What's Your Philosophy of Mathematics?

[apeiron]

Maybe one brain "figures out the recipe" for math, while another "figures out the recipe" for foreign languages, or music, or whatever. It doesn't mean these different endeavors are themselves dichotomies, but can be successfully analyzed in terms of a rich enough set of dichotomies to choose from.

True, but this is talking about the divergent variety rather than the convergent deep structure. You do of course have both because what polarities make possible is the emergent spectrum that emerges inbetween (as various mixtures of what gets separated).

Again, you want to argue that models are just arbitrary ideas that we project onto the data. So if my chosen idea just happens to be "dichotomies" then I can go in and carve up some phenomenon in convincing fashion using as many dichotomies as it takes.

I agree that modelling does have an arbitrary, free, basis. We can try whatever works. But then it becomes interesting that only certain ideas seem to work really well, even universally. These ideas look to be the way nature actually works - although we can never "know" that, just observe it to be likely.

Reductionism (that metaphysical mix of atomism, determinism, monadism, mechanicism, local reality, effective causality, etc) is one general idea that works really well.

And then there is the complementary tradition of holism which is about dichotomies, hierarchies, top down causality, indeterminacy, etc. Which works better when it comes time to tell the whole story of course!

Would a dichotomies approach be stronger if all the brain's architectural divisions could be reduced to just a single description? Yes, it would certainly seem less arbitrary (a projection onto the data) and more like the deep structure of the data.

I would start out by saying we shouldn't expect a simple single answer because the brain is a product of both evolution and development. Development is free potential but evolution locks in past history. So the story on brain evolution is a complex interaction between accumulated design and the addition of new possibility (such as by creating new room at the top by expanding the cortex).

But if we step back to the purposes of brains, they are there to make decisions. To make choices. And how can you make a choice unless you have alternatives? And how can you make the most definite possible choices unless the alternatives are dichotomous - reduced to either/or, to a binary yes/no, like retreat/advance, attend/ignore, expected/surprising.

Again, you will probably say that intelligence is defined by having a variety of choices. But as I say, that describes the variety that emerges as a result of the deeper structure - the ability to break the world down by polarities.

My favourite example of the primitiveness of this is the flagella that drives a motile bacterium. Spin one way and the threads tangle, driving the cell forward. The bacterium can follow a chemical gradient, head towards a food source. But then reverse the spin and the threads untangle, the bacterium begins to tumble randomly. So if falling off the scent trail, the bacterium can switch to search or escape mode.

The asymmetry of choice - as determined/random - in a nutshell.

Yes, the power of the yin-yang symbolism again. I agree there is great merit in thinking along those lines. But is it Platonic in the sense that dichotomous juxtaposition is really what is happening, or is that just how we like to think about it?

I agree it is a legitimate question. And the default position will be "all models are the free creations of the human mind". We should be automatically suspicious of any jump from the epistemic to ontic.

But on the other hand, reality must actually have some kind of deep causal structure. It does not seem like an arbitrary bundle of happenings does it? It does seem to have a developmental history, a systemic and patterned materiality. So it is not impossible that our models of its deep structure could be essentially correct.

I have in mind an effect akin to sensitivity to initial conditions in dynamics-- a seemingly small difference is leveraged into an extremely different outcome simply because we don't recognize the significance of the difference.

The butterfly effect is not a good analogy for biological processes because that is dynamics unconstrained (the system is unpredictable even if deterministic because measurement error compounds exponentially).

The whole point of biology (and its use of languages to construct constraints) is that such dynamism is harnessed. Constraints are applied to channel what happens.

There would not be life/mind without this trick of being able to harness dissipation-driven dynamics. So this is why we can say what "math is". It is not some unpredictable consequence of blind evolutionary change, it is instead the very predictable development of the constraint machinery which in fact defines life/mind.

You want to argue that the brain could have evolved any old how. It's just one accident on top of the other. But this is old-style Darwinism (the "modern evolutionary synthesis" of the 1960s). Today you would talk about evo-devo, and this is based on the idea that there are in fact deep structural principles at work. Existence is based on the dissipation of gradients. Life/mind arise as informational structure that locally accelerates the entropification of the Universe.

So there is a deep general principle at work. But then also some happenstance about how things actually work out.

For example, life/mind arose on the back of one kind of language - genes to code for enzymes that could control dynamical chemical cycles. But then H.sapiens stumbled upon actual language - words to control the thoughts that determine our actions.

Was it Platonically inevitable that human grammatical language would arise? Would it have to happen on any planet where some kind of life/mind was happening in sufficient abundance - given enough variety, would some species have to luck into this structural attractor, this pre-existing, ready-waiting, niche?

Personally I would say there is a healthy dose of both - of both random luck and Platonic inevitability. The luck is down to the fact that brain evolution was not headed in that direction. The evolution of an articulate vocal tract - the imposition of a new kind of serial output constraint on vocalisation - looks a pretty chance direction for events to have taken. On the other hand, it was then a very short step for this exaptation to be exploited for symbolic/syntatic purposes. Once there was a species that could chop up a stream of sound into discrete syllables, the machinery for a new level of coding could be used for exactly that.

That is indeed a theme that runs through the different choices in the poll, but again none of those choices make sense in isolation-- math can't be a Platonic truth any more than a map can be a territory, but similarly a map doesn't mean anything unless there is a territory to map in the first place.

We seem to agree then. Because I am saying that maths is not monadically anyone kind of thing. Which is what the poll wants to make it.

And definitely this is all about modelling.

But then, modelling is dichotomous - not just in terms of the relationship between the map and the terrain, but even the map itself has the tension of an internal division.

Our mental mapping of the world divides into ideas and impressions, the theories or formal constructs that are a general inductive understanding, and then the measurements, or expectations, or predictions, that are the local deductive particulars.

Measurement is often claimed to be the objective part of the process of modelling, but of course it always remains some mind's particular impression (such as a reading on a dial, a number on a counter, etc). I know you favour the Copenhagen stance on these things!

So again, where does math stand in all this? It is caught up in the general business of modelling, so it is fictional, intuitive, constructive, etc, foundationally. But at the same time, it is trying to stand at one extreme pole of the modelling process. It is trying to go and stand over at the end of our most general possible ideas. It is trying to be a pure description of form. And then to the extent this division that emerges in our mapping is also true of reality, of the terrain, then maths is going to end up "Platonic".

As I say, this may yet be telling only half the story. But that can only be clear once the foundations of maths is actually clarified.

But are the interactions of the world really self-constraining as you imagine, or is that just how you make sense of them? We must not beg the question by building the Platonism right in from the start.

It should be clear by now that I would only argue for Platonism (the fact that reality has a deep structure which our modelling can hope to map) to the extent that observation appears to confirm it.

Yes, another dichotomy that is actually a unity-- the axiom/theorem dichotomy, but axioms mean nothing until they are used to make theorems that allow us to judge the axioms, and theorems mean nothing independently of the axioms that lead to them. It's material/form once again-- the axioms are like the Platonic forms, and their theorems are like the material, the flesh on the axiom's bones. We can't claim that if the axioms are Platonic, then so are the theorems they inevitably lead to, because we can only judge the truth of the axioms by their theorems, since attributing meaning to an axiom is a type of theorem, or consequence, of that axiom. The structure falls apart unless it is anchored at both the form and material end, so we cannot say that math is accessing truth of forms that are independent of the materials, nor can we say that math is a study of the materials without having underlying forms to axiomatize those materials.

Yes, I agree. You seem to have me now arguing for Platonic fundamentalism when I want to make it plain that Platonism can "exist" only as one of a pair of complementary bounds.

So maths is extreme because it goes as far towards Platonic rationalism as we can imagine going. Which is good because that then makes the other side of the equation, the need to measure the local material particulars of the world, a matchingly precise task.

The legitimacy of the maths is wholly dependent on empiricism as a result. If triangles in flat Euclidean space do not have angles that sum to pi, then the formal model is screwed.

for math is not the sound of one hand clapping, if you will.
Bingo, that's why I cannot feel the Platonic picture can provide the whole story.

