One of the branches of western philosophy is metaphysics, which asks about the nature of being and the world. It is the extension of what was once known as natural philosophy. Modern science is empirical natural philosophy. Instead of trying to answer questions about how the world is the way it is by thinking about it, it makes hypotheses and tests them experimentally or observationally. The late twentieth century was a time when physics, specifically string theory, drifted back towards metaphysics. String theorists attempt to answer questions about our reality by constructing theories that are mostly grounded on mathematically aesthetic principles. I have no real problem with string theory per se, except in its claim to be more “fundamental” than other branches of physics. As I have argued before (e.g. here), there are fundamental concepts at all energy and length scales.
What I will argue here is that we have been misguided in trying to reunite metaphysics with science. As I have argued before (e.g. here and here), it is not even simple to define what is meant by “fundamental laws” or a “theory of everything”. If our universe can be approximated arbitrarily accurately by a computable one (yes I know some of you disagree with this assertion), then what constitutes the underlying theory? Is it the program that generates the universe? Is it the most simple description (in which case it is not computable)? Or is it something else?
While metaphysics as science is a dead-end for me, metaphysics as mathematics is ripe for very interesting insights. Instead of asking directly about “our” reality, we should be asking about hypothetical realities. We should be doing philosophy of science and metaphysics on artificial worlds. This would then be a controlled situation. Instead of speculating about the underlying laws of our universe, we can simply specify a given set of properties in some hypothetical or simulated universe and probe the consequences. We can do this at arbitrary levels as well – universe, multiverse, meta-multiverse and so forth.
I think ironically that doing such a thing would give more insights into our universe than what we are doing now. For example, if we started to investigate what types of simulated worlds would generate life, it may inform us more about how probable life exists in our universe ( as well as force us to come up with some quantitative definitions for life) then sending out space probes (e.g. see here). It could also give us an idea of how variable life can be. We seem to be stuck on looking for biochemical life. Well maybe there are electromagnetic plasma life forms out there. If all it took to generate complex life-like objects was a nonlinear rule that didn’t blow up, then the answer to why our universe seems so well-tuned for us would be that any old rule would have worked although it would give entirely different looking life forms. Also, if we thought more about how we could generate or detect any type of consciousness in a simulation, that may help us better understand the consciousness we have.
7 thoughts on “Metaphysics as mathematics”
Interesting thoughts and it reminded me of (fellow Swede) Max Tegmarks work (also before I saw the multiverse link where it is mentioned). From a mathematical point of view, the approach seems quite natural. I would say that it might even be one of the basic principles of mathematics development: pick a some phenomenon in some “concrete” representation. Reformulate and make it generalizable, ie possible to formulate in a very general setting. Then slowly add structure until you pretty much have a general representation that work like your original concrete one. Ie think of R^n, generalize to a topological space, add structure until you have a locally compact Haussdorf space or something like that.
Doing the same thing with “the universe” as your basic concrete object is an interesting idea. A basic first thought could be: “what would an “almost naked” universe look like, one where hardly anything would happen. Or perhaps one should start with the opposite. A so general universe that almost everything will (ie is allowed to) happen.
Here’s a conjecture: There are only two possible consistent models of a dynamical system that can carry out its own replication. This is far beyond a quine.
It is hard to find others who seriously think on these topics. I do agree with Max Tegmark about the fundamentalists of math to the nature of the universe but mathematical analysis is always map. However, there is a language of the universe like a song and we know this because all paths currently being explored tell us to look at the universe from a Fourier perceptive rather than a spacial perspective. The secret to all of this is for the mathematical and physics community to get off there afraid butts and finally take seriously addressing the Consciousness issue. It is key to taking any next steps in physics, mathematics and even metaphysics. All of these are just maps to for the purpose of helping consciousness, express through our conscious awareness, realize itself as a being. Few realized being have talked about this in a modern way but Ram Dass and Alan Watts have many things to say that will be verified in the math eventually if we stop ignoring the glaring issue of consciousness.
No way. We cannot guide our experience by hypothetical scenarios.
That would just increase our already big dissonance.
We must accept that either existence is mathematical and determined fundamentally or is not. And since our current comprehension tell us that at least in part is. Then it is determined and mathematical.
If existence is mathematical and we developed a physical model that complies with math principles, then metaphysics must be ruled by mathematics we just haven’t figured the pattern yet. And at some point it will be the convergence of the metaphysical mathematical model and the physical mathematical model that will bring us the unification model.
Westerns are terrified about mathematical metaphysics. That would be the end of no personal accountability.
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Which mathematics would you propose for developing such a thing?
I think you could do a lot with just well known methods of applied math but the opportunities are endless.