Oh, I see. Apologies. I thought you were saying enactivism is false because if it meant 4 + 1 = 3, it must be bonkers. I suppose, in theory, different worlds might afford different outcomes, though that is highly theoretical and difficult to comprehend given how deeply embodied we are within our current situation. Perhaps over time the world will change so dramatically that it begins to resemble another reality altogether. Would that affect mathematics? I’m innumerate, so I can’t say. But coming back to logic, perhaps our forms of reasoning could shift if our thought takes on more assumptions from postmodern philosophy.
But it is correct in the elementary school math.
4 +(-1) = 3
Nice. And there’s so often a way to find an outcome.
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I believe that Enactivism is true.
But as you say, postmodernism may shift what we now think is logical.
Postmodern philosophy
According to David Novitz, philosophical postmodernism challenges the notion that truth can be achieved
Perhaps this includes our truth that 1 + 1 = 2.
Yes, and 11 + 2 = 1, on the clock. But piling up rocks suggests ( to earthlings like us, for now ) the normal addition of positive integers.
Both of my three friends are good at math.
Numbers are just a language for describing the objects and motions.
In some other languages, their alphabet letters are used for numbers instead of the standard numbers.
Yes, negative things exist in mathematics, but do negative things exist in the world?
Does mathematics mirror the world?
It is supposed to. You need to use your imagination sometimes for more abstract and complicated situations or parts of the world to mirror, describe or interpret them with math.
For instance, -1 rock is not for a rock existing, but it is the situation where it needs 1 rock, but it is missing, where it needs to be but absent, or taken away by someone.
Hence it is not logic, but imagination and understanding which is required for knowing the world and reality.
Enactivism is good.
But lets not conflate two different things.
The postmodern challenge is primarily aimed at contingent truths dressed up as necessary ones.
1+1=2 is a different kind of thing entirely.
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……
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Logic is grounded in ontology. That is why Banno says:
We have a choice of ontologies and the logic follows from the ontology in a way which is coherent, but the form of coherency is determined by the ontology.
This is somewhat misleading. It is metaphysics which ties us to logic, and the relation is one of necessity, because once we have derived the logic from the ontology we can turn around and apply those principles of logic onto the relation with the metaphysics which is believed in, and which grounds those principles. If the principles of logic do not adhere to what is necessitated by the metaphysics which is believed, the logic can be designated as unsound.
The issue which arises, is that if we like the appearance of (eloquence, facility of application, etc.), and therefore choose, a specific form of logic, then we must also accept the ontology which grounds it. Refusal to accept, and to believe in the truth of, the grounding ontology, renders the use of the logic as unsound.
Therefore one’s choice of logic does, in a very real way, tie that person to a particular metaphysics, as a relationship of logical necessity. The logic which one chooses must be consistent with the metaphysics which one believes in, or else the use of the logic will be unsound.
For example, set theory logic is grounded in Platonist ontology. To use set theory, and not believe in Platonism is an unsound use of the logic.
For some thinkers logic is ontology is logic. No gap between inquiry and world. The “whole story” about the world includes this ever-on-the-way hole story.
Don’t want to sidetrack the thread too much, but is this so obvious ? I somewhat object to set theory but have a take on Plato that would allow his work some distance from it.
Partially, although I would say the singular focus on stepping ‘beyond’ or ‘above’ is more of a post-Reformation/Enlightenment framing projected onto other traditions.
On the view that we are already “inside” our own isolated subjectivity, interpretations, language, theories—what have you—any awareness of what is ontologically prior to these is going to require “stepping out of/above them.”
@Banno has already made that point many times in this thread; it’s a pretty common one with its own arguments in favor of it. However, what I would note is that this view still requires a particular metaphysics of language, meaning, appearances, etc. to substantiate. It is not simply that all past traditions missed these conclusions because they were “too dogmatic;” the issue is that they reject the assumptions of the later tradition. Various versions of the “trapped inside” view are dominant today because its assumptions are fairly endemic in post-Enlightenment Western thought (and from being “trapped inside,” you can obviously progress to “nothing exists outside…”). However , as a matter of historical fact, these assumptions are also quite unique to the tradition that comes out of Latin Christendom’s Reformation and its various theological debates, even if its biggest advocates are how “secular” (also a modern Western category as used today).
The core differences would probably be, very generally:
A. The earlier tradition doesn’t see contemplative knowledge as sui generis (a strong natural/supernatural and nature/grace dichotomy itself being unique to the modern West). The higher unitive intellectual faculty isn’t only being engaged in ecstatic moments, but whenever thought has any content at all. This faculty is simply more potent in higher degrees of revealedness.
