The Grounding of Logic

[Wayfarer]

@Jay

“Principles” here refers to the laws of thought, or logical laws, yes?

So you’re saying that logical laws constitute the structure within which the subject/object distinction is first made. And finally, that another name for this structure which is constituted by logical laws is “consciousness itself.”

I think I’m on firm ground saying that logic provides the ‘laws of thought’. That’s pretty well textbook, isn’t it? One of the essays I encountered in the very early days of forums was Tyler Burge, Frege on Knowing the Third Realm from which:

Thought contents exist independently of thinking “in the same way”, (Frege) says, that a pencil exists independently of grasping it. (The artificial character of pencils plays no role in his understanding of the analogy, as other examples indicate.) He says that 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”

But on the other hand, they’re not really objective, in the sense that the distinctions that logic rely on are not inherent in the objective domain to which they are applied:

Just as the geographer does not create a sea when he draws boundary lines and says: the part of the ocean’s surface bounded by these lines I am going to call the Yellow Sea, so too the mathematician cannot really create anything by his defining. Nor can one by pure definition magically conjure into a thing a property that in fact it does not possess—save that of now being called by the name with which one has named it.

So that essay states throughout Frege’s confidence that ‘mathematical primitives’ (real numbers for instance) are ‘objective’. But is ‘objective’ the right word? They’re not ‘inherent in the object’. I would rather think that mathematics is more frequently utilised to determine what is more or less objective. Hence a contemporary of Frege’s, Bertrand Russell, makes this point about universals:

Consider such a proposition as ‘Edinburgh is north of London’. Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. The part of the earth’s surface where Edinburgh stands would be north of the part where London stands, even if there were no human being to know about north and south, and even if there were no minds at all in the universe. This is, of course, denied by many philosophers, either for Berkeley’s reasons or for Kant’s. But we have already considered these reasons, and decided that they are inadequate. We may therefore now assume it to be true that nothing mental is presupposed in the fact that Edinburgh is north of London. But this fact involves the relation ‘north of’, which is a universal; and it would be impossible for the whole fact to involve nothing mental if the relation ‘north of’, which is a constituent part of the fact, did involve anything mental. Hence we must admit that the relation, like the terms it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create ~ Bertrand Russell, Problems of Philosophy, The World of Universals.

‘Apprehended by thought but not created by it’ is key to this. Such distinctions, I say, underlie nearly all our conscious acts - we see the world ‘through’ them, so to speak, but they’re not part of the world. They’re embedded in the way the mind ‘constructs’ its world.

[Tom_Storm]

@Leontiskos

If you read someone like Aristotle you will find that he rejects the notion that first principles are known in the same way that conclusions are known. In the Metaphysics he says explicitly that there is no proof for the law of non-contradiction.

Coming back to this, do you support his view and is one reading of this that logic isn’t grounded?

[Joshs]

@Tom_Storm

Subject–object distinction seems to be a fundamental organising principle, and I’d be interested in a sketch of how this could be overcome. I assume you’d point to practices aimed at exploring higher consciousness rather than philosophy itself?

This is how Husserl overcomes the distinction. Subjective consciousness is an empty zero-point of activity, like the way my body is the zero point for my perception of spatial objects (here and away, close and distant, up and down). Think of this zero point of consciousness as the NOW, which has a horizon of memory trailing away behind it and a horizon of anticipation pointing ahead of it.

This whole structure of retention-now-anticipation moves as one in a constant temporal flow. This retention -now-protention structure of consciousness is always aimed at (intends) something new. It is always about something. It singles out (synthesizes, constitutes) something in the flow based on similarity with previous experience. It anticipates durther dimensions of likeness and in this way gradually constitutes patterns from experience that it elaborates and refines into self-identical objects.

It doesn’t discover these objects as though they were already there as unitary identities, it constructs out of the flux these identities by reading into the phenomena concepts like ‘self-identical object’. It then builds on and uses the abstractions it constructs, compares its constructs with those of others, and from that intersubjective comparing produces the idea of the empirical object, available to everyone identically. So objectivity is a fabrication based on the relatively harmonious way we subjectively experience patterns of phenomena.

