The Grounding of Logic

[RussellA]

@Corvus

With use of imagination and interpretation, math mirrors reality very well.

I agree that maths mirrors reality as it exists within our imagination, but this is not the same thing as reality as it exists outside our imagination.

[Corvus]

@RussellA

but this is not the same thing as reality as it exists outside our imagination.

Of course not. Math is description or interpretation of reality. It is not reality itself.

Same goes with language. Language is not reality itself. It is a tool for description and interpretation of reality.

[RussellA]

@Corvus

Of course not. Math is description or interpretation of reality. It is not reality itself. Same goes with language. Language is not reality itself. It is a tool for description and interpretation of reality.

But where exactly is this reality being described or represented, in the mind or in a world external to the mind?

For example, I see a red postbox. The experience of red certainly exists in the mind, but where is the philosophical justification that red exists outside the mind’s experience of it?

[Leontiskos]

@Tom_Storm

You may be right about this, although I suspect there are some who can do it. Some people seem to have a gift for inhabiting multiple realities with concomitant immunity to contradiction.

Well, it’s not really about inhabiting multiple realities. That entails no contradiction. People have a work life and a family life. There is no contradiction in this, even though they are two different realities inhabited.

But if someone has two families in two different cities, and they try to keep one of the families hidden from the other, then they are living out a contradiction (because at least one of the families bring with it the expectation of exclusivity and monogamy). Or if someone heads up a peace organization but makes all their money from arms trading, then there will be a lived out contradiction.

More simply, humans cannot lie without consequence. To lie is to immediately create a potential problem for oneself, and that potentiality is not avoidable. No one could say, for instance, “I lie constantly about everything and there are never any negative consequences.”

@Tom_Storm

Can I ask you then, in simple terms, what would it mean to ground logic? What follows from that idea: does it involve some kind of guarantor of logic’s validity or reliability that would otherwise be missing, and without which our discourse would collapse into meaninglessness?

To ground logic is to justify that which logic relies upon. So for the modern logic is deduction and grounding logic requires induction as applied to the presuppositions of logic.

The principle of non-contradiction is always the most central example. If the PNC is central to logic, then grounding the PNC will be central to grounding logic. At minimum we would say that one has failed to ground X if there is nothing more to be said for X than against X. So the PNC would be fully ungrounded if there is nothing more to be said for the PNC than against the PNC. Faced with the PNC, ought one affirm it or deny it? If there is absolutely no reason to incline in one direction rather than another, then the PNC can uncontroversially be said to be ungrounded.

[Jay]

@Banno

logic does not tie us to a particular metaphysics.

That’s a nice simple way of stating what I see as the outcome of my questions about “A” and “Either A or ~A”. We appear to have a choice – or a confusion! – about how these terms ought to refer. And logic itself can’t provide the answer, though as you point out elsewhere, it limits the plausible choices. It would be a drastic misunderstanding of traditional logic to claim that the domain of “A” is squirrels.

This question shouldn’t be confused with a genetic question about how humans came to adopt the laws of logic – did we start counting rocks and develop logic, or did the logic lightbulb go on and so we started counting rocks? An interesting question, no doubt, but not the question raised here.

@Banno

what the world is made of, which things our logic is to be about

Same point. What we’re going to quantify over is, to some degree, up to us.

@Banno

We can’t step outside our representations of the world.

This connects with a theme in the Pragmatism thread. Granted that this is true, how should we understand the pressure, the attraction, to do so? Is it merely a mistake, a longing for something pre-philosophical that we desire? Or does “a world beyond representations” point us toward a regulative ideal of truth, in Peirce’s sense?

@Banno

@Tom_Storm

Isn’t the point of higher awareness and contemplative traditions about stepping outside, if not beyond?

Sure.

But if you step outside, then you can’t say anything.

That’s the error made so often here - to pretend to talk about the ineffable.

Well, not so fast. I think what you mean is that we can’t say anything within the discourse of rationality, perhaps of philosophy tout court. But that still leaves an awful lot of uses of language in which to say the ineffable – and I insist that “say” is the right word, because I won’t limit articulacy to the rational sphere.

@Wayfarer

What I’m grappling with is that ideas - by that I don’t mean, whatever happens to occupy one’s stream-of-conscoiusness at any given time - really are structures within consciousness. They are the necessary form that thought must take - hence the whole idea of ‘logical necessity.’

A somewhat related point to what I was saying above: I don’t think you mean that ideas (understood not as stream-of-consciousness events but as something closer to propositional content) are necessarily “the form that thought must take.” Unless you want to pin down “idea” and “thought” very inflexibly to rational content. In practice, we have all sorts of thoughts that aren’t structural at all, and aren’t experienced or evaluated according to “logical necessity.” I think what you mean is what @Banno meant: If we choose to enter the realm of rational discourse, then certain necessary forms present themselves.

