True mathematics takes philosophical intuition. 5+5 is 5 and 5 and we call it ten. But that is naming, not adding to equal something. Mathematics is a process, not just an identity game. I don't know how a computer does computations if it became alive but it would be another species so we couldn't really know anyway

of course, intuition frees us from the baseless dichotomy of the act and the concept. Recourse to intuition overlays the dichotomy with universals that have not yet become integrated with our subjectivity.

Once the intuition is fully ‘subjected’ such as “we do addition to…” then we are fully back in the dichotomy again. But without a doubt the recourse to intuition is essential to mathematics.

Explain further why act and concept might be opposed

To compute is to enact, which aims ultimately to destroy the concept as its opposite. — kudos

Au contraire, over many years I have found that computation enriches and supports concepts. :roll:

To compute is to enact, which aims ultimately to destroy the concept as its opposite. In our day by day reality we polarize computation (act) and concept (theory), such that there are institutions devoted to research and those that create consumer products. — kudos

This is a linear perspective of what is a multi-dimensional relation, polarised as abstraction. Computation as act refers to minimal variability and Concept as theory to maximal variability - the qualitative limitations beyond which a ‘concept’ cannot be defined.

In our day to day reality, the act of creating consumer products must be informed by the research, or risk creating a product without a consumer. In this sense, computation can refer to minimal adjustments only, through to redefining properties of the product or the consumer - ie. the range of qualitative variability in the concept/theory.

Conversely, it is in the act of creating products intended for consumers that continually ‘enriches and supports’ theoretical research, as describes. To create a consumer product is not to destroy the research, but to challenge its accuracy.

@Gregory I'm a little confused, are you trying to say that computation and the theorems and axioms of Mathematics are opposed, or that in our society we don't seek to reify that opposition? That computation enriches and supports concepts is as if to say that you believe them to be to some extent different or separately defined ideas, which is really how I interpreted that; is that true?

To a certain extent what we really call 'computation that is not conceptual' occurs when we are told that two things are mutually related and we have a natural need to see this for ourselves. Most rigorous students of mathematics will require some form of proof. But I argue that proof is not so separate from what we consider as computation. When we think of the meaning of the word 'proof,' associations come to mind of testing, demonstrating or approving. In some ways what renders those concepts valid is that they can be shown, so much that this showing exposes the conceptual relationship.

This is why we don't learn simply by being told that the relationships of mathematics are true but are given our own problems and examples in which to demonstrate that the relationship to a certain extent is part of an abstract whole with it's context joining with it, and that we only separate the two in a sort of contingent manner.

Working on math problems is computation. What does this oppose? It is concept as act. I don't know how this relates to technology

@Gregory I am taking it that you disagree that in our lives there is this type of opposition I’m referring to? Developing a consumer product requires knowing various concepts it’s true. However, few companies are developing products by investing in ‘reinventing the wheel’ when they can just as easily use an off-the-shelf model. Those models are developed by companies who invest heavily in building new concepts but usually don’t directly implement them into products for mass production.

So more and more we work in such a way that the idea is that there is one entity whose ‘job’ it is to develop the ideas and another that implements them. It’s more of an analogy to computation than anything; in ideal form the implementer sees a ‘black box’ —not of course how it would practically happen — that they need not understand anything else but the output for the given input. It’s just one example.

Are you trying to say that I’m simplifying my observation that as a whole Western civilization has built this dichotomy through it’s activity, or are you saying the dichotomy itself is oversimplified as an absolute fixed idea?

I'm unclear as to what problems this is causing

To commit to polarization would make the concept less and less real, as its computation became easier and easier it would require less and less intervention of mind. — kudos

If you could give a specific example, your post would be more clear. As it is, I can't figure out what you're saying.

