Thanks for the lengthy reply.
What's true is this. Computationalism s the claim that the mind (or the universe, in a more grandiose version) is a computation. Now those neuroscientists who are computationalists believe that thoughts are informational processes; and those who aren't, don't.
I hope you will agree with me that this is a true statement about the states of belief of neuroscientists, and that this is NOT a settled issue by any means. If nothing else, if mind is a computation, what's the algorithm? When you bring me some computer code and say, "Here, this is how you implement an mind. It's 875,356 of C++. Some grad student figured it out," then maybe I'll believe you. Till then, the burden of proof is on you. — fishfry
I'm definitely not claiming computationalism - or at least not Turing machine computation as you seem to suggest. The mainstream neuroscience view - since Sherrington's "enchanted loom" or Hebbs's learning networks - is some kind of neural net form of "computation".
And more to the point, it is mainstream to emphasise that the brain is involved in informational activity, not merely biochemical activity. Otherwise why is neuroscience interested in discovering the secrets of the neural code, or brain's processing architecture? It knows the biophysics of what makes a neuron fire. But how that firing then represents or symbolises something with felt meaning is the big question. And that can only be approached in terms of something other than a biochemical materialism. It demands a semiotic or information theoretic framework. Which in turn has already considered Turing computation and found it not the answer.
So broadly speaking, neuroscientists think thoughts are informational processes and not biochemical events. At the same time, they don't think the brain is literally a Turing machine or programmable computer. That might be a helpful analogy, like calling the eye a camera. But just as quickly, the caveats would begin.
There are important things in the world that are not computations. Like mathematical truth. — fishfry
Computers are machines. They are devices that construct patterns. So yes, of course, human minds seem to operate in a fundamentally different fashion. We can grasp the whole of some pattern. We can understand it "organically" as a system of constraints, rather than as an atomistic construction.
Our abductive or intuitive approach to reasoning begins with this ability to see the whole that "stands behind" the part. We can make inferences to the best explanation. And then, having framed an axiom or hypothesis, we are also quite good at deducing consequences and confirming by observation.
So when it comes to mathematical truth, that is what we think we are doing. We notice something about the world. We then leap towards some rational principle that could "stand behind" this something as its more general constraint.
Turing machines are really bad at making such a holistic generalisation. Neural network computers are our attempt to build machines that are good at implementing this precise inferential leap.
However if you DON'T believe that mind is a computation, you no longer necessarily have substrate independence. I hope you would grant me this. — fishfry
Yeah. I don't claim complete substrate independence. But then my "computationalism" is a semiotic or embodied one. The whole point is that it hinges on a separation which then allows an interaction.
A Turing machine does not self-replicate. A Turing machine does not have to manage its material flows or compete with other TMs. But a living thing is all about regulating its physics with information. So an independence from physical substrate (an epistemic cut) is required by life and mind. But only so as to be able to regulate that physics - bend it in the direction which is making the autopoietic wholeness that is "an organism".
The only way to do that is to execute the algorithm on physical hardware. That is a physical process involving an input of energy and an output of heat. Something a physicist could observe and quantify. — fishfry
Yes, you can measure one side of the computational story in terms of entropy production. But how do you measure the other side of the story in terms of "negentropy" production? The fact that your computer runs either hotter or colder doesn't say much about whether its eventual output is righter or wronger.
Where does the algorithm itself live? Well it lived first in Euclid's brain. But isn't Euclid's mind a physical process? His abstract thoughts are physical processes, and his thoughts can be implemented as physical processes. But I don't see why we need dualism. — fishfry
We are labouring the point. If you really can't see the difference between syntax and semantics by now, things are likely hopeless.
You keep talking about the physical
events as if they are the informational
processes. Of course a neuron or a transistor or a membrane receptor or a speedometer can be described in terms of their "physics". But it is hardly the level of description that explains "the process" which we are interested in.
To reduce functional or informational processes to atomistic material events becomes a nonsense. Especially for true computationalism. The only time we are interested in the physics of a logic gate is when it doesn't behave like a logic gate - that is when it has some uncontrolled physical process going on.