In sum, new phenomena are flowing into experience every instant of time via our synthetic activity of intending. But the difference between the objective pole of our intending and the idea of an empirically objective world is that the latter is a useful fabrication based on how we synthesize the senses of meaning which enter into the now.

The subject isn’t separated from the object, subject-object simply IS the activity of constitutive synthesis.

[Tom_Storm]

@Jay

But let’s even say it did hold in every case. (Again, you have to exclude fuzzy formulations and assume we’re discussing statements, or phenomena, that have clear yes/no alternatives.) The question is, In what kind of domain are these cases to be found? What does the term “A” in “Either A or ~A” refer to? Is A a piece of language? A state of affairs in the world? Or something called “propositional content”? Maybe all of the above? To repeat my earlier point: We don’t have a ready-made, obvious answer to the question of what “Either A or ~A” is meant to refer to. That’s why the “Is it thought or is it the world?” conundrum can continue to puzzle us, I’d say.

Yes, which is a much better way of putting my initial questions about the nature of logic. And to me there seems to be a further question underlying all of this: in what way does language map onto the world? Does language mirror the structure of the world? My very limited understanding of Wittgenstein suggests that (in his later work at least) he thought of logic as a product of language, a set of practices that allow us to act.

[Tom_Storm]

@Joshs

his whole structure of retention-now-anticipation moves as one in a constant temporal flow. This retention -now-protention structure of consciousness is always aimed at (intends) something new. It is always about something. It singles out (synthesizes, constitutes) something in the flow based on similarity with previous experience. It anticipates durther dimensions of likeness and in this way gradually constitutes patterns from experience that it elaborates and refines into self-identical objects.

It doesn’t discover these objects as though they were already there as unitary identities, it constructs out of the flux these identities by reading into the phenomena concepts like ‘self-identical object’. It then builds on and uses the abstractions it constructs, compares its constructs with those of others, and from that intersubjective comparing produces the idea of the empirical object, available to everyone identically. So objectivity is a fabrication based on the relatively harmonious way we subjectively experience patterns of phenomena.

In sum, new phenomena are flowing into experience every instant of time via our synthetic activity of intending. But the difference between the objective pole of our intending and the idea of an empirically objective world is that the latter is a useful fabrication based on how we synthesize the senses of meaning which enter into the now.

The subject isn’t separated from the object, subject-object simply IS the activity of constitutive synthesis.

Wow. I need to mull over this. It’s complex. And while this isn’t exactly recent thinking, it seems clear that the implications of this have not really entered mainstream discourse. It flies in the face of many philosophical approaches advocated here.

@Joshs

So objectivity is a fabrication based on the relatively harmonious way we subjectively experience patterns of phenomena.

If objectivity is a construction based on the relatively harmonious way we subjectively experience patterns of phenomena, does it follow that it would be helpful to disrupt this approach because it holds back our “development” and perhaps encourages dualistic, overly concrete and judgmental thinking?

[Joshs]

@Tom_Storm

If objectivity is a construction based on the relatively harmonious way we subjectively experience patterns of phenomena, does it follow that it would be helpful to disrupt this approach because it holds back our “development” and perhaps encourages dualistic, overly concrete and judgmental thinking

Yes, we can disrupt it by enriching it with the senses of meaning it obscures and flattens. This was the subject of the recent book ‘The Blind Spot of Science’.

[Banno]

Excellent topic.

@j_j’s approach has much to admire, a refreshing change to the usual pat stuff. But having said that, I must admit to finding it quite difficult to read. No doubt this is a result of my more analytic background.

But @Jay’s suggestion shows a way forward.

The first observation I would make is that in modern formal logic, the law of noncontradiction does not occupy a sacred place, in the way it did in older logics. Logic is no longer seen as a monolithic whole, but as a series of tools, some, but not all, of which include LNC. Its metaphysical significance has been replaced by a semantic significance.

So we have a choice of logics, some of which include LNC. There is then the potential to talk about the world using a logic that does not presume the usual truth-functional negation or that involve more truth values than just T and F.

And what this demonstrates is that logic does not tie us to a binary metaphysics.