The op sounds like Hegelian marxism to me

Well imagine a perfect programming language so easy to use every citizen could create any program they wanted no matter how complex by simple computations without having to know much about programming. What would be the long term effects of having these types of programs? Would you say it would promote a deeper experiential understanding of the mechanics and interrelationships within those functions not to have any experiential interaction with them any more? Certainly it could, but do you think it would?

certainly I owe most of what I know about philosophy to others, but we’re here to do philosophy and that’s not easy having to avoid using others’ methods and ideas to some extent. I’d prefer not to directly credit other writers in the forum because I’ve found it tends to be less creative that way; if you’re accusing me of plagarism, it was not my intention at all to say all this came solely from my own mind. But if you want to discuss those writers’ and their bearing on this topic please be my guest.

We all get our ideas from giants

Well imagine a perfect programming language so easy to use every citizen could create any program they wanted no matter how complex by simple computations without having to know much about programming. — kudos

Like COBOL, "Common business-oriented language," hyped in the 1960's as a way to let business people write their own programs without the need for professional programmers?

What would be the long term effects of having these types of programs? — kudos

The fantasy would fail, just as it did for COBOL, graphical programming, and every other "non-programmer" programming paradigm ever hyped. You could do your homework and write an article on the history of failed approaches to the idea of programming without programmers.

Would you say it would promote a deeper experiential understanding of the mechanics and interrelationships within those functions not to have any experiential interaction with them any more? Certainly it could, but do you think it would? — kudos

Not only don't I think it would, but we have six decades of actual real-world experience that the idea doesn't even work. It turns out that you need programmers to write programs. COBOL became a success only because professional programmers used it. Business people never did.

But how would higher-level tools to let nonspecialists write programs enable a "deeper experiential understanding?" Does driving an automatic transmission give you a deeper experiential understanding of how transmissions work? Does flipping a light switch give a deeper experiential understanding of power generation and distribution? Of course not. The higher-level the interface, the less actual understanding is involved.

The entire purpose of high-level abstractions is to relieve the end user from the burden of understanding what's going on under the hood. If you want someone to understand how software works, they should program in assembly, not high-level languages. You go down the stack, not up, in order to understand what's going on. You go up the stack to get things done without the need to know what's going on.

None of this his anything whatsoever to do with your OP, which seemed to be about the distinction or dichotomy between programming and mathematics. Here you're talking about methods of letting non-programmers write programs, an idea with six decades of abject failure behind it. [I'll concede spreadsheets as the one known success. Maybe simple SQL queries executed by business people, though the organization still needs to employ an army of database administrators]. You didn't explain your OP at all.

Most rigorous students of mathematics will require some form of proof. But I argue that proof is not so separate from what we consider as computation. — kudos

For most mathematicians proof is separate from computation. But one can go down the rabbit hole of computerized proofs if one is so inclined. For me, I use programs I have written to gain insights into problems I pose for myself. For example, if a number of computer examples imply a certain idea is not true, I will adjust my thinking, and move in another direction.

I think your ideas of proofs and computation are suspect.

Does driving an automatic transmission give you a deeper experiential understanding of how transmissions work? Does flipping a light switch give a deeper experiential understanding of power generation and distribution? Of course not. The higher-level the interface, the less actual understanding is involved.

Here we can see clearly the dichotomy, so if it were unclear before it should be very much clearer now. In our day to day life we have light switches and power generation as separate entities. In the mind we have it organized that way as well. Our subjective relation to technological means conditions us to believe in things that do and things that make do. Shouldn’t it make sense that we think of Mathematics in the same light? After all, we all use Matlab/Octave/etc. Nobody wants to compute a giant integral that will take all day.

This type of reasoning is tempting but can be fallacious, for the reasons previously explained. The concepts of mathematics are most commonly acknowledged as valid through proof; proof that heavily involves the form of computation. We can only create once we have seen for ourselves that the dualism was never wholly and fully mutually exclusive. If you had never heard of power generation perhaps the best way to prove it to you might be to use the switch, at least as an aide as opposed to persuading you by recourse to theories of electron interactions that haven’t been observed and haven’t been synthetically proven from prior knowledge. Those theories are like light switches to the subject of what that switch means to us as human beings.

Here we can see clearly the dichotomy, so if it were unclear before it should be very much clearer now. In our day to day life we have light switches and power generation as separate entities. — kudos

Programmers know that distinction as interface versus implementation. It's not a particularly deep idea. If you swapped out a coal-fired power plant for a nuclear one, the operation of the light switch would not change even though the underlying implementation is completely different.