Yes, maths goes to one extreme - tries to be the one hand clapping. And this works because it creates its own complementary extreme. It creates with equal decisiveness the idea of a local, particular, material measurement. The other hand needed to make some noise.

The maths comes to seem like it is "all subjective". It is a realm of ideal forms discovered rationally. And the measurements likewise come to seem "all objective". They are the brute material facts that exist out in the world.

Yet really, both formalised models and material measurements are only ever in our heads as part of the dichotomy of mapping.

This is just a restatement of Copehagenism (which followed from Bohr's shocked need to deal with a world that actually appears foundationally dichotomous - always at root complementary in nature).

The problem with the Copenhagen interpretation is then that once the simple mechanical view of causality had been shown to fail (at the extremes of its range), the choice was to reject then any chance of a "true" model of causality. The observation were whatever they were within whatever the framework of observation happened to be. It was all taken to be quite arbitrary, with no possibility of systematisation.

Yet in my view, a constraints-based approach to causality fits QM like a glove. Asking questions of reality can reduce its inherent uncertainty to the point it seems very certain - but cannot in principle eliminate all uncertainty.

You can see how these themes keep repeating. We spend so much time trying to disentangle epistemology from ontology - to form that crisp foundational dichotomy between map and terrain. And then we find that the two seem in fact deeply entangled.

In the realm of our minds, the maps are dichotomised into "subjective" rational forms and "objective" material measurements.

Then the bigger shock (perhaps). Out in the world, the terrain is also ontically dichotomised into its "subjective" forms and "objective" materials. Or rather, the self-constructing causality of global constraints in dynamic interaction with local degrees of freedom. A Universe that decoheres itself into structured being via some kind of semiotic or "self-observation".

So this would be where we differ.

I think we can develop a legitimate model of reality in which the ontology involves an epistemic aspect - the necessary decohering observer is made part of the entire system (in the guise of top-down constraint, the contextual information, a generalised environment). We can hope to make a map of the entire process.

But you would defend the more agnostic Copenhagen position where there is a map, and there is a world, and we can never say much more except that epistemology and ontology are fundamentally divided in this fashion. So the default philosophy is that modelling-associated activities like maths are arbitrary at the foundational level, even if useful in a pragmatic fashion.

As world views, we thus have naive reductionist realism, agnostic Copenhagenism, and constraints-based systems thinking.

I agree Copenhagenism is the correct default position - the place you have to retreat back to under pressure. But naive realism is a highly pragmatic choice. It works in the middle ground where humans mostly live. And systems thinking holds out the hope of getting "closer to the ultimate truth", to seeing the whole of reality within the one model.

 

[Ken G]

Very interesting post, it stimulates a lot of reactions on my part.

But if we step back to the purposes of brains, they are there to make decisions. To make choices. And how can you make a choice unless you have alternatives? And how can you make the most definite possible choices unless the alternatives dichotomous - reduced to either/or, to a binary yes/no, like retreat/advance, attend/ignore, expected/surprising.

That is a valid way to slice the choices our brains make, yet I would still argue it is how our brains think constructively about what brains do. The brain making sense of itself will model itself, but the model will, on purpose, take a projection and throw away what doesn't fit. It's a kind of template, the dichotomous analysis. The irony is, we can apply the same template to that analysis-- we can dichotomize, or unify, so we even have complementary choices around the issue of complementarity itself.

I think what happens is, each of our choices, taken to an extreme, tends to come "full circle" back to the seemingly opposite choice. Complete unity is too bland to convey meaning, while contrast is "crisp", as you might say. But crispness is a kind of intentional illusion, inventing distinctions out of the unity that underlies those distinctions-- nothing is ever actually crisp, crispness is not the way of the world. I recall a famous military general, I forget, who joked that he never retreats-- but sometimes he advances in an opposite direction. It was intended to get a laugh, but there is also a truth to it-- the attack/retreat dichotomy is invented from the unity of strategic military maneuvers, just as a cornered animal might lash out aggressively in what is actually a desperate attempt at escape, or a retreating army might actually be luring their pursuer into a trap.

A classic example of this "coming full circle" effect in philosophy is the rationalist/empiricist dichotomy. We all know that we combine mental analysis with sensory perception to make sense of our environment, but the rationalist emphasizes the mental analysis as the "truth" of the matter, while the empiricist emphasizes the sensory perception as the deeper arbiter of what is real. But if we take the empiricist approach to its logical extreme, we say that a sensory perception is not the light entering the eye, for light can enter the eye of a dead person-- the perception is the signal in our brain that is made when light strikes our retina. And it is not just the neuron that fires, for a neuron can fire even if we are distracted and fail to register the perception, it is a complex process going on in our brains that registers the perception. But complex processes going on in our brains are just what we normally call thought, and that's the seat of rationistic truth! So extreme empiricism is actually a form of rationalism, the crisp dichotomy disintegrates under the microscope.

Similarly, if we take rationalism to its logical extreme, we say that the mind is able to connect with truth, but the way we connect with truth is we perceive our own thoughts. Since our brains are also natural systems, presumably, then perceiving our own thoughts is also a form of empiricist truth, something that has a place at the table of reality simply because we perceive it to be there. These dichotomies we make as a useful tool are not actually true in any deeper sense.

Again, you will probably say that intelligence is defined by having a variety of choices. But as I say, that describes the variety that emerges as a result of the deeper structure - the ability to break the world down by polarities.

We agree that the variety is what is crucial, I'm just saying the way we break down that variety is itself a kind of simplified replacement. We write the digits of a number as a replacement for the number, and we can manipulate those digits in ways that mirror how numbers are manipulated, but the manipulation of a number is not entirely syntactic the way the manipulation of digits is-- the digitization does not replace the semantic meaning of the number, it is merely a placekeeper for it. I see dichotomies similarly, as placekeepers for the varieties, a useful labeling tool, but which does not actually capture the underlying variety-- that variety is irreducible, any syntactic construction of that variety is just a shell, like a robot programmed to mimic the actions of a human being.

My favourite example of the primitiveness of this is the flagella that drives a motile bacterium. Spin one way and the threads tangle, driving the cell forward. The bacterium can follow a chemical gradient, head towards a food source. But then reverse the spin and the threads untangle, the bacterium begins to tumble randomly. So if falling off the scent trail, the bacterium can switch to search or escape mode.

The asymmetry of choice - as determined/random - in a nutshell.

Yes, I like that metaphor a lot. I think it underscores the fallacy of "choosing sides" in any debate centered on a dichotomy (like "is life deterministic or random", when we find that life sometimes follows a deterministic scheme and sometimes a random one). I'm just taking that a step farther, and saying that even the dichotomy itself is not something we should commit to, for one such dichotomy is "embrace dichotomies vs. reject dichotomies." The moment we assert a dichotomy is true we find that taking it to an extreme causes it to be a circle rather than an axis, but if we use that logic to assert there is not that dichotomy we lose the analytical power of invoking it. I think there must be some truth to the idea that all analysis is judicious lying.

I agree it is a legitimate question. And the default position will be "all models are the free creations of the human mind". We should be automatically suspicious of any jump from the epistemic to ontic.

Indeed. We should also be suspicious there is any true distinction between the two, or that either of them even exists. Yet we must not completely reject Platonic thinking, for then we lose its analytic power. A map is a particular kind of lie, but a good map is a judicious lie that leads us where we want to go.

But on the other hand, reality must actually have some kind of deep causal structure. It does not seem like an arbitrary bundle of happenings does it? It does seem to have a developmental history, a systemic and patterned materiality. So it is not impossible that our models of its deep structure could be essentially correct.

I think that is indeed impossible. The problem is that if an atom cannot know itself, then neither can a huge and complex array of atoms. The only difference is the atom has not the required structure to invent a judicious lie, but the array of atoms has. That's the key shortcoming of pure reductionism, I agree with the systems perspective there.