Now choosing a binary logic of true/false might well commit one to a binary metaphysics of being/non-being, involving identity and difference, substance and property, object and subject; but we are not obligated to begin with a binary logic.

Then the first point I’d make is that logic does not tie us to a particular metaphysics.

Next

[Tom_Storm]

@Banno

Logic is no longer seen as a monolithic whole, but as a series of tools, some, but not all, of which include LNC. Its metaphysical significance has been replaced by a semantic significance.

Would this be a controversial claim with some?

@Banno

And what this demonstrates is that logic does not tie us to a binary metaphysics.

This is an import part of my OP. How “solid” is logic and where does this lead us?

@Banno

Then the first point I’d make is that logic does not tie us to a particular metaphysics.

But I am assuming that the type of logic one privileges does lead towards some forms of metaphysics (or not)?

If you had to define what the laws of logic mean to humans as thinkers, how would you describe them? As part of a language game?

[Wayfarer]

@Joshs

@Tom_Storm

Subject–object distinction seems to be a fundamental organising principle, and I’d be interested in a sketch of how this could be overcome. I assume you’d point to practices aimed at exploring higher consciousness rather than philosophy itself?

This is how Husserl overcomes the distinction. Subjective consciousness is an empty zero-point of activity, like the way my body is the zero point for my perception of spatial objects (here and away, close and distant, up and down). Think of this zero point of consciousness as the NOW, which has a horizon of memory trailing away behind it and a horizon of anticipation pointing ahead of it.

I would like to think that there is not a radical discontinuity between what I posted above from Frege and Russell, with wha you are saying here. The difference being that Husserl explicitly sees logic and mathematics as ‘structures within consciousness’.

From SEP entry on Husserl

Logic is not an empirical science and is not concerned with the genesis of spatiotemporal objects or processes, but with the validity of ideal structures and laws. Psychology by contrast is an empirical science that investigates the empirical nature of consciousness. Whereas the domain of logic is characterized by certainty and exactness, the domain of psychology is characterized by the same mere probability as all empirical sciences. A further mistake made by psychologism is that it doesn’t distinguish sufficiently between the object of knowledge and the act of knowing. Whereas the act of knowing is a subjective process that elapses in time and has a beginning and an end, the objects of logic, the logical truths, theories, principles, propositions, sentences, and proofs are not subjective experiences with temporal duration, but atemporal idealities. When I think of the theorem of Pythagoras and when you think of it, we must be able to think about the same theorem, even if our respective thought processes are different. If the content of our thought was reducible to our processes of thinking, we would never be able to repeat and retain the same content across numerically different acts.

And Russell makes an almost identical point:

It is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental. We can think of a universal, and our thinking then exists in a perfectly ordinary sense, like any other mental act. Suppose, for example, that we are thinking of whiteness. Then in one sense it may be said that whiteness is ‘in our mind’. …The connected ambiguity in the word ‘idea’, which we noted … also causes confusion here. In one sense of this word, namely the sense in which it denotes the object of an act of thought, whiteness is an ‘idea’. Hence, if the ambiguity is not guarded against, we may come to think that whiteness is an ‘idea’ in the other sense, i.e. an act of thought; and thus we come to think that whiteness is mental. But in so thinking, we rob it of its essential quality of universality. One man’s act of thought is necessarily a different thing from another man’s; one man’s act of thought at one time is necessarily a different thing from the same man’s act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.

Husserl: ‘When I think of the theorem of Pythagoras and when you think of it, we must be able to think about the same theorem, even if our respective thought processes are different’ Russell: ‘Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice.’

This is what I meant above by saying that the idea (eidos) a where thought and being coincide. Eidos are preserved in Husserl, not as static objects in the so-called platonic realm, but as invariant structures within thought or consciousness. It’s a more dynamic interpretation but still preserves something of the Platonic insight.

[Banno]

@Tom_Storm

Would this be a controversial claim with some?

Wait and see.

Small steps.

[j_j]

@Wayfarer

Eidos are preserved in Husserl, not as static objects in the so-called platonic realm, but as invariant structures within thought or consciousness. It’s a more dynamic interpretation but still preserves something of the Platonic insight.