In the mind we have it organized that way as well. — kudos

Well yes, civilization is composed of layers of abstractions.

Our subjective relation to technological means conditions us to believe in things that do and things that make do. — kudos

It's unavoidable. You can't master auto mechanics to drive a car, and power generation to turn on the light. You are stating everyday commonplaces as if they held some kind of deep insight.

Shouldn’t it make sense that we think of Mathematics in the same light? — kudos

Sure, and we do. We take theorems as given without necessarily caring about the centuries of hard work it took to develop the insight to prove the theorem. It's human progress. You don't have to invent concrete to lay down a highway.

After all, we all use Matlab/Octave/etc. Nobody wants to compute a giant integral that will take all day. — kudos

You seem to be confusing the computation aspects of mathematics with actual mathematics. Possibly you're not overly familiar with the latter.

This type of reasoning is tempting but can be fallacious, for the reasons previously explained. — kudos

Yes but you're the only one committing the fallacy. You talk of Matlab is if it were a stand-in for actual mathematics. And it's not clear what fallacy you are talking about. It's not a fallacy to use a light switch. It's just an example of a user interface, just as a web browser frontends the entire global communications infrastructure of the Internet.

The concepts of mathematics are most commonly acknowledged as valid through proof; proof that heavily involves the form of computation. — kudos

I'm guessing that you haven't seen much math, because once again you conflate mathematics with computation. Some proofs involve computation, but most don't.

We can only create once we have seen for ourselves that the dualism was never wholly and fully mutually exclusive. — kudos

Yeah ok. Whatever point you are trying to make is deeply unclear, and muddled by your lack of specific experience with mathematics, as opposed to computation.

If you had never heard of power generation perhaps the best way to prove it to you might be to use the switch, at least as an aide as opposed to persuading you by recourse to theories of electron — kudos

But the operation of a light switch proves nothing to anybody about power generation. The entire purpose of a light switch is to relieve the end user of the burden of even thinking about power generation.

interactions that haven’t been observed and haven’t been synthetically proven from prior knowledge. Those theories are like light switches to the subject of what that switch means to us as human beings.
15 minutes ago — kudos

Buzzwords and word salad. You are saying nothing. Your exposition is devoid of meaning. Feel free to convince me otherwise.

You seem to be making a big deal out of the fact that there are interfaces and implementation. Which is fine, if trivial. But your attempt to connect the idea to mathematics falls flat, since you think mathematics is computation. And you haven't made any point about it in any case.

ps -- I'm not giving you a hard time just to do that. I can not understand what you are saying, and the parts that I do understand, are wrong. I'm challenging you to be more clear.

Yes of course computation and proof aren’t the same thing, but to prove involves a lot of showing, that has a lot in common with computation. Most mathematicians start to prove something to themselves first by carrying it out and seeing if the results are as expected. We are not seeking a mindless computational model but we seek to carry out computation to expose something. An example from Euclid:

If in a triangle two angles be equal to one another, the sides which subtend the equal angles will also be equal to one another.

Let ABC be a triangle having the angle ABC equal to angle ACB; I say that AB is also equal to AC. For, if AB is unequal to AC, one of them is greater. Let AB be greater; and from AB the greater let DB be cut off equal to AC the less; let DC be joined. Then, since DB is equal to AC, and BC is common, the two sides DB, BC are equal to the two sides AC, CB respectively; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC will be equal to the triangle ACB, the less to the greater, which is absurd. Therefore AB is not unequal to AC; it is therefore equal to it.

In this proof Euclid employs some computation of a number of prior theorems of his own to demonstrate the relationship. Who knows, maybe that’s even how this theorem was proven in the first place.

This type of reasoning is tempting but can be fallacious, for the reasons previously explained. The concepts of mathematics are most commonly acknowledged as valid through proof; proof that heavily involves the form of computation. We can only create once we have seen for ourselves that the dualism was never wholly and fully mutually exclusive. — kudos

Your confusions look to stem from thinking there is a problem with dialectics. Yet reasoning depends on being able to divide the world in a way that allows it to be reduce to a model - a rational system of general rules and particular instances, or deductive theory and inductive confirmation.