There would not be life/mind without this trick of being able to harness dissipation-driven dynamics. So this is why we can say what "math is". It is not some unpredictable consequence of blind evolutionary change, it is instead the very predictable development of the constraint machinery which in fact defines life/mind.

I would agree, yet I would still call that a judicious lie. It's like when I tell a class that planetary orbits are ellipses, I know that I am lying, judiciously. Feynman said that science is a way to avoid fooling ourselves; I would add it is a way to avoid fooling ourselves that works by lying to ourselves judiciously.

Life/mind arise as informational structure that locally accelerates the entropification of the Universe.

And yet entropy, as an ontology, is a classic example of a judicious lie. The universe is in one state-- so always has zero entropy, formally speaking. But the concept emerges when we, as analysts, decide that we don't know that state, we know only a class of states that satisfy what we care about. We know not the territory/state, we know the map/class of states. So the concept of entropy is born-- the natural log of the number of states in the class. The map has entropy, the territory does not. But entropy is a mapmaker's key, one of the most judicious lies of all time that some feel underpins at the deepest level all of our understanding of nature.

For example, life/mind arose on the back of one kind of language - genes to code for enzymes that could control dynamical chemical cycles. But then H.sapiens stumbled upon actual language - words to control the thoughts that determine our actions.

An interesting point, the way one form of language gave rise to another. Yet I would say that DNA is not really a language, it is we who understand language who also understand DNA that way. A gene has no need for even the concept of language, so certainly has no need to participate in one. It is we who need to see the gene's action in that light, the judicious lie comes from us-- in fact, we invented judicious lying when we invented language.

And of course, even that last statement is a judicious lie about judicious lying, it can't really be true because humans cannot be separated well enough from language to say we invented it, for as you put it, as soon as we say we invented language, we find that DNA satisfies our meaning, but then DNA invented us, so we end up with one language inventing another, which tells us nothing about what language is or where it comes from.

Logic is no better off than language. If we say that logic is based on the true/false dichotomy, then I say it is based on a lie, albeit a very judicious one. So what do we do with logic when we see it as a lie that works? You could claim that a lie that works is not a lie, but I don't mean it is lie in the sense that something else would be true, I mean it is a lie in the sense that truth is something we just invented, and logic is its syntax. If we invented truth, then Platonic truth is a lie, but it is a judicious lie that allows us to invent the concept of truth in the first place. Truth requires a lie to even be possible, and the true/false dichotomy comes full circle.

Once there was a species that could chop up a stream of sound into discrete syllables, the machinery for a new level of coding could be used for exactly that.

Which raises another interesting question: what is the meaning of syntax? Syntax is supposed to be distinct from meaning, yet it requires a meaning or else we don't know how to use it in a sentence. We can't connect vocal patterns with DNA patterns unless we understand that the patterns represent something deeper. Another dichotomy comes full circle. And can whatever is the meaning of syntax be a Platonic truth about DNA and language, when we cannot even enforce a Platonic separation between syntax and semantics? The escape hatch is to recognize they are all judicious lies, all of them: syntax, semantics, language, DNA, the works.

We seem to agree then. Because I am saying that maths is not monadically anyone kind of thing. Which is what the poll wants to make it.

Yes, getting back on topic, we agree there. The poll is trying to get us to commit to a lie about mathematics that is not judicious because any of the choices either sell math short, or are grandiose and unsubstantiated wishful thinking. A more judicious lie about math is that it combines all those elements in a complex way, but of course if that were really true, then it would have to be true in some Platonic sense, which would make math Platonic, so the argument would come full circle.

As I say, this may yet be telling only half the story. But that can only be clear once the foundations of maths is actually clarified.

And I would say the very idea that math has foundations at all is another judicious lie. Math has attributes that let us recognize it, that's all we can really say because that's how we defined it ourselves. Everything on that list is like a hobo jumping a train simply because it is going in the same direction that they want to go.

It should be clear by now that I would only argue for Platonism (the fact that reality has a deep structure which our modelling can hope to map) to the extent that observation appears to confirm it.

But this isn't really any kind of confirmation, because it is our nature to frame our analysis of observations in those terms. We are looking into the mirror, not at something that transcends us. What observation could come out X if our way of understanding that observation is also something Platonic, or Y if our way of understanding it comes from us, when it is the outcome itself that we are trying to understand?

Yes, I agree. You seem to have me now arguing for Platonic fundamentalism when I want to make it plain that Platonism can "exist" only as one of a pair of complementary bounds.

That form of existence is probably pretty close to what I mean by a judicious lie, so perhaps we are not so far apart on this. I'm just adding that the complementarity is also part of the lie, as is seen by how it tends to come full circle if you take it to its extremes. The opposite poles are just directions, they don't exist as destinations because the destinations come full circle.

So maths is extreme because it goes as far towards Platonic rationalism as we can imagine going. Which is good because that then makes the other side of the equation, the need to measure the local material particulars of the world, a matchingly precise task.

Here I believe you echo a similar sentiment.

As world views, we thus have naive reductionist realism, agnostic Copenhagenism, and constraints-based systems thinking.

Yes, and I see each as a hat we put on when it serves us. Three different maps that each lie about the terrain in different ways, like a bus schedule, a road map, and a topographic map-- lies when regarded as the full story that become judicious enough to help us achieve our goals when not so framed. Like the poll itself.

I agree Copenhagenism is the correct default position - the place you have to retreat back to under pressure. But naive realism is a highly pragmatic choice. It works in the middle ground where humans mostly live. And systems thinking holds out the hope of getting "closer to the ultimate truth", to seeing the whole of reality within the one model.

Yes, there are different times when each flavor of falsification becomes the closest thing we get to a truth that does not, in fact, exist in the absence of falsification.

 

[apeiron]

The irony is, we can apply the same template to that analysis-- we can dichotomize, or unify, so we even have complementary choices around the issue of complementarity itself.

Is it an irony or instead a logical truth that for once is successfully self-referential? The set that now includes itself without contradiction?

But crispness is a kind of intentional illusion, inventing distinctions out of the unity that underlies those distinctions-- nothing is ever actually crisp, crispness is not the way of the world.

All of this is about limits and dynamics, so yes, actual crispness is never attained. It is just the bounding limit of a process.

If we come up with some standard metaphysical dichotomy like discrete~continuous, then the claim would be that these are the two extremes of what might be the case, and material reality would lie within these extremes. But it could never definitely attain either of them (because then it would become just perfectly one of these things).

I recall a famous military general, I forget, who joked that he never retreats-- but sometimes he advances in an opposite direction. It was intended to get a laugh, but there is also a truth to it-- the attack/retreat dichotomy is invented from the unity of strategic military maneuvers, just as a cornered animal might lash out aggressively in what is actually a desperate attempt at escape, or a retreating army might actually be luring their pursuer into a trap.

Proper metaphysical strength dichotomies have the quality of being asymmetric or orthogonal. So attack/retreat is a simple and thus unstable, because easily reversed, anti-symmetry. To go forward is just much the same as going backwards - an inverse operation.

But real dichotomies are reciprocal operations. It is a symmetry breaking across scale that leaves the two extremes as unlike as possible.

So again take a full-strength dichotomy like discrete~continuous, as might be illustrated by a dot marking a line. The dot is so infinitely small, it no longer even has dimensionality, whereas the line is infinitely large as a dimension. The relationship is an asymmetry, a really, really broken symmetry.

But complex processes going on in our brains are just what we normally call thought, and that's the seat of rationistic truth! So extreme empiricism is actually a form of rationalism, the crisp dichotomy disintegrates under the microscope.

Yes, as I say, mental processes are dichotomous in this way. Impressions build ideas and ideas form our impressions. Or in other words, empiricism is the basis for rationalism and rationalism the basis for empiricism.

This is the basis of CS Peirce's triadic metaphysics. Or models of the brain such as Stephen Grossberg's ART neural networks.

