done" in civil society- the everyday aspect of work, consumption, public utilities, etc. I realize however, this is not Pragmatism proper- the philosophy that Peirce described as ""Consider the practical effects of the objects of your conception. Then, your conception of those effects is the whole of your conception of the object."

Overall doing is more important than reflecting I would propose in American values. Reflecting is for idlers and idlets are bad. It's always go go go. If you are doing something, what is its use towards improving your survival, comfort, or entertainment levels would be the implicit assumption. Where are you going? What are you doing? Not what are you thinking, not what is the meaning of. But again, this is probably most societies. Most people dont want to reflect why they should do anything at all or what motivates all this doing in the first place. It assumed an action with some outcome shod just happen.

Added more to the post above.

Hey Wayfarer, I do not have the time for a considered reply to this, but I can reply to the issue about imaginary or fictional objects, so I will do that first and will get back to this.

I'm not sure. Kornelius what would be the difference between numbers and leprechauns in Frege's conception of objects? I realize that question is funny as I write it :) — schopenhauer1

This is hitting on a point that is actually somewhat contentious and deeply philosophically interesting.

For Frege, the term "leprechaun" is an empty name (or, rather, an empty noun). It does not refer to an object.

The term "three", on the other hand, refers to an object.

But here is the issue. If I say, for example:

(1) "Sherlock Homes is a great detective"

This sentence does have a meaning. But, for Frege (as for many), the name "Sherlock Holmes" is an empty name. But, at the same time, "Pegasus" is also an empty name, and while the sentence:

(2) "Pegasus is a great detective"

Clearly has a different meaning than "Sherlock Holmes is a great detective", the referential semantic components of the two sentences (1) and (2) are the same, given that the names in each do not denote an object, and the rest of the sentence is identical! I say they have different meanings because many would believe (1) to be true, but (2) false, and it wouldn't be because they are mistaken about Sherlock Holmes or Pegasus (or what it means to be a detective).

So how do we make sense of this?

Frege has a differentiated notion of semantic content. That is, terms, sentences, etc., are have both a reference (as part of their semantic content) and a sense (as part of their semantic content). So while the names "Sherlock Holmes" and "Pegasus" don't differ with respect to their reference (they both do not refer to an object), they do differ with respect to their sense.

Now there is a lot of literature on Frege's views on this, and whether he had successfully clarified his notion of sense to properly account for empty names.

But, in short, that is the response. "Leprechaun" behaves semantically differently (so to speak) than number terms since the latter have reference and the former does not.

This is not the only possible view, however. While Frege would not have agreed, many philosophers have since argued for the existence of fictional characters, and thus for the existence of objects that would be the referents of the term "leprechaun". Mostly because it solves a lot of the technical philosophy of language/logic issues (but at the expense of not being consistent with our common sense views about these terms).

Hope this helped!

For Frege, the term "leprechaun" is an empty name (or, rather, an empty noun). It does not refer to an object.

The term "three", on the other hand, refers to an object. — Kornelius

What is the object referencing? Presumably reference is a "real" thing, but how does he explain this without being self-referential? If he says it is somewhere in the world, then where is this "three"? But if he says it is in the realm of the imagination, then he once again has no way of differentiating it from the leprechaun.

What is the object referencing? Presumably reference is a "real" thing, but how does he explain this without being self-referential? If he says it is somewhere in the world, then where is this "three"? But if he says it is in the realm of the imagination, then he once again has no way of differentiating it from the leprechaun. — schopenhauer1

An abstract object. In fact, for Frege it references as extension (of a second-level concept). To be a bit more modern: it would pick out a particular set. Leprechauns are not sets. Sets have properties leprauchauns don't have (and vice versa).

Frege's way of differentiating abstract objects is via definition. For him, a definition must settle all mixed identity claims. So, the definition of the number three would settle whether or not:

leprechaun = 3

is true or false (and it would come out false).

Let's be a bit more modern again, and not use Frege's explicit definition but a semi-analagous one:

$3 :=_{Df} \{\varnothing, \{\varnothing\}, \{\varnothing, \{\varnothing\}\}\}$

It follows from this, for example, that $\varnothing\in 3$ or that the empty set is an element (or part of) the number 3. But this is not true for leprechauns, i.e., empty sets aren't parts of leprechauns. So they can't be the same thing.

An abstract object. In fact, for Frege it references as extension (of a second-level concept). — Kornelius

Why can't leprechauns be an abstract object? It may not be a mathematical object, but why not an abstract one? Being a set would be a definition of a mathematical object perhaps, but not all abstract objects are subsumed in that. Economics for example is an abstract object. creativity is an abstract object, etc. How does his definition differentiate between any of these?

Why can't leprechauns be an abstract object? It may not be a mathematical object, but why not an abstract one? Being a set would be a definition of a mathematical object perhaps, but not all abstract objects are subsumed in that. Economics for example is an abstract object. creativity is an abstract object, etc. How does his definition differentiate between any of these? — schopenhauer1

They can be, I didn't mean to exclude this possibility; I was only explaining Frege's position on this. But yes, we could allow that fictional entities are real objects of some sort and that the number 3 would not be the same thing as a Leprechaun, because a number is a set, and a leprechaun is a fictional object but genuinely existing object (whatever fictional might mean). It would be an abstract object of some sort and not a physical object.

This would mean that names for fictional characters have a genuine referent. This is definitely a view that is held by many philosophers. You may be interested in the SEP article on fictional entities.