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
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
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
What would be the long term effects of having these types of programs? — kudos
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
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
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. — kudos
In the mind we have it organized that way as well. — kudos
Our subjective relation to technological means conditions us to believe in things that do and things that make do. — kudos
Shouldn’t it make sense that we think of Mathematics in the same light? — kudos
After all, we all use Matlab/Octave/etc. Nobody wants to compute a giant integral that will take all day. — kudos
This type of reasoning is tempting but can be fallacious, for the reasons previously explained. — kudos
The concepts of mathematics are most commonly acknowledged as valid through proof; proof that heavily involves the form of computation. — kudos
We can only create once we have seen for ourselves that the dualism was never wholly and fully mutually exclusive. — kudos
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
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
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.
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
… reasoning depends on being able to divide the world in a way that allows it to be reduced to a model.
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
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
but those presuppositions remain unexamined by it. — Joshs
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
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
Out of curiosity, why is it a dilemma?My point is that Peirce in particular offered a foundation that absorbs both horns of the dilemma to leave the Hegelian synthesis.
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
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
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