So maths has its general rules - its algorithms. Proofs show that the algorithms are sound according to various reasonable-seeming axiomatic principles. There are even more general ways to test some particular algorithmic generality!

And then you can test an algorithm by running it with actual measurements, actual data, actual numbers instead of generalised variables. You can plug the particular values into the general statement and make a further judgement about whether the computational result seems sound when matched against the reality of whatever it purports to be modelling.

So your muddles start by wanting to reject the dichotomies at the heart of any rational modelling exercise. They are in fact the essence of the intellectual enterprise. It's the same for maths, science and philosophy.

My intent wasn’t to claim that there is no difference and only unity, so if that was what came across it must have been miscommunicated. Yes, what you say is true, and the fact that you included computation in your definition of proof only goes to show that it is not quite so different and separate from the Mathematic concept. However, your statement that,

… reasoning depends on being able to divide the world in a way that allows it to be reduced to a model.

is where our thoughts depart, because I’m not sure how you mean the word ‘model.’ And the world does not need to be divided for reason to exist; that is, if we take division to mean creating separate mutually exclusive parts from a whole. Take reference to post-Newtonian physics (an area I admittedly don’t have a great deal of experience with), wherein many new and interesting discoveries have taken place in which divisions in reality — as you call them — have been blurred; space, time, mass, acceleration, etc. A model is something man-made and man-invented that is fashioned in the likeness of something else. But on the contrary, much of what constitutes reason could be attributed to factors beyond the reach of the individual.

The points you raise are fair but also already incorporated into what I say.

My position is Peircean (CS Peirce). So the dichotomous division of things is only to create the separations that then allow the third thing of their interaction. This is the basis of a holist metaphysics.

And then - again as argued by Peirce - modelling may be a human practice but it is also completely general as the logical process of semiosis. We don’t have a free choice about how to model as the essential reasonableness of a logical relationship is something which even the Cosmos can’t avoid in developing its own concrete state of being.

So humans can construct models of reality anyway they choose. They can live according to magical or animistic thinking. But as soon as they start down the path to a dialectical logic, they are embracing the same symmetry-breaking logic of physical existence itself. It is the only route to evolving complex order as we find either in our models of particular physical phenomenon, or in physics as a general metaphysical phenomenon.

This is why maths proves to be “unreasonably effective”. The process of its own development apes the constraints that self-organised consistency places on any form of uncertainty - informational or material.

Maths of course has its own ideas about its metaphysics. It is torn by a reductionist dilemma about whether to call itself an arbitrary modelling exercise or a revelation of Platonic necessities. Folk get very passionate about which side to bat for.

My point is that Peirce in particular offered a foundation that absorbs both horns of the dilemma to leave the Hegelian synthesis. The arbitrary and the necessary are the division that must emerge into the light to allow for the third holistic thing of them standing in an interesting variety of relations to each other.

Maths enjoys its game of playing off absolute necessities (axioms) against absolute arbitrariness (x = pick any number). And in constructing two exactly opposed extremes, it makes itself a large enough model of a rational world to encompass a world that is in fact rationally organised.

So it is all connected. There is a world to model because it has general organisation plus arbitrary detail. Physics works because it models the world as laws and measurements. Maths works because it enshrines that same division at a level so abstract it feels possible to talk about all possible worlds.

Embrace the dichotomy and move on to find why triadic holism is what works when it comes to rational inquiry.

Physics works because it models the world as laws and measurements. Maths works because it enshrines that same division at a level so abstract it feels possible to talk about all possible worlds. — apokrisis

Physics works in a certain way and with certain limitations. The limitations are imposed by the fact that physics begins with certain presuppositions that make both it and maths possible, but those presuppositions remain unexamined by it. Even as physics moves beyond the notion of materiality and naive objectivty , it retains the idea of the object as persisting presence to itself. This makes possible duration and extension , which in turn make possible counting, measurement, calculation. But the enduring thing-form-pattern is an idealization. As an idealization, it is quite useful
within certain limits as a way to anticipate our world, but it’s presuppositions are profoundly leas useful in making sense of human behavior, particularly the relation between affectivity, cognition and action.