The mind starts off in the unity of ignorance - vague unformed potential - and then becomes organised by discovering structure in experience. In a newborn brain, visual pathway neurons will fire off to just about anything. Then quickly they learn to narrow their responses as higher level ideas (top-down constraints) develop.

These dichotomies we make as a useful tool are not actually true in any deeper sense.

Well they seem true both by observation and reason surely? Not all dichotomies would have to be true of course. But the ones that seem philosophically deep - such as discrete~continuous - do seem to be both what is fundamental about the world, and also self-referentially true in the logical sense.

From the rational standpoint, if things are not continuous then they must be broken up into the discrete. And if things aren't broken, then they must be continuous. All other possibilities are exhausted by these mutually exclusive universal concepts. The only third possibility is the unifying one - things are too vague for us to tell.

And then by observation, things are generally either discrete or continuous. When we actually stop to make particular material measurements, that is what we find.

I see dichotomies similarly, as placekeepers for the varieties, a useful labeling tool, but which does not actually capture the underlying variety-- that variety is irreducible, any syntactic construction of that variety is just a shell, like a robot programmed to mimic the actions of a human being.

Yes, there may be many varieties of dichotomies. But then that very statement is saying there is only the one underlying process - dichotomisation.

And again, there would be two levels of claim here. One that dichotomisation is the universal operation underlying epistemology, and then the stronger claim that it underlies ontology as well.

If the second is true, the "irreducible variety" of reality will have been generated by dichotomies (ie: symmetry-breakings).

I'm just taking that a step farther, and saying that even the dichotomy itself is not something we should commit to, for one such dichotomy is "embrace dichotomies vs. reject dichotomies."

As said, there is a consistent position here because holism and reductionism are taken to be mutually contradictory views of causality. So holism "rejects" reductionism - and in doing so, proves that it is a complementary truth.

Reductionism of course sees itself as the sole truth. Which is why it can only be ever half the truth.

You are quite right to keep pointing to the fact that dichotomies demand to be understood in a dichotomistic light. But that is a strength rather than a weakness. It is a logic that applies to itself with consistency.

A map is a particular kind of lie, but a good map is a judicious lie that leads us where we want to go.

Or another way of putting it is that a map tells the least amount of truth needed to do its job. The terrain has the complete information. A useful map represents what is meaningful by using the least possible information.

Maps don't actually lie. They are judiciously selective about the truth they represent. And less information results in more meaning.

Tor Norretranders wrote a good pop sci book based on this principle - The User Illusion.

Truth requires a lie to even be possible, and the true/false dichotomy comes full circle.

I know what you mean by lie, but it is misleading. As I say, the point of modelling, or maps, is to reduce the truth to a bare minimum - to discard as much information as possible so as to focus all attention only on what matters.

And my claim is that actual Reductionism is dichotomistic. But it wants to reduce too far by saying things are either/or. But even atoms require the matching "truth" of a void. You end up needing both, even though the claim is that only one "actually exists".

So the least truth you can get away with boils down to the "both" of a dichotomy. The simplest map has to be both the line that sketches the path, and the blank paper that symbolises all the rest that has been actively discarded. The information deliberately left out because it is just "noise".

But this isn't really any kind of confirmation, because it is our nature to frame our analysis of observations in those terms. We are looking into the mirror, not at something that transcends us. What observation could come out X if our way of understanding that observation is also something Platonic, or Y if our way of understanding it comes from us, when it is the outcome itself that we are trying to understand?

Well, if you frame your hypothesis in dichotomous fashion, you can reject one of the choices. So here, the choice is between the Platonic unity that would follow from the existence of deep structure, and the alternative of an unstructured variety - a mereological bundle.

If on observation the sum of the angles of triangles always measured differently, then you might suspect the hypothesis that a triangle was a Platonic truth.

I'm just adding that the complementarity is also part of the lie, as is seen by how it tends to come full circle if you take it to its extremes.

Coming the full circle is again a strength rather than a weakness here. Again, a true dichotomy is a difference that is broken across scale - it is the canonical local~global division of systems science or hierarchy theory. So what you call a circular relationship is in fact an interaction across scale. It is the fact that there is the bottom-up in interaction with the top down.

Just as I said about the easily reversibility of an inverse relationship, unless you have a scale difference, any symmetry breaking is only weak, unstable. But break across scale and things are far enough apart for their interactions to become interesting because they now look very different in kind. They are no longer going around in a tight circle that leads nowhere. The interactions are coming from opposing limits of scale.

 

[Ken G]

Coming the full circle is again a strength rather than a weakness here. Again, a true dichotomy is a difference that is broken across scale - it is the canonical local~global division of systems science or hierarchy theory. So what you call a circular relationship is in fact an interaction across scale. It is the fact that there is the bottom-up in interaction with the top down.

Just as I said about the easily reversibility of an inverse relationship, unless you have a scale difference, any symmetry breaking is only weak, unstable. But break across scale and things are far enough apart for their interactions to become interesting because they now look very different in kind. They are no longer going around in a tight circle that leads nowhere. The interactions are coming from opposing limits of scale.

I think we are largely in agreement about the importance of dichotomization in analysis, and the way seemingly opposite options tend to come full circle when pressed to their limits. We agree that a dichotomy is not "truth" in an either/or sense that one or the other extreme should be regarded as correct. This is relevant to the math poll-- if we juxtapose math as Platonic truth vs. math as arbitrary human construct, we might tend to expect math to have to be one or the other, for how could it be two opposite things at once, yet on further thought we see no difficulty at all in being two opposite things at once, since they are not actually "opposite choices" but more like "elements in opposition".

What I'm adding to this already somewhat controverisal view is an objection to the following stance. It might be said that the opposite poles of the dichotomy should be viewed as opposite destinations that could each have their own "Platonic truth", as it were, such that the real truth is some kind of mixture, like splitting time between a Winter and Summer home. But I'm framing those opposite poles as "judicious lies" (where "lie" is chosen to be somewhat melodramatic for effect more so than precision) because neither one actually exists at all-- their lack of an independent existence is revealey by pushing on each until they turn into the other. They break a symmetry, yet introduce a new one, an interchange symmetry, like in this Escher print: http://4.bp.blogspot.com/-btPpdTyzL3k/TdDwi8al6wI/AAAAAAAAABQ/qOeXVRlgN28/s1600/escher.gif The print gives the illusion of crispness, but a moment's reflection reveals the paradox behind that crispness.

Your point about rationalism and empiricism being responsible for each other is very much along the same vein-- I'm merely saying that this means neither of those concepts can really be a potential truth, for if they could, they could exist independently of each other. It's like, if you go too far to the left, you end up on the right (as even happened in the book Animal Farm), so there is "leftness" and "rightness" as relative orientations, but there is no such destination as "the left" or "the right." This means "the left" is a judicious lie to give us a concept of "leftward", the latter being a relationship with rightward. More to the point of this thread, I would say that every choice on the math poll is a judicious lie-- none of those options really exist, they only have meaning in relation to each other, as pointers to certain relative directions or angles of perspective.

I think the issue of broken symmetries across scale is crucial to this point. In string theory, there is a concept of "duality", which seems like it is trying to become the next really profound insight in physics. Though I am no expert, the basic idea of duality is that two seemingly different theories or descriptions of nature can be mapped into each other if one simply inverts the large and the small-- so if each theory has very different behavior at large and small scales, then one acts like the other at the opposite scale (say, in quantum mechanics we have indeterminacy at small scales yet macroscopic determinacy by the correspondence principle, so there should be some theory which hasn't been found yet that is indeterminate at large, say cosmological, scales, but determinate at atomic scales). So I agree that the symmetry breaking across scale is what has significance there, but not the scales themselves-- there is no large, no small, no left, and no right. Simply changing our perspective swaps these, all that is retained is their relationship to each other.