I see the value in this. But could we see these “invariant structures” as things in the shared world ? We “perform” the identity of the river, by synthesizing its many manifestations to each of us. The identity of the river is “ideal” in something like a normative sense. Logic is normative. The telling of the world is not apart from the world, if we don’t presuppose that “ideas” are “mental stuff.” We “live ideas” in our deeds in the world, including the sounds and marks we trade.

[Banno]

The second point I would make is a directly analytic one, and not unrelated to my first point. It is to do with individuation, with what the world is made of, which things our logic is to be about.

And again, we choose. What counts as a simple, an atom, an individual changes with our purpose.

The arguments here should I hope be familiar. Quine’s “gavagai” argument and Wittgenstein on simples, at around PI §48., and the “myth of the given” form Wilfrid Sellars.

What counts as an individual is not given, but a choice.

Of course, not just any choice will do. Our choices are constrained. Perhaps the best way to understand “the world” is as that which imposes that constraint.

Nevertheless, our ontology is not entirely fixed; it is underdetermined by the world.

Next

[Tom_Storm]

@Wayfarer

I would like to think that there is not a radical discontinuity between what I posted above from Frege and Russell, with wha you are saying here. The difference being that Husserl explicitly sees logic and mathematics as ‘structures within consciousness’.

Wouldn’t it be fair, however, to say that Husserl brackets most metaphysical questions such as survival after death and idealism proper as lying beyond the scope of his method? And don’t you see this approach as a first step toward moving beyond physicalism and toward a more Hindu or Buddhist style ontology?

[Tom_Storm]

@Banno

Of course, not just any choice will do. Our choices are constrained. Perhaps the best way to understand “the world” is as that which imposes that constraint.

I have sometimes pondered a frame very close to this, myself.

@Banno

Nevertheless, our ontology is not entirely fixed; it is underdetermined by the world.

Well, this could lead some into much more extravagant notions than others, right?

[Wayfarer]

@j_j

But could we see these “invariant structures” as things in the shared world ?

Sure. If I ask you for two of something, you will know exactly what I mean.

@j_j

We “live ideas” in our deeds in the world, including the sounds and marks we trade.

Right. That’s pretty well what I’m getting at all of the time. The construction we have of our ‘otherness’ to the world, while it’s in some sense fundamental and unavoidable, it’s also the source of existential angst.

@Tom_Storm

Wouldn’t it be fair, however, to say that Husserl brackets most metaphysical questions such as survival after death and idealism proper as lying beyond the scope of his method?

Sure - but that’s also the zeitgeist, the spirit of the times. Ancient Greece was ‘the axial age’ where those questions were front and centre. As for whether that is ‘idealism proper’ - I don’t know if Platonism can even really be called ‘idealism’ without it being anachronistic. Idealism as a term in the philosophical lexicon only came into being in the early modern period. ‘Consciousness’ was a term coined by the Cambridge platonists. Looking at Greek philosophy through our modern eyes, it may seem ‘idealist’ but that is not a term they would have understood.

[Tom_Storm]

Cool. I guess I wanted to separate transcendental idealism from a more Schopenhauer-like form of metaphysical idealism, which makes more specific claims.

[John]

For me the provenance of logic is the most central question about our, and sentient animal in general, relation to the world, and as such it is the most important and fascinating question. Just as sex is the dance from which all dances come, so this question is the question from which all questions come.

The way I think about it life originates with the membrane―the strict separation between inside and outside. Sentient beings must be able, at least functionally if not consciously, to enact this separation, or perhaps better: living organisms are functions of this separation.

Thus begins the primordial identification of difference, of “self and other”. To survive as living beings we all must be able to identify things in the world―sources of sustenance, prey and predator and so on. Identification only works for us and the other organisms if it is unambiguous.

Processes of unambiguous identifications of things are the forerunners and constitute the structural underpinnings of language with its dualistic, binary character; a thing either is “whatever” or it isn’t. The Law of the Excluded Middle and the Law of Non-contradiction are the elaborated exemplars of what is necessary in the context of pre-linguistic perception and action, and thus by extension to its linguistic expressions. This can also be seen in the common parlance of “making sense”. What is logical makes sense, what is illogical not so much.

