141–150 of 179 posts
I have liked intuitionism from the very moment I first heard about it. I often entertain the idea that all the patterns we observe are merely things that match our capability of understanding. This could explain the "unreasonable effectiveness of mathematics in the natural sciences". It may also help to guide us away from the "why is there something rather than nothing" problem. If existence is total chaos, then we a…
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Well, we try to discover math. That’s straight forward?
Again, definitional issues are critical here. I can make up all sorts of math that isn't really "discovered", it's more "invented". Most of it won't correspond usefully to the physical universe. See e.g.: https://plato.stanford.edu/entries/formalism-mathematics/ : > "mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitmen…
The older I get the more I feel like pursuing these trains of thought will lead to mental instability and sadness. We model the world and the world follows the model and the exceptions add to our refinement of the model and that’s what makes it true. Perception and reality are yin and yang and that is about as deep as my philosophy needs to go here
I started being much happier about philosophy in general once I realized a very important truth: "unlike hard sciences, philosophy only affects philosophers" For example the toplevel article says things like "independent existence in an objective reality".. this sounds important, right? Perhaps depending on the truth of the intuitionism, we might discover some facts about real world? Nope. The whole "is intuitionism…
It's now widely known that an intuitionistic proof has computational content (through the curry-howard correspondence)
Those things have a real world impact
>mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality In the context of the Godel Incompleteness Theorem I have always found it difficult to reconcile mathematics w/ an objective reality. A mathematical system would simply be incapable of completely encompassing objective reality.
What is the opposite of an objective reality?
I guess the opposite would be something like solipsism though.
This is post-modernism applied to math. It concludes in solipsism. Since the mind and its mental constructs are a part of the objective reality, they will end up describing aspects of objective reality. If they don't, they break down, become chaotic and incomprehensible to those grounded in the objective reality.
I was initially surprised to read this because when I hear Intuitionism, I hear Intuitionist Logic. But IL doesn't have anything to do with denying objective reality; it can use facts on the way to proof. So I don't really know why Intuitionism is so much more adamant about denying constructive reality, or why it's thought to "give rise" to Intuitionist Logic, which at this point seems like a totally different thing.…
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The offer of 'objective reality' as the antithesis to solipsistic mental constructs is exactly the naivety that give both of these impotent families of epistemology any continued sway. Both bad, both wrong, and the crowd swings from one to the other, and at each arrival, anew recognizes the flaws of the mode and turns back.
Thank god a philosopher has arrived to tell us we're all wrong. Being so wise, you must have the correct answer for us. What's it going to be today "you're not smart enough to understand my genius solution" or "enlightenment can't be taught, only achieved"?
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> mustn't this in turn depend on some pre-existing regularity (i.e. order) in the universe? Yes. And such order exists within the observer, the mediators. We are measuring instruments. Scales are bound to the ruler and not to what’s being ruled. So mathematics represents order only in as much as there are people to validate it. Should all rulers be broken and forgotten, then there’s no measure at all. This is the sam…
Does your "principle which allows order" presume the existence of space and time, and more specifically the ordering of time? I would say that in a universe without time, "cause and effect" have little meaning. I think I lost your train of thought when you say that numbers are qualities of Unit. Does your universe involve only "Unit", or are there other principles at play as well?
[1] https://www.reddit.com/r/holofractal/comments/6wnekw/this_be...
Because humans never experience anything in and of itself, but only the output of the interaction between sensory data and a brain, literally everything is purely the result of human mental activity.
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> math describes (fragments) of reality; This is only possible if math itself is real. Note that I am not saying that a particular axiom system like Euclidean geometry has some sort of "real physical manifestation". No, what I am saying is that logical reasoning itself is real. And our reasoning about logical reasoning is certainly real as well, even if logical reasoning itself happens in very abstract form. Math its…
I like to draw a distinction between real and ideal. I insist that math is ideal. it models reality ideally. this distinction is important because otherwise we mix together something, and the ideas and concepts (e.g. symbols and rules) we use to describe and model said something. the game is not real. people playing the game are real, the game getting played is real. the game on its own as may be described in symbols…
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I agree with you here, at least in the sense that the system is definitely not physical. You didn't answer my question, though. Is it real?
All information that exists is physical, encoded in a physical substrate. Beads in an abacus, holes in a punched card, distributions of charge in a computer memory. Hypothetical information that is not encoded physically cannot be causal. A book or computer program that have not been written can have no effects. Only information that exists in a physical encoding can be causal, by virtue of it’s physicality.