So if one takes this perspective to its logical conclusion, and applies it to all dichotomies, one can also apply it to the dichotomy "do dichotomize, don't dichotomize". When we do that, we find that what matters is we have the choice to dichotomize, but it doesn't matter which choice we make, because whatever choice we make, in some other perspective we will have made the opposite choice, especially if our choice is taken to its extreme limit. If you choose to treat reality as discrete, I will take your choice to break reality up, and break it into fewer and fewer pieces until it is just one piece-- at which point it is back to a continuous description. There cannot be a law that says "reality is fundamentally about dichotomies", for then the dichotomous perspective is "reality is fundamentally about unities." So presenting a dichotomy, on grounds that the dichotomy is the truth of the matter, is choosing a judicious lie.

The reason I choose "lie" and not "reduce the information to its minimum necessary truth content", as you framed it, is that I feel the danger of imagining that a dichotomy represents destinations applies to the most fundamental of all dichotomies, "true/false." Referring to the Escher print above and imagining this is truth and falseness in that picture, we see that even the invention of the concept of "what is true" is a judicious lie. We cannot hold that "Platonic truth" underlies any of these other dichotomies, or maps, because the only way we can even give meaning to the concept of "truth" is by giving meaning to the concept of "false." Since neither exist without the other, neither is a destination in itself. What's more, I suspect a duality there as well, where a change of perspective interchanges everything we regard as true and false, with no effect on the overall structure because the "deep structure" only required the opposition between truth and falseness, the structure does not identify one or the other independently any more than it does left and right. Truth is one hand clapping, so there is "no such thing" as truth, so we invented it-- it is itself a judicious lie (of course, so are lies).

I think the reason that we do all of this can be summed up in this other Escher concept:
http://thefalloutgirl.files.wordpress.com/2011/10/escher.gif
Our goal is to understand an environment that has us in it, so all we will ever be able to do is look over our own shoulders. This forces every concept, every word, every meaning we glean, to be a kind of judicious lie, because a brain is a device for doing that.

 

[apeiron]

What I'm adding to this already somewhat controverisal view is an objection to the following stance. It might be said that the opposite poles of the dichotomy should be viewed as opposite destinations that could each have their own "Platonic truth", as it were, such that the real truth is some kind of mixture, like splitting time between a Winter and Summer home.

Yes, the further step in this ontological story is that what is simply divided then gets complexly mixed. So this was what yin-yang/I Ching said about dichotomies, and also it was the metaphysics of Anaximander.

It is also the QM/classical story I would suggest. All material entities are complex mixtures of position and momentum for example. At least that is how they look over the middle range of scale between the complementary poles of the Planck energy and the Planck distance. But then eventually that breaks down asymptotically as you approach the Planck limits. Try to make one pole of being "the truth" - to obtain an exact value for position or momentum - and the other pole becomes radically indeterminate.

So we seem to in fact have strong empirical support for this very ancient, if somewhat controversial, metaphysics. The world does actually seem like an isotropic, homogenous, scalefree mixture of polar properties over its middle range of scale. And then it breaks down if you attempt to push all the way towards one or either of the limits.

So the basic principle of differentiate~integrate holds I believe. It makes sense that to have anything definite, you have to have some fundamental division into complementary "truths". And then what gets separated must be also freely mixed. If things get separated by splitting across scale, then across scale is where they will be evenly mixed. This type of logic is well modeled mathematically these days by scale-free networks and nested hierarchies, for example.

But I'm framing those opposite poles as "judicious lies" (where "lie" is chosen to be somewhat melodramatic for effect more so than precision) because neither one actually exists at all-- their lack of an independent existence is revealey by pushing on each until they turn into the other. They break a symmetry, yet introduce a new one, an interchange symmetry, like in this Escher print:

Again, the Escher print is a misleading image because it portrays a symmetric symmetry breaking rather than the asymmetric or hierarchical one that I am talking about. (Anyone who has read Gödel, Escher, Bach: An Eternal Golden Braid will know that this was the same mistake Hofstadter made in his attempts to make sense of "strange loop" causality).

An asymmetric dichotomy is divided across scale and so pushing in one of its two direction cannot eventually lead back to where you started. Again, think of HUP uncertainty. The more precise your measurement of one direction, the increasingly indeterminate becomes the other. You don't eventually go from measuring distance and breaking through the Planck scale to find yourself measuring energy.

Your point about rationalism and empiricism being responsible for each other is very much along the same vein-- I'm merely saying that this means neither of those concepts can really be a potential truth, for if they could, they could exist independently of each other.

I agree that they cannot exist independently. They exist only in opposition.

And then the further assertion - if they really are a legitimate dichotomy and follow the logic of asymmetric (or hierarchical!) dichotomies - the practice of maths would have to mix the two over all its scales of action. So maths would have some standard balance of empiricism and rationalism over all its scales of operation. As argued, maths is in fact quite distorted in this regard because it attempts to reduce its empirical content to a minimum so as to maximise its rational content. It is trying to be "in the limit" Platonic, deductive, etc. And it does this by constraining the empirical, the inductive truth, to the business of forming axioms. And perhaps also the subjective checks necessary at each stage of a deductive proof to "know" that each step is watertight.

This means "the left" is a judicious lie to give us a concept of "leftward", the latter being a relationship with rightward.

Again, this is symmetric symmetry breaking not asymmetric or hierarchical symmetry breaking. In the asymmetric case, the polar directions would seem orthogonal. On a sphere, going westward, you might indeed end up going eastward. But you could keep going forever and never find yourself going north- or south-wards. So you are working with a different mental intuition here.

More to the point of this thread, I would say that every choice on the math poll is a judicious lie-- none of those options really exist, they only have meaning in relation to each other, as pointers to certain relative directions or angles of perspective.

I agree, with the difference that I am arguing a foundational view would be based on a single dichotomy ideally. Or maybe a pair.

So one obvious dichotomy they all try to orientate themselves by is the modelling relation - the map~terrain. Either maths is just a map, or it is actually a terrain. But this is a general foundational issue for epistemology, not just maths. It is true of all knowledge. And the modern resolution would be that we only just map, and then that it is the map which is dichotomised into models and measurements, or general ideas and particular impressions. This is what actually fits what we know about how brains work.

So again, the foundational dichotomy for maths would seem to be that maths is a language, a machinery, for constructing constraints. It describes the forms that bound materiality. And describes them in an atomistic fashion so the forms can actually be built additively, step-by-step, as a series of effective causes.

So maths is formal syntax that can construct states of materially constrained semantics. The world just is. Maths is a tool that can rearrange it within its limits. And those limits actually "exist". The material world is ontically bounded. The Universe is constrained (somehow) to be Euclidean flat (over the middle range of our observation at least) and so triangles add up to 180 degrees as a "Platonic truth".

I think the issue of broken symmetries across scale is crucial to this point. In string theory, there is a concept of "duality", which seems like it is trying to become the next really profound insight in physics. Though I am no expert, the basic idea of duality is that two seemingly different theories or descriptions of nature can be mapped into each other if one simply inverts the large and the small-- so if each theory has very different behavior at large and small scales, then one acts like the other at the opposite scale

Yep, these are reciprocal dualities - scale based. There are three of them (which suggests that they might reduce to a single duality in some fashion). And there are arguments that you can go through the Planck scale and come out the other side. With topological or T-duality, a wound string would become an unwound vibrating string by this manouvre and going east would be suddenly going north. Though this seems more a mathematical passing through the eye of a needle than a physically realistic story.

With S-duality, or "soliton" like duality, you could pass from what looks like a solid particle with weak interactions to a clump of excitation bound by its strong interactions.

And then there is the AdS/CFT correspondence that people are so excited about. Note how it depends on a "conformal world" - the kind of scaled realm where mathematically you represent both a space and its bounding extremes of scale. You take a limit and can then place another complementary "world" on the other side of that boundary, making one the simple description of the complex mixture.