But as soon as they start down the path to a dialectical logic, they are embracing the same symmetry-breaking logic of physical existence itself. It is the only route to evolving complex order as we find either in our models of particular physical phenomenon, or in physics as a general metaphysical phenomenon. — apokrisis

Again, a Peircian dialectical logic is useful for physics in its present form, but at some point it will recognize the need to move beyond this, as many in philosophy and psychology already have.

In this proof Euclid employs some computation of a number of prior theorems — kudos

By computation do you mean reasoning?

but those presuppositions remain unexamined by it. — Joshs

Nonsense. The history of physics shows a continual revision of the suppositions in exactly the way I describe. Newton comes along with one mathematical framework that embeds a set of particular symmetries. Then Einstein comes along and shows how that classical dynamics is just a special case of an even more general symmetries (needing even less in terms of those particular presuppositions).

The way forward has thus been clearly marked for many decades. Okun’s cube describes how all the more particular physical schemes must eventually arrive at a quantum gravity theory that successfully generalises all three Planck constants - c, G and h.

So you can challenge the game plan. And there is a whole academic industry in that. But also there is a reason why physics thinks it has got a grip on the way to formulate its ground suppositions, and even better, how to attain ever greater generality by eliminating the need for as many of them as possible. The correctness of this approach is proven by its experimental success.

it is quite useful within certain limits as a way to anticipate our world, but it’s presuppositions are profoundly leas useful in making sense of human behavior, particularly the relation between affectivity, cognition and action. — Joshs

Now you are talking about the grounding of life and mind science. And I am the first one to say that physics - of the Newtonian kind - is inadequate to the task.

Again, a Peircian dialectical logic is useful for physics in its present form, but at some point it will recognize the need to move beyond this, as many in philosophy and psychology already have. — Joshs

The irony there is the Peircean view is quite the other way around. It goes from the psychology of cognition to a description of the material world as itself a semiotic system. So it is as anti-Newtonian as you can get. But it also turns out to predict the informational turn that physics had to take once it encountered the dialectical marvels of quantum theory.

My point is that Peirce in particular offered a foundation that absorbs both horns of the dilemma to leave the Hegelian synthesis.

Out of curiosity, why is it a dilemma?

Out of curiosity, why is it a dilemma? — kudos

Because folk see dichotomous opposition as a logical contradiction rather than a relation of logical reprocity.

Nonsense. The history of physics shows a continual revision of the suppositions in exactly the way I describe. Newton comes along with one mathematical framework that embeds a set of particular symmetries. Then Einstein comes along and shows how that classical dynamics is just a special case of an even more general symmetries (needing even less in terms of those particular presuppositions). — apokrisis

I have no doubt. But even with all these revisions there are still core presuppositions going back to Galileo and Descartes that have not been challenged within physics itself , only outside of physics , in particular by Husserlian phenomenology and Heidegger.

Heidegger traces the origin of empirical science to the concept of enduring substance.
“Mathematical knowledge is regarded as the one way of apprehending beings which can always be certain of the secure possession of the being of the beings which it apprehends. Whatever has the kind of being adequate to the being accessible in mathematical knowledge is in the true sense.
This being is what always is what it is. Thus what can be shown to have the character of constantly remaining, as remanens capax mutationem, constitutes the true being of beings which can be experienced in the world. What enduringly remains truly is. This is the sort of thing that
mathematics knows. What mathematics makes accessible in beings constitutes their being. Thus
the being of the "world" is, so to speak, dictated to it in terms of a definite idea of being which is embedded in the concept of substantiality and in terms of an idea of knowledge which cognizes beings in this way. Descartes does not allow the kind of being of innerworldly beings to present itself, but rather prescribes to the world, so to speak, its "true" being on the basis of an idea of being (being = constant objective presence) the source of which has not been revealed and the justification of which has not been demonstrated. Thus it is not primarily his dependence
upon a science, mathematics, which just happens to be especially esteemed, that detennines his ontology of the world, rather his ontology is determined by a basic ontological orientation toward being as constant objective presence, which mathematical knowledge is exceptionally well suited to grasp.* In this way Descartes explicitly switches over philosophically from the development of traditional ontology to modem mathematical physics and its transcendental foundations.”(Being and Time)