@RussellA

Suppose in the world I see four rocks. Suppose I added another rock and every time the result was three rocks.

Because of Enactivism, where the mind emerges from its environment, within our numbering and linguistic practices it would be logical that 4 + 1 = 3.

Anyone who behaved as if 4 +1 = 5 would be sent back to school.

I’ve always loved this thought experiment. There are grave issues about whether such a world is conceivable, but let’s say it is. Would we have to revise mathematics? I don’t think so. But it would put us in a position to make, finally, a discrimination about what “the laws of logic” refer to (if you agree that math is branch of logic). We could say that, in the case of items in the world, the physical laws are thus; in the case of reasoning, the logical laws are this. And the fact that we may not even be able to conceive a world in which rocks multiply in this fashion? It could mean that there will never be a way to conceive of these two distinct “domains of law.”

[RussellA]

@Jay

And the fact that we may not even be able to conceive a world in which rocks multiply in this fashion?

But we can conceive of such a world, because we are talking about it.

@Jay

We could say that, in the case of items in the world, the physical laws are thus; in the case of reasoning, the logical laws are this.

Suppose there is a world where the physical laws are such that 4 rocks plus 1 rock is 3 rocks.

What logical laws should we use? We could use the logical law that 4 + 1 = 5. But we could also use the logical law that 4 + 1 = 6. In fact, we could use any one of a countless number of logical laws.

So why choose one logical over another?

The only reason would be that our logical law mirrors the physical world, which is why we would still in this strange new world use the logical law that 4 + 1 = 3

[Jay]

@RussellA

But we can conceive of such a world, because we are talking about it.

No. We are talking about rocks multiplying non-standardly. We have not even attempted to conceive the world in which this might occur. The physics alone are breath-takingly incoherent.

@RussellA

we would still in this strange new world use the logical law that 4 + 1 = 3

And this is part of what we would have to conceive: Does the strange new world include number lines? Is abstract counting a human achievement? If “4+1=3” is an axiom of mathematics, is there any consistent math that can be derived from it? etc. We may find, trying to conceive this, that we wind up being forced to claim that “5” is unsayable. For all arithmetic that tries to use 5 would be self-contradictory. (Maybe this world would develop a taboo against uttering “5”!)

So . . . better to save “4+1=3” for a description of how the physical world behaves.

[Joshs]

@Wayfarer

So that ‘associative synthesis’ still culminates in the grasping of something which is not in itself constructed. So while you say ‘he brackets and reduces these universal idealities to more fundamental constituting processes in subjective consciousness’, I say it’s more than just subjective, in the sense of pertaining to an individual. They are necessary structures within consicousness itself, not yours or mine. Which is why it is still a form of transcendental idealism

I think there is a residual platonism in Husserl’s transcendental subjectivity. For Husserl, the transcendentally reduced ego is self-identical , purely present to itself. This isn’t a constituted meaning, it is presupposed by Husserl. But it is important to distinguish what is necessary in an a priori sense from what is not. There is a major difference between the self-identity of the transcendental ego as subjective pole, and the constituted ideal identity intended as an object, including numerical identity and logical unity.

While on the one hand, number, as ‘unit’, ‘same sense different time’, has a genesis, its basis in the self-identity of the ego does not have a genesis. The self-identity of the subjective pole of consciousness is necessary, number and formal logic are not. The concept of number is an intentional synthesis. It is constituted for practical purposes. Numerical objectivity emerges from acts of collecting,grouping, distinguishing, iterating, unifying and identifying sameness across multiplicity.The prereflective “mineness” or self-givenness of consciousness is more primordial than the constituted concept of numerical identity.

Your position concerning formal and mathematical logic is much more Platonic than Husserl’s. Contrary to Husserl, you treat these as necessary a priori objective rational forms. This position is closer to Neoplatonism, Augustine, rationalist idealism and Kantian transcendentalism than to post-Hegelian approaches like pragmatism, hermeneutics and phenomenology.

@Wayfarer

And another point is that zero was never something that could be encountered. It is the conceptual placeholder par excellence.

Husserl considers zero to be a secondary and derivative mathematical concept For him plurality is more primordial than abstract unitary number. The experience of “twoness” is phenomenologically richer and more originary than the later abstract formalization of “1” or “0.” The concept of “two” has a special status because it emerges directly from the experience of collecting distinct items together into a unified multiplicity.

A solitary object is first simply “this.” Only within the context of possible plurality does “one” become numerically thematic. Zero is even more derivative because it depends upon a sophisticated conceptual operation, the representation of an empty multiplicity or null collection.
Zero is therefore highly mediated and symbolic compared to primitive acts of collective apprehension.