(say, in quantum mechanics we have indeterminacy at small scales yet macroscopic determinacy by the correspondence principle, so there should be some theory which hasn't been found yet that is indeterminate at large, say cosmological, scales, but determinate at atomic scales). So I agree that the symmetry breaking across scale is what has significance there, but not the scales themselves-- there is no large, no small, no left, and no right. Simply changing our perspective swaps these, all that is retained is their relationship to each other.

I think it is an error here to equate the Planck scale with just a single limit. It is in fact a dualised description of an inflection point, a yo-yo point, the vertex of a parabolic relationship.

So the Planck scale describes two dichotomous (orthogonal) extremes - the greatest heat and the smallest distance. It is how small can you shrink in spatiotemporal terms, how large you can grow in material density or other measures of energy. So again, a classic form vs substance dichotomy - the least degree of one and the maximal presence of the other.

This of course then requires a further "dimension" to our ontology. Back at the Big Bang, the Universe seems to have been both very small and very hot. The two aspects of reality were united - and therefore in the logic of dichotomies, we would say that existence was radically vague, or indeterminate. It is only once the Universe expanded/cooled that you could actually make crisp measurements that might say some event was definitely small (in relation to the general largeness of the Universe), or hot (in relation to its generalised coolness).

So through the construction of constraints - setting up the kind of experiments that can measure the quantum boundaries of our existence - we can recover this naked quantum indeterminacy either by making things really hot (as in a collider) or very small (as in observing single buckyballs going through twin slits at near absolute zero).

There cannot be a law that says "reality is fundamentally about dichotomies", for then the dichotomous perspective is "reality is fundamentally about unities." So presenting a dichotomy, on grounds that the dichotomy is the truth of the matter, is choosing a judicious lie.

But the full ontological position is that it is not just about dichotomies. Dichotomies refer only to the middle bit, the process by which a vagueness (Anaximander' apeiron, Peirce's firstness, QM's indeterminacy) becomes transformed into a hierachical, complex, realm (Peirce's thirdness, Classical crispness, etc).

So there is monadic unity in the initial vagueness. And also a kind of unity in the stability of the final triadic outcome, a hiearchical order where you have the three things of bottom-up atomistic construction, top-down global constraint, and then the ambient equilibrium balance of those two complementary actions that creates a conformal spectrum inbetween.

If this is all a judicious lie, it is a lie with an intricate causal structure.

The reason I choose "lie" and not "reduce the information to its minimum necessary truth content", as you framed it, is that I feel the danger of imagining that a dichotomy represents destinations applies to the most fundamental of all dichotomies, "true/false."

I don't follow that. True/false would be a false dichotomy, in the technical sense of being forced to chose one pole over its alternative. It is the step too far that reductionism makes.

A dichotomy is A and not-A. A division of reality (or of our ignorance) into a something and everything that it is not. And both sides of this partitioning would still by definition be "the real". At most, all we are saying is that there is one side of the partitioning of reality that we are chosing to ignore, or to generalise away.

All I am talking about then is returning to the fact that this is what logic is about - the process of excluding middles so as to set up dichotomous alternatives. And instead of rejecting one pole (labelling it "the false"), or ignoring one pole (labelling it entropy, or noise, or void, etc), actually giving it an equally definite name (making it also "the true" because it is the yin to the yang, or the continuous to the discrete, or the position to the momentum, etc).

The logic of dichotomies is not about the simplicities of true/false. It is about the complexity of crisp/vague. Things only become definitely anything if they are dichotomous. So in terms of our maps of the terrain, we are talking about knowledge/ignorance. If we can definitely frame a view of reality based on an A~notA distinction, then the law of the excluded middle applies and we are lifted out of vague, indeterminate uncertainty about what may be the case.

Truth is one hand clapping, so there is "no such thing" as truth, so we invented it-- it is itself a judicious lie (of course, so are lies).

Truth can only be true if lies are also true? Where have we heard these modal paradoxes before? Yes, and the logic of dichotomies would demand that complementaries have equal claim to "truth". Except as I say, the actual dichotomy by which the antimonies would be measured would be vague~crisp, or indeterminate~certain. So for a truth to be certain, so does the not-A that is the lie. Truths cannot just simply exist, they have to be formed within an equally definite context that allows the process of a judgement.

Truths thus imply always a knower of the truth - an observer. Modal logic generates paradoxes because it fuzzes over this issue. It wants to take the limit and presume that truths can have brute existence, independent of the business of any measurement process.

So the reductionist view of "truth" based on truth/lie is a really big judicious lie (both very useful and extremely untrue), and the dichotomistic view of truth as a process of discrimination is still a lie, but not so much of one, perhaps.

I think the reason that we do all of this can be summed up in this other Escher concept:
http://thefalloutgirl.files.wordpress.com/2011/10/escher.gif
Our goal is to understand an environment that has us in it, so all we will ever be able to do is look over our own shoulders. This forces every concept, every word, every meaning we glean, to be a kind of judicious lie, because a brain is a device for doing that.

That is the AdS/CFT correspondence again. Conformal symmetry can represent the full story of a world and its limits. And by imagining a world like that, you can step outside it to see it all.

It is no accident that every direction you turn, people are backing into the same story. Worlds are the product of limits - of global constraints on local degrees of freedom. And to model this fully, you have to be able to model the development of those global constraints as well.

Do I have to mention the whole renormalisation schtick? Or holography? As our vision of reality has expanded far enough to now observe its bounding limits of scale, we are now groping towards the models that can include those limits as the final facts. And slippery dualities are what must be tamed. You have to have ways (in the language of maths and logic!) to hold both ends of the beast pinned down. Reductionists are stuck in the game of wondering which end they need to pin down (and so always getting whacked on the back of head by the other end flailing about).

 

[Evo]

I am re-opening this thread under the condition that the thread return to specific discussion of the topic.

 

[chiro]

One thing about mathematics is that, in my opinion, we are simply re-discovering what already existed and what was always possible from the very beginning.

Some people might interpret this to mean that since humans don't actually 'invent' anything but rather just 're-discover' it, that we are not really that special in the fact that we didn't 'invent' something per se. In the above case, if people are thinking that way then are placing way too much importance on the importance of self and are missing the point completely.

In this sense, the above might correspond to a form of Platonism with respect to the above rant.

 

[Evo]

Please stop the nonsense posts.

 

[dimasalang]

i like the way we used the symbols of math by using logic behind it.



nature don't need an intuitive conscious mind, like us to understand itself., were just merely a helpless creation of infinitely small particles. govern by incomprehensibly and mind boggling laws of nature.

 

[Ken G]

One thing about mathematics is that, in my opinion, we are simply re-discovering what already existed and what was always possible from the very beginning.

Would you say that the painting "Mona Lisa" was always possible from the beginning, and does that imply that Da Vinci "rediscovered" it when he painted it? Or is mathematics demonstrably different from art in terms of which comes from us and which is built into nature? Can you trace the details of how each is done to reach this conclusion using pure logic, or do you just have to assume it as a postulate?

I would argue that any attempt to make the above claim true is fundamentally circular-- it can only be true if it is assumed to be true from the outset. So the opinion being expressed is that we should just assume the above. I'm not sure that simply assuming away what we don't actually know is the best way to make progress in philosophical inquiry, isn't a better question, what do we get if we assume that, and what do we get if we don't? Isn't it true that both approaches give us a different perspective on what mathematics is, and don't we want to see mathematics from all valid perspectives? This is the "nonsense" I've been arguing: we are incorrect to imagine that mathematics is only one of the things on that list, for all that amounts to is putting on blinders about what mathematics quite demonstrably is and can continue to be, if we just don't don those blinders.

 

[bohm2]

Or is mathematics demonstrably different from art in terms of which comes from us and which is built into nature?