We have provisionally taken into consideration
the question about "being-in-time." It is easy to see that we cannot deal with it as long as we have not clarified what "time" is and as long as we have not clarified what "being" means, as it relates to a thing, and as it relates to the human being, who exists.
The question is exciting specifically with regard to natural science, especially with the advent of Einstein's theory of relativity, which established the opinion that traditional philosophical doctrine concerning time has been shaken
to the core through the theory of physics. However, this widely held opinion is fundamentally wrong. The theory of relativity in physics does not deal with what time is but deals only with how time, in the sense of
a now-sequence, can be measured. [It asks] whether there is an absolute measurement of time, or whether all measurement is necessarily relative, that is, conditioned.* The question of the theory of relativity could not
be discussed at all unless the supposition of time as the succession of a sequence of nows were presupposed beforehand. If the doctrine of time, held since Aristotle, were to become untenable, then the very possibility of physics would be ruled out. [The fact that] physics, with
its horizon of measuring time, deals not only with irreversible events, but also with reversible ones and that the direction of time is reversible attests specifically to the fact that in physics time is nothing else than the
succession of a sequence of nows. This is maintained in such a decisive manner that even the sense of direction in the sequence can become a matter of indifference. “

The irony there is the Peircean view is quite the other way around. It goes from the psychology of cognition to a description of the material world as itself a semiotic system. So it is as anti-Newtonian as you can get. But it also turns out to predict the informational turn that physics had to take once it encountered the dialectical marvels of quantum theory. — apokrisis

Pierce’s model of firstnessn shows the same limitation as that of physics. It tries to model change and transformation by beginning with intrinsicality and immediate self-presence and processing from there to relation and change. Instead, difference and transit must be considered primary and the intrinsic and self-present drives from it.

“Let us begin with the body as we just re-conceived it, rather than the traditional order in philosophy which begins with perception first. Then relations or interactions are added, and then language and thought.
For example, Peirce called sensations "firstness." They are assumed to be opaque: What I mean by opaque is exemplified by bits of color, smell, or touch. These are just what they are. Examine them as deeply as you might, in color there is just color. (See Moen, 1992, for a reading of Peirce in which firstness is not opaque.)
When reality is assumed to have opaque things at the bottom, then any relations among them must
be external relations, brought to them. Nothing within a color or a smell inherently insists on its being related to some other color or smell. There is nothing within a color, but color. To relate these opaques, some force or movement must impact on them. Peirce called it "secondness."
Then, thirdly come the relations of language, thought, and universals, kinds, conceptual forms. This order stems from the seeming opaqueness and unrelatedness of the sense-data of perception.Anything more complex must be brought to them, imposed on them from the top down.
Empiricism depends on adding our procedures to nature, "torturing nature" as Bacon said. You must always bring something to the sensations because they have nothing within themselves.

Merleau-Ponty moves far beyond all this but his "first flesh" and "second flesh" still retain something of the old order of first and second. Let us upset that ancient order altogether. If one begins with the body of perception, too much of interaction and intricacy has to be added on later. Perception is not the bottom. There is an implicit interactional bodily intricacy that is first—and
still with us now. It is not the body of perception that is elaborated by language, rather it is the body of interactional living in its environment. Language elaborates how the body implies its situation and its next behavior. We sense our bodies not as elaborated perceptions but as the body-sense of our situations, the interactional whole-body by which we orient and know what we are doing.” Gene Gendlin

can you clarify a little more, I’m not sure I’m totally following. You mean if you were to say, ‘x is red,’ someone may think this is invalid because it is a determination? These would be kind of misinterpreting Hegel’s work pretty badly though, wouldn’t you agree?

By computation do you mean reasoning?

Yes, I do mean that in a certain sense too. Do you suggest it is an example of reason and no computation?