B. This is because being is not opaque. So appearances are already suffused with the “higher” reality from the beginning. One doesn’t need to “step outside” anything because one is already in contact with reality.
The spatial metaphor is being used in an equivocal way by dispute traditions then. For the post-Enlightenment thinker, traditions with a higher noetic faculty speak of the “higher” in terms of ascending above the tools of discursive reason (which is for them, all reason) to “stand outside” history, culture, etc. This has to be the case because these represent barriers of a sort; rather than the means of nuptial union with being—the various “representations” or “interpretations” are rather always what is known. They are not transparent or participatory.
Whereas, the higher in the older sense is “higher” because it is closer to its source, more ontologically full. It is more pure, a fuller revealedness and union. It is more of a realization in this sense. For example, Hindu sages describe the realization of non-dualism as something that was always true “on the inside,” (Maya is ultimately illusion) and Dante discovers that the entire cosmos, even Hell, was always in a sense “*in *the mind of God,” (not outside it) and so self-knowledge of the self-as-divine is both the ascent, and also a revelation of what was true the whole time.
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.
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.
I don’t know if there is a “most true way.” I would say it’s more that one has to be clear what one is talking about, else broad claims about the intelligibility of being, its logos, get confused with claims the classical logic is built into physics (or something like that), and we risk talking past one another.
I don’t think ancient people like Aristotle tried to account for logic. His work is more like a person turning to view the apparatus of thought, identifying elements of it. Later, the Stoics appeared. They viewed logic as a kind of divinity, but I think their view of logic would best translate into contemporary language as natural law. When Newton reached for natural law to explain why apples fall toward the earth, he was using an ancient Stoic scheme.
So we really have two different things here: logic and natural law. They aren’t equivalent, and though logic informs us about some aspects of natural law, natural law doesn’t inform us about logic, so logic is the master.
The alternative to seeing logic as built into the universe as a sort of guiding hand, would be to see it as innate. We were born with these imperatives. I don’t think there is any clear path from labelling logic as innate to explaining it by virtue of evolution. A hint as to why that’s the case is in the fact that we’re using it while we’re trying to explain its origin. Whatever we come up with will comply with innate logic. So the problem is that we don’t have a vantage point on it from which to speculate.
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If you paid someone £100, then it is -£100 to your bank balance.
If you returned 1 book from 5 books you bought, then it is -1 book from total 5 books you bought.
You need imagination and interpretation of the world situation via simple apprehension (not logic) to be able to use math.
It is not negative things, but the things which paid for, and the things returned and things missing etc, the negative numbers stand for.
Enactivism is the idea that the evolution of an organism is determined by its environment, with the consequence that any ideas of a thinking organism are also determined by its environment. For example, a thinking organism living in a world where if one rock is added to another rock then there will be two rocks will inevitably evolve the logic that 1 + 1 = 2.
Postmodernism is a scepticism towards ideas that are promoted as universally true rather than contextually true. Therefore, if the logic that 1 + 1 = 2 is doubted as a universal truth, in favour of being a contingent truth, then even what one sees with one’s eyes will be doubted, including that adding one rock to another rock will result in two rocks.
Gaslighting, the manipulation of someone into questioning their perception of reality (Wikipedia - Gaslighting), may be said to be one consequence of this postmodernist scepticism.
In maths, 1, O and -1 exists.
In the world, 1 rock may exist. If 0 rocks exist, then we have the logical problem that something that doesn’t exist exists. If -1 rocks exist, can this be philosophically explained.
It seems that mathematics is fundamentally incapable of being able to mirror the world, with the consequence that it is fundamentally unable to reveal anything about the structure of reality itself.
You need to use imagination to be able to tell, that 0 rock means, no rock exists.
If -1 rock exists, then it means a rock is missing at the place where it should be.
With use of imagination and interpretation, math mirrors reality very well. No philosophy or logic need to be involved at this simple apprehension stage.
Perception supplies you with the added concepts on the objects and reality, to which you apply imagination and interpretation.
Kids with no knowledge of logic or philosophy do very well in math just by using their imagination and interpretation of reality using direct apprehension and perception.
I was going to post something similar. In Kripkean terms, we’re equating “referent” with “thing”. Of course, this is conceptual - and may, or may not, map to something ontological. But it seems to me to be a reasonable basis for an ontological theory: that existence consists of things.
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