I tend to think that both comes from us but it seems mathematics is much more useful as a scaffolding to attach our claims about physical systems. It seems that there is something more to physical reality (or even our models of physical realty) over and above the mathematics. It seems that the mathematical theories/objects are not the same type of entities that appear to exist in the physical world. We can't get to the physical world without using mathematics because non-mathematical versions of scientific theories just seem to be practically very difficult to do. But, even though the mathematics may be indespinsible and the mathematical equations we use ultimately decide what we believe about the physical world there still seems to be this difference between the two and this just adds fuel to many of the interpretative debates in science, I think.

 

[micromass]

Please stop the nonsense posts. This thread is about mathematics and its philosophy, it's not about the Mona Lisa nor about determinism nor about the existence of reality, etc.

There are a few interesting points which are touched on, but there is also quite a lot which is not relevant to this thread what-so-ever.

Sure, short analogies are allowed. But as soon as you're saying more about about the analogies than math, then it becomes nonsense. For example, typing 50 sentences about the mona lisa and then saying that mathematics is the same thing, is not allowed.

Please make sure your posts are actually about mathematics, and not about something else.

You've been warned three times now. If it doesn't stop, then more serious actions may be taken.

 

[Ken G]

Please stop the nonsense posts. This thread is about mathematics and its philosophy, it's not about the Mona Lisa nor about determinism nor about the existence of reality, etc.

Art is just a useful comparison, and ontological issues are relevent, for they are referred to in the OP itself (just look at choices #4 and #5, which directly connect mathematics to things that actually exist, i.e., claim that mathematics is explicitly ontological). I understand that you must decide what elaboration is off topic, and I might not agree with you, but it's your place to do that not mine. All I'm saying is that this whole thread is about whether mathematics is something inherently semantic and ontological (connecting with meaning in the real world, choices #4 and 5), or something inherently syntactic and epistemological (a kind of procedure for knowing that follows a fixed set of rules and has nothing to do with anything outside those rules, expressed in all the other choices). Since I am not allowed to actually support my stance, I can only state it: neither of those answers could possibly do justice to what mathematics actually is, because what mathematics actually is is a juxtaposition of those two possibilities. Mathematics takes on its meaning in the place where those things come into contact, because neither of them have any value on their own, they are both vacant notions until they are juxtaposed. To actually describe my reasoning might seem verbose, or might need to bring in how art and language also avail themselves of an interplay between syntax and semantics, so I won't belabor the point.

 

[John Creighto]

Art is just a useful comparison, and ontological issues are relevent, for they are referred to in the OP itself (just look at choices #4 and #5, which directly connect mathematics to things that actually exist, i.e., claim that mathematics is explicitly ontological). I understand that you must decide what elaboration is off topic, and I might not agree with you, but it's your place to do that not mine. All I'm saying is that this whole thread is about whether mathematics is something inherently semantic and ontological (connecting with meaning in the real world, choices #4 and 5), or something inherently syntactic and epistemological (a kind of procedure for knowing that follows a fixed set of rules and has nothing to do with anything outside those rules, expressed in all the other choices). Since I am not allowed to actually support my stance, I can only state it: neither of those answers could possibly do justice to what mathematics actually is, because what mathematics actually is is a juxtaposition of those two possibilities. Mathematics takes on its meaning in the place where those things come into contact, because neither of them have any value on their own, they are both vacant notions until they are juxtaposed. To actually describe my reasoning might seem verbose, or might need to bring in how art and language also avail themselves of an interplay between syntax and semantics, so I won't belabor the point.

I tried to separate out the topic of contention into a separate thread:

Time, Ontology & Platonic Reality vs Material Reality

and I hope this will be satisfactory to the moderators. I presume that given your infraction count you will be reluctant to respond but the thread is now created in case you decide to do so. I was thinking yesterday of creating a thread of posting suggestions to help people better stay within the guidelines of the philosophy section of this forum but haven’t done So.

Peace out.

 

[audioloop]

an interesting reading about the theme...Much of modern theoretical physics assumes that the true nature of reality is mathematics. This is a great mistake. The assumption underlies most of the paradoxes of quantum mechanics, and has no empirical justification. Accepting that the assumption is wrong will allow physics and mathematics to progress as distinct disciplines...
http://fqxi.org/community/forum/top...3/__details/Schlafly_fqxischlaflynomath_1.pdf

 

[Ken G]

Yes, I agree with Schlafly. The objection is to the currently favored highly rationalistic framing of modern physics-- that it is the search for the mathematics that actually governs reality. We've made that mistake so many times in the history of physics I'm amazed we're still vulnerable to it, but it must stem from the extreme successes (not something new) that rationalistic descriptions have produced. But it seems demonstrably clear that this is just not the way mathematics is used in physics-- mathematics is part of physics, but it's not all of physics, because physics is a kind of collision between mathematics and observations, between rationalism and empiricism. Just as with the Platonism vs. arbitrariness of math that is central to this thread, or the semantics and syntax of any language (or other examples that are viewed as off topic), physics requires both rationalism and empiricism to make any sense. Neither of them by themselves is a coherent destination, and we only set ourselves up to be "shocked" yet again if we fail to remember that. So we should not attempt to decide if math is Platonic or arbitrary, or if language is semantic or syntactic, or if physics is mathematical or empirical, we should just study the interactions of all those things-- because that's what math, and language, and physics, actually are.

 

[StephenofCaly]

I tend to think that both comes from us but it seems mathematics is much more useful as a scaffolding to attach our claims about physical systems. It seems that there is something more to physical reality (or even our models of physical realty) over and above the mathematics. It seems that the mathematical theories/objects are not the same type of entities that appear to exist in the physical world. We can't get to the physical world without using mathematics because non-mathematical versions of scientific theories just seem to be practically very difficult to do. But, even though the mathematics may be indispensable and the mathematical equations we use ultimately decide what we believe about the physical world there still seems to be this difference between the two and this just adds fuel to many of the interpretative debates in science, I think.

I like this offering very much. When we discuss mathematics, we consider the mapping of an Ideal Form that exists in pure abstraction. We proceed in advancing mathematics by adding to the structure of the internal correlation in the Ideal Form of Mathematical Thought.

Mathematics has proven to be a useful tool in generating implications about the "real world," the physical world which physics studies. We once searched for the simple rules by which the real world operates, and believed that we had a finger of the laws of physics. Now, we find that we are better served by testing the consequences of a certain suggestion in Ideal Thought (Mathematics) in the physical world. This was Bohr's take on quantum mechanics, as I understand it.

Platonism (Idealism) takes the stand on the pure world of Ideal, where Forms themselves - the pure and absolute thought - are the only things that are true, and "physics" is a representation of the True. On the other hand, nominalists find that the idea of Forms is an unreal abstraction which is useful for the handling of what IS real, i.e. the physical world.

Notice how the idea of reality shifts its focus.

In any case, mathematics can be a helpful guide for how to proceed in physical inferences, and yields hypotheses readily. To date, where our concepts in physics have failed spectacularly, it is where the rules of physics which we have crafted fail to extend efficiently into particular circumstances - the very small and the very fast, for instance. We have yet to see an absolute collapse of our fundamental understandings as expressed in physical mathematics - so far, what we consider the rules of the physical world seem pretty predictable. Whether we are reading God's Mind, or just hammering together some practical observations, is the difference between Platonic Idealism and the more nominalist approaches.

"I think I think, therefore I think I am."​

 

[sigurdW]

The Philosophy of Mathemathics is essentially the Philosophy of Language!

WHY?

No Formula of Mathemathics cannot in principle be "translated" into ordinary language.
Its awkward to manage without formulae,
but there are no "pure formula" that is not a simplification of language.

 

[John Creighto]

The Philosophy of Mathemathics is essentially the Philosophy of Language!

WHY?

No Formula of Mathemathics cannot in principle be "translated" into ordinary language.
Its awkward to manage without formulae,
but there are no "pure formula" that is not a simplification of language.

This argument is like: if A is a subset of B and B is a subset of A then A=B. Yet you say math can be translated into language which I can sort of buy but when we think about language we think about non mathematical things. A cow is not a mathematical object but we can represent various aspects of a cow with mathematics. Of course you may contend that language does not really represent the cow either. Yet when we speak of a cow we at least know what we mean independently of some AI recognition system.