The larger point is that number is not a necessary construction, and it is conceivable that at some point in the future, mathematicallogic will not be required for further scientific and technological
progress.

[Corvus]

@RussellA

For example, I see a red postbox. The experience of red certainly exists in the mind, but where is the philosophical justification that red exists outside the mind’s experience of it?

You don’t need philosophical justification to be able to experience a red postbox. Your direct apprehension can perceive it with the concept of red postbox.

Why are you worried about philosophically justifying your experience suddenly?

[tabemann]

I just made a thread on the topic, before I started reading this thread, but I will repeat here that math is not a mere human approximation of the physical world, but is fundamental to it, as all the physical laws that hold despite our best efforts to falsify them are ultimately rooted in math, and in many cases the math well preceded the observations despite having very little in the way of good reason to be true if math did not have a special place in the world. 4 + 1 cannot equal 3, for the simple reason that the universe cannot exist in any recognizable form with this being true.

The idea that math is merely a social construct is postmodernist gobbledygook put together by people with a poor knowledge of how the universe works, and I suspect a poor knowledge of postmodernism itself.

[Joshs]

@tabemann

The idea that math is merely a social construct is postmodernist gobbledygook put together by people with a poor knowledge of how the universe works, and I suspect a poor knowledge of postmodernism itself.

Which postmodernists would you say have a good knowledge of postmodernism?

[tabemann]

I’m saying that those who boil postmodernism down to “nothing is true, everything is subjective, everything is a social construct” are clearly following the stereotype of postmodernism without actually realizing that it is a stereotype.

[Wayfarer]

@Jay

I don’t think you mean that ideas (understood not as stream-of-consciousness events but as something closer to propositional content) are necessarily "the form that thought must take

Yes, that’s right. It’s based on the understanding that there are necessary truths.

@Joshs

Your position concerning formal and mathematical logic is much more Platonic than Husserl’s

And I’m not afraid of owning it.

[Jay]

@Wayfarer

@Jay

I don’t think you mean that ideas (understood not as stream-of-consciousness events but as something closer to propositional content) are necessarily "the form that thought must take

Yes, that’s right. It’s based on the understanding that there are necessary truths.

Good – you’re saying that it’s the truths that are necessary, not that consciousness must necessarily make such a move. The logical forms are not “constitutive” of consciousness in that sense, consciousness being much broader.

[Wayfarer]

@Jay

Good – you’re saying that it’s the truths that are necessary, not that consciousness must necessarily make such a move. The logical forms are not “constitutive” of consciousness in that sense, consciousness being much broader.

Where is truth to be found outside the knowing of it? Truth is not endowed by the mind, but recognised by it. Seeing is fundamental to the grasp of ‘that which is’. And ‘that which is’ is not the subject of isolated propositions, the pedagogical trope of ‘this is an apple’ and what not. It is realised through participatory knowing.

[Tom_Storm]

@Joshs

The larger point is that number is not a necessary construction, and it is conceivable that at some point in the future, mathematicallogic will not be required for further scientific and technological
progress.

A tantalising idea I’d like to hear more about some time.

[Tom_Storm]

@Count_Timothy_von_Icarus

One could be a lot more technical and specific with this, but I wanted to point out an interesting issue here. If truth is always “truth within a tradition/language game,” then we face the problem that traditions outside the modern Western paradigm reject this very statement. So is it “true for them” that they are not so limited?

I guess the tension here is between truth always being “true within a tradition,” and this itself requiring a particular metaphysical tradition to assert. Quietism about metaphysics or ethics works the same way. It isn’t a presuppositionless conclusion, and indeed doesn’t make much sense at all on something like an Augustinian view of the sign and language. It is, historically, and outlier.

Thanks for your thoughtful response. Yes, all you say is fair and, for my own part, I used language like “beyond” because that matches how we generally describe things. I spent the 1980s with the Theosophical Society, so I was exposed to a range of framings.

Yes, “truth within a tradition” for me often reads as, “here’s a fence we have put around some territory, and we will confine our discourse only to what lies within it.” I don’t believe in any presuppositionless philosophy; everything has some kind of foundational thinking, even as it disputes foundations.

Philosophy is about many things. For some of us, it is more about a generalist survey of themes and some of what people have held over time and what they are saying now. I’m not particularly allergic to the current era and don’t hold the view that “we took a wrong turn at Albuquerque”, as Bugs Bunny used to say. These days everyoen seems to hate the enlightenment.