So algorithms are extreme mechanistic dualism in fact. You don't even have to run a programme for it to "have a result". The result could only be different if the physics of the real world somehow intruded, And then we would say the computer had a bug. It over-heated or something.
And maths is kind of like that. We imagine it as transcendent and eternal truths - things that would be true without ever needing the reality of physical instantiation. Pure information. It is crazy to talk of Euclidean maths as existing in some geezer's long dead brain.
Jeez that sounds a little mystical. You're saying that Euclidean geometry is the midpoint between elliptic and hyperbolic geometry. Yes this is a true mathematical fact, but it is not mystical. — fishfry
Why do you interpret that as a mystical statement? My point was that it is not a mystery because it is what you would expect from principles of physicalist symmetry. If every kind of difference gets cancelled (as the negatives erase the positives) then what you are left with is the mid-point balance. It would be natural to expect "flatness" as the emergent limit state.
So I'm not going to try to think about this. You have to start somewhere, and perhaps we could agree that for purposes of this conversation, there is the number pi and there is a rock, and that we don't have to consider their quantum relationship to each other, if any. — fishfry
Well it is your choice to ignore what we know to be fundamental in preference for what we know to be emergent.
I can't agree that it makes for good metaphysics. And I think you just want to avoid having to make a better argument.
To a number theories, integers are as real as rocks. I doubt Wiles would agree that he's written a work of fiction. Or even give the matter any thought at all. — fishfry
Fine. The philosophical issue here is not the pragmatics of mathematical research. And I even agree that mathematical research - in being an informational theoretic exercise - would deliberately insulate itself from such fundamental metaphysical issues. Maths doesn't really want to even concern itself with geometry - the physical constraints of space - let alone with actual materiality, or the constraints of energy, the possibilities of change. So - as institutional habit - integers are as real as rocks.
Except they are then ... ideas? Constructs? Thoughts in the head?
You seem to want it both ways. And that winds up in Platonism.
That is why my own position is the semiotic one where the integers are the ideal limits on materiality. That is a formula of words that both accepts a strong difference and a strong connection between the two sides of the semiotic equation. Information is real if it is causal. And being an actual limit on material freedom is pretty clearly causal.
Ooh you are on shaky ground here! Gödel told us that math is NOT an informational process! No algorithm can determine the truth of mathematical statements. — fishfry
See earlier where I spoke about abductive reasoning and our ability to make inferential leaps. Gödel validates my approach here. The failure of logical atomism is the solid ground for the holist. It is why a semiotic approach to reality is justified.
Yes but you're going all woo-woo about a trivial mathematical fact. Well not trivial, non-Euclidean geometry was a big deal when it was discovered. — fishfry
You mentioned pi. I am just highlighting how the usual woo-woo aspect - the fact that there is just this "one number" picked at random out of all the numbers on the number-line - masks a bigger story. The woo-woo evaporates when you see there is a "material" process that picks out a value for "being flat". Two kinds of possible curvature had a mid-point balance. Pi is a number that emerges due to something more holistic going on. The fact that it emerges "right there" on the number-line is not some kind of weird magic.
It is even easier to see with other constant like e that are directly derived from growth processes. There the contrasting actions that produce the emergent ratio are in plain sight. It is funny that e should be 2.71828. But then that becomes obvious when it is realised that growth always has to start from some thing that is just itself 1. There is no reason to think of e as anything but natural after that.
You and Kant. He was wrong. You're wrong. Euclidean geometry's not special. It's just something we seem to have an intuition of. — fishfry
But I am not Kantian, except in a loose sense. I'm Peircean in the way Peirce fixed Kant.
And I'm arguing flatness is special as the mid-point of opposing extremes of curvature. It has physically important properties too. Only flat geometries preserve invariance under transformations of scale. That is a really important emergent property when it comes to things like Universes.
It's true that it's the ratio of a circle's circumference to its diameter is pi, but if it were 3 or 47 or 18, you'd be asking why it's that? It's just what it is. The only really interesting thing is that the ratio is always the same no matter what size the circle is! That's the real breakthrough here, that was a great discovery once. [Edit - You made the point that this is only true in Euclidean geometry. Point taken]. — fishfry
And as I repeat, it is very important metaphysically that absolute scale invariance only appears at a particular numeric value of pi. That is how a Universe is even possible.