So a thing as identified cannot be both itself and something else. There is no room in the local context for such ambiguity. But then the abstractive, abstractional character of our language enables us to analyze and introduce ambiguity. On reflection we come to understand that when we see a thing, we do not see all of it. Science informs us that all the things of the perceptual world, even the apparently most stable, are all changing. Thus enters the insoluble puzzle of identity and difference, of being and becoming.

Kant (perhaps not the first) introduces the logical distinction between the thing as perceived and the thing in itself. There seems to be a contradiction now―we see the thing and yet we do not see the thing. In the world of perception there cannot be any ambiguity―the LEM and the LNC rule! But Kant has pointed to another “context”―the “in itself”―and between the “for us” and the “in itself” ambiguity insinuates its unsettling tendrils.

The best formulation of this I have come across (found in reading Brook Zyporyn’s Being and Ambiguity) is (referring to the determinability of the everyday object) “It is locally coherent, but globally incoherent.” Ziporyn’s idea is that that every local determinacy is accompanied by global indeterminacy. Zyporyn is a scholar of Daosim and Buddhism and he relates this ambiguity to the Tiantai Buddhist conception of ‘Provisional Positing vs. Emptiness’.

So, this ambiguity originates in a mixing of contexts―the familiar context of perception and judgement and the (imaginary) “context which is no context” or to relate to an alcoholic reference some may be familiar with: the “Clayton’s” situation―“the situation you are having when you are not having a situation”.

[Banno]

The third point is even more broadly based, with a background stretching from Husserl to Davidson, with all stations in between.

The world is always, already, interpreted. We can’t step outside our representations of the world.

One corollary of that is that there is no neutral ground from which we might choose between the logics available to us.

Another corollary, if we accept that language is inherently communal, is that our representations of the world are also inherently communal.

And from that we might welcome a preference for those representations, those explanations, that are more widely accepted, that are not true for one, but true for many. Not the view from nowhere but the view from anywhere.

Conclusion

[Count_Timothy_von_Icarus]

We had a few threads on this on the old forum. One difficulty is the potential for equivocation. Today, as an academic subject, logic is strictly “formal logic” (really to the exclusion of material logic, which gets rolled into “application”).

Interestingly, you can find plenty of scholarship on the well-developed ‘logic’ of Indian thought. Yet it is notable that Indian logic, AFAIK, never makes the strong distinctions between form and content, syntax and semantics, that you see in the West due to Aristotle. As such, it remains even more firmly epistemic and ontic.

Contemporary formal logic is sort of on the opposite side of the spectrum.

But I don’t think the advocates of any sort of “thick” grounding of ‘logic’ generally mean to appeal to any particular aspect of contemporary formal logic. Actually, they normally want to roll mathematics into these arguments, or even all causal inference, or even the possibility of any noetic content to thought at all. This is why I think ‘logos’ might be a better term for these discussions than logic. Just a thought though.

That doesn’t really tilt things in any direction either. Generally, what someone thinks about the grounds of logic is fairly informative about what they think about the grounds of mathematics, or the need to ground causality and the intelligible whatness (quiddity) of thought.

[Tom_Storm]

@John

For me the provenance of logic is the most central question about our, and sentient animal in general, relation to the world, and as such it is the most important and fascinating question.

Yes it struck me as a fundamental question too and so much else seems to fan out from it. Hence this:

@Count_Timothy_von_Icarus

Generally, what someone thinks about the grounds of logic is fairly informative about what they think about the grounds of mathematics, or the need to ground causality and the intelligible whatness (quiddity) of thought.

@John

Science informs us that all the things of the perceptual world, even the apparently most stable, are all changing. Thus enters the insoluble puzzle of identity and difference, of being and becoming.

You seem to take an enactivist approach?

@John

So, this ambiguity originates in a mixing of contexts―the familiar context of perception and judgement and the (imaginary) “context which is no context” or to relate to an alcoholic reference some may be familiar with: the “Clayton’s” situation―“the situation you are having when you are not having a situation”.

Ha! I remember those ads. Just so I’m clear are you saying it’s much ado about nothing or something far more subtle?