@Count_Timothy_von_Icarus

Basically, if all traditions are true for themselves, then the post-Enlightenment tradition is false outside its limited confines, even in its own terms. Hence it faces the challenge of finding a way to assert itself beyond the very confines it has set for itself. The “groundless ground” cannot simply be assumed, on pains of a dogmatist fideism, and so it is argued for from broader metaphysical and anthropological assumptions. But then, these function as at least something of a “ground” that can be challenged.

There are certainly philosophers like Hilary Lawson who would hold that all eras of philosophy and even science are wrong and that we will never get to truth, reality, or whatever the current God surrogate might be. But what we can do is provide workable interventions in the world using models that will eventually date and be replaced. Something doesn’t need to be true to work. Lawson rather charmingly even holds that his own views are no doubt erroneous.

I think Mww’s got a point here:

@Mww

I’m perfectly happy with the notion that our particular relational form of intelligence is the grounding of logic, in keeping with the thread title, and logic itself, in its turn, merely that intellectual construct following from it, by which is represented in judgement, the validity of those relations.

Then it’s off to the philosophical rodeo…

The part about the rodeo seems insightful. Although sometimes it can seem more like a conflagration or a freakshow.

@Count_Timothy_von_Icarus

I guess the tension here is between truth always being “true within a tradition,” and this itself requiring a particular metaphysical tradition to assert. Quietism about metaphysics or ethics works the same way. It isn’t a presuppositionless conclusion, and indeed doesn’t make much sense at all on something like an Augustinian view of the sign and language. It is, historically, and outlier.

I’m sure there are several ways actual post structuralist thinkers would deal with what you have set out here. I wish there were more around so we could showcase some of their thinking.

I suspect most postmodernists would agree that it might be impossible to escape metaphysics and that their ideas are not meant to float above history. The real disagreement is whether our thought must rest on some final, stable foundation to avoid incoherence, or whether human understanding can remain contingent, revisable, and historically situated, etc, without collapsing into meaninglessness or relativism.

[Banno]

@Jay

This question shouldn’t be confused with a genetic question about how humans came to adopt the laws of logic – did we start counting rocks and develop logic, or did the logic lightbulb go on and so we started counting rocks? An interesting question, no doubt, but not the question raised here.

There’s a genetic fallacy common to any explanation of logic or mathematics in evolutionary terms. An idea’s genesis usually has no bearing on it’s truth.

There’s also the possibly benign circularity that understanding evolution requires logic.

What is clear is that counting rocks already involves applying a coherent grammar. And in the end, that’s what logic is - keeping what we say consistent.

On the limits of language, Your approach is cogent; we do more with words than merely state what is the case.

[Tom_Storm]

@Banno

On the limits of language, Your approach is cogent; we do more with words than merely state what is the case.

Since you are back and perhaps agree with the Count on some philosophical matters, what is your response to the below? This is a repudiation of the logic of post-structural thinking, which I suspect you also view with some asperity.

@Count_Timothy_von_Icarus

I guess the tension here is between truth always being “true within a tradition,” and this itself requiring a particular metaphysical tradition to assert. Quietism about metaphysics or ethics works the same way. It isn’t a presuppositionless conclusion, and indeed doesn’t make much sense at all on something like an Augustinian view of the sign and language. It is, historically, and outlier.

Basically, if all traditions are true for themselves, then the post-Enlightenment tradition is false outside its limited confines, even in its own terms. Hence it faces the challenge of finding a way to assert itself beyond the very confines it has set for itself. The “groundless ground” cannot simply be assumed, on pains of a dogmatist fideism, and so it is argued for from broader metaphysical and anthropological assumptions. But then, these function as at least something of a “ground” that can be challenged.

This seems to claim that if truth is only valid within each tradition, then the Enlightenment tradition would be false outside its own framework and therefore fail by its own standards. But I don’t think this follows, because “truth within a tradition” does not mean a view becomes false outside it, only that standards of truth are always shaped by some historical/cultural framework.

[Tom_Storm]

@tabemann

The idea that math is merely a social construct is postmodernist gobbledygook put together by people with a poor knowledge of how the universe works, and I suspect a poor knowledge of postmodernism itself.

Is anyone saying that?

A defender of postmodern thinking wouldn’t usually claim that maths is “just made up,” so that feels like a bit of a straw man. The more incisive point is that maths is a human practice shaped by language, history and abstraction, rather than something we access from a neutral, “God’s-eye” standpoint. That doesn’t mean that 3+3 will stop being 6, or turn maths into some arbitrary plaything of human subjectivity, what it just says is that meaning and use depend on shared rules and practices. So the debate here isn’t about whether maths works, but about whether it is discovered as a fully mind-independent structure or developed through the ways we model and organise experience. This is complex thinking and beyond my simple minded survey of ideas.