So you are focused on the triviality of pi being given some particular position on the number line - look guys, its 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408 ...
And that is what makes folk go woo. It seems both weirdly specific and weirdly random. There seems no natural reason for the value.
But it's a ratio derived from the radius being granted as the natural unit. Let's call the radius 1. Let's get a grip on this weird thing called curvature by starting with the "most natural part of the story" - a line segment. That gets to be "1" on the number-line.
Well, as I say, once mathematicians woke up to the fact that flatness was a rather special case of curvature, and once physicists in turn woke up to the fact that scale invariance was essential to any kind of workable Universe (its called rather grandly the cosmological principle), well, maybe it is the ratio that should be called "1". A straight line segment is only a natural unit in the context of an already flat space which supports unlimited scale transformations. It depends on the emergent fact of parallel lines or infinite rays being an actual possibility.
You are really into pi mysticism. What I mean is, what you wrote here is pretty word salad-y. I have to repeat, I only picked pi because it's a good candidate to make the point that numbers are abstract and not physical. I could have made the exact same point with 3, but people have a harder time understanding that 3 isn't any more physical than pi. — fishfry
I am being anti-mystical in pointing out the very physical basis of pi as a number. It is a ratio that picks out a critical geometric balance.
The number 3 is trivial by comparison. Well there are physical arguments for why the geometry of universes are optimal if they have just three orthogonal spatial directions. But 3 as a member of the integers has no numeric specialness by design. The special or natural numbers are 1 and 0. We see this in the symmetries captured by identity operations. There is something basic or universal when we hit the bedrock that is a symmetry or invariance.
You would call it a mystical fact perhaps. I see it as quite reasonable and self-explanatory.
* So to sum up:
- You are arguing from a computationalist point of view, but I'm not sure what point you are trying to make. Looking back I see that now. Even if I agree with you that mind is computation, there are still numbers and rocks. I possibly did not follow your argument. — fishfry
Nope. At least not your notion of computation as Turing machine/programmable computation.
I take an information theoretic perspective. And more specifically, a semiotic one. In technology terms, neural networks come the closest to implementing that notion of computation.
And numbers vs rocks is a distinction that relies on a classical metaphysics - one in which the divide between observers and observables does not present an epistemic difficulty. The epistemic cut - the necessary separation of the information from the physics - can be treated as an ontological fact.
So my positions on both "mind is a computation" and "reality is classical" are the same. Semiotics starts from the view that there is no fundamental ontic division of observers and observables. But that is also the division which must emerge via some epistemic cut. It is the basis of intelligibility. And even the Universe can only exist to the degree it hangs together in intelligible fashion.
Hence why maths tends to be unreasonably effective at describing the Universe. Or being in general.
- You are wrong that math is a computation. And like many computationlists, you underestimate or ignore the importance of non-computable phenomena in the world. Remember even Tegmark distinguishes between the mathematical universe hypothesis and the computable universe hypothesis. Computationalism is a very strong assumption. — fishfry
Labouring the point still, but I'm sorry. I'm not a computationalist in the sense you are hoping for. Indeed, that was what I was accusing you of. You seem to believe reality is a machine. An account of physical events is sufficient.
But yes, you also seem to say the opposite. This is a symptom that your metaphysics is "commonsensical" and not well thought out.
* Mathematicians do math, not philosophy. My sense is that the vast majority of working mathematicians never give any thought to philosophy. When an engineer is building a bridge, do you want him spending his time contemplating the fact that there is no difference between him and the bridge? Or do you want him calculating the load factors according to state of the art engineering principles? — fishfry
Again, bully for mathematicians. Bully for engineers. Bully even for most physicists (as very few are employed in frontier theory construction).
But it is curious to be complaining about metaphysics where metaphysics is appropriate.
And so far you haven't put forward any clear exposition of your own epistemic position, let alone given a clear justification for it. You just hoped to be able to label me with some obviously weak ontology that I spend most of my time arguing against.