Math describes the structure while language describes the meaning. What is meaningful to us depends upon structure, rules and order but not all structures are meaningful to us. Perhaps an algorithm could be devised to identify which types of structures are meaningful to us or perhaps it is just a convenient mix of convention and utility.

 

[sigurdW]

This argument is like: if A is a subset of B and B is a subset of A then A=B. Yet you say math can be translated into language which I can sort of buy but when we think about language we think about non mathematical things. A cow is not a mathematical object but we can represent various aspects of a cow with mathematics. Of course you may contend that language does not really represent the cow either. Yet when we speak of a cow we at least know what we mean independently of some AI recognition system.

Math describes the structure while language describes the meaning. What is meaningful to us depends upon structure, rules and order but not all structures are meaningful to us. Perhaps an algorithm could be devised to identify which types of structures are meaningful to us or perhaps it is just a convenient mix of convention and utility.

An insightful riposte John!
Every formula is translatable into ordinary language
but not the other way round,
maths is an idealization of language.

 

[chiro]

This argument is like: if A is a subset of B and B is a subset of A then A=B. Yet you say math can be translated into language which I can sort of buy but when we think about language we think about non mathematical things. A cow is not a mathematical object but we can represent various aspects of a cow with mathematics. Of course you may contend that language does not really represent the cow either. Yet when we speak of a cow we at least know what we mean independently of some AI recognition system.

Math describes the structure while language describes the meaning. What is meaningful to us depends upon structure, rules and order but not all structures are meaningful to us. Perhaps an algorithm could be devised to identify which types of structures are meaningful to us or perhaps it is just a convenient mix of convention and utility.

You might want to think about information in terms of its role in information theory as opposed to the intuitive ideas of most people called language which is a relative and contextual thing.

Information theory defines information to have no context or interpretation at all: you have an alphabet, a collection of sentences (both finite) and a probability distribution characterizing the event space for the nature of the grammar and subsequent mappings of probability to constructed sentences.

Context basically relates pieces of information together and most language (including mathematics but it does it in a very different way to the spoken languages) is contextual and relative.

Each word that you read and the existing context creates relationships automatically in comparison to say a string of random letters which probably just confuses people.

Mathematics is actually relative and doesn't just describe structure. There are dualities everywhere in mathematics and this gives it part of its relativity. For all and there exist are dualities. The AND/OR statements in set theory are dualities. The inequalities have dualities. There are dualities within the language itself everywhere.

The dualities themselves are important because they give context to the actual descriptions just like the combination of words in a sentence give context to the other words, the entire sentence, and anything even remotely related to the ideas and terms of the sentence.

 

[sigurdW]

You might want to think about information in terms of its role in information theory as opposed to the intuitive ideas of most people called language which is a relative and contextual thing.

Information theory defines information to have no context or interpretation at all: you have an alphabet, a collection of sentences (both finite) and a probability distribution characterizing the event space for the nature of the grammar and subsequent mappings of probability to constructed sentences.

Context basically relates pieces of information together and most language (including mathematics but it does it in a very different way to the spoken languages) is contextual and relative.

Each word that you read and the existing context creates relationships automatically in comparison to say a string of random letters which probably just confuses people.

Mathematics is actually relative and doesn't just describe structure. There are dualities everywhere in mathematics and this gives it part of its relativity. For all and there exist are dualities. The AND/OR statements in set theory are dualities. The inequalities have dualities. There are dualities within the language itself everywhere.

The dualities themselves are important because they give context to the actual descriptions just like the combination of words in a sentence give context to the other words, the entire sentence, and anything even remotely related to the ideas and terms of the sentence.

Hi Chiro! You are delightfully confusing
"Duality" "Context" "information theory"?

The context of the sign is Mind and its relation to Reality
(Whatever they might be.)

 

[chiro]

Hi Chiro! You are delightfully confusing
"Duality" "Context" "information theory"
The context of the sign is Mind and its relation to Reality
(Whatever they might be.)

Duality in the above context just means a separation in the way of an inversion. A duality to a duality is just itself. In set theory, the term is "complement". If you have a universe of possibilities then the duality of A is U\A and the duality of U\A is U\(U\A) = A.

Information theory is the standard definition started mostly by Claude Shannon.

Context is just a way of saying that things are relative to one another. An example is a duality, but it is not the only form of relativity since you can have a duality relative to a subset of the universal space much like you have conditional probability that is relative to the set it is conditioned on.

In conditional probability we have P(A|B) = P(A and B)/P(B). If we let B = U (universal set) we get P(A|U) = P(A and U)/P(U) = P(A).

The duality of the event A has the probability 1 - P(A) and this has a standard interpretation in probability.

 

[sigurdW]

Excuse me my "friends". I am not all rational. I am a poem. And a formula. Fused into one.
Again:Theres pure thought. And its echo: "Rational thought"

You temporarily overload me my dear chiro. Next year? I might return? 1/Zen to you all..

 

[chiro]

Excuse me my "friends". I am not all rational. I am a poem. And a formula. Fused into one.
Again:Theres pure thought. And its echo: "Rational thought"

You will get quite a number of interpretations and they all depend on context.

A mathematician will complain that it's not logical. A linguist might make a complement regarding the creative use of grammar. An english poetry major might make some waffle comment on the prose of the piece.

A computer scientist or a logician will think of contradictions in terms of some order logic and probably think about all the paradoxes that come with logical systems.

Some people in general will think your nuts and others will think you're brilliant.

The point is that there is no unique interpretation because everyone has their own idea of what these terms mean because they all have their own context.

Also what one person calls "irrational" another finds "rational".

Usually what people try and do in all instances of trying to find an agreement when it comes to terms is that both people go back and forth until they are both satisfied coming up with something gives both parties the context that both they and the other party has.

Both party can label their own contextual definition of what something means with their own labels, but eventually the agreement will be done in a language that both can converse in, create in, and use.

But even then trying to explicitly capture context is a difficult thing because know one really knows the extent of what they know unless they get it all out explicitly. Furthermore, know one knows what others know until they do the exact same thing.

One final thing about rationality:

Think of a situation of a gambler (a problematic one: a compulsive gambler). To a statistician and a close family member of the gambler, they see what they are doing as irrational and completely without any real kind of cognitive functioning.

The gambler though has a rationale for what they are doing: they are trying to get a "return on their investment" just like a lot of people want to get a return on their investment. The investment doesn't have to be financial: it can be a time-based investment like a personal or sexual relationship or it can be a career based investment or any other "investment".

The gambler rationalizes that if they leave now, they will risk "losing" the return on their investment even though they are un-aware that the whole game is rigged so that they lose.

All actions are rationalized in some way. Whether they are "right" or "wrong" is not the main issue here: the main issue is the context and other impetus surrounding those decisions and rationalization of thoughts.

It's the same kind of mistake mathematical economists make with rational agents.

A lot of people think that being rational is maximizing your utility and doing whatever it takes to come out on top. This might be how they and their friends think, but not everyone has the same rationalization process that they do.

 

[sigurdW]

I am TRAPPED! I can't stop reading you... Youre all on my sense!
Even your errors/arrows hits target. I was leaving this poor excuse for (eh...forget it!)

Repeat ad inf.

EDIT

Youre brilliant. Your linear sharp reasoning hurts my eye!

Im retreating into a formula: Q= Reality times Reality/Ourselves

Here is a minor proof of your multi_mentality wit: "because know one really knows"

I sea it as: "because now no one really Knows" (QED)

So Y am I, a Musician, aBeing here?
I got a problem for you, lovers of truth,,,
Maths rests on PROOF! Doesnt it?

Then please prove that sentence three below does not follow,
and mind you,you are not allowed to exclude self reference!

1 Sentence 1 is not true
2 Sentence 1 = " Sentence 1 is not true "
3 Sentence 1 is true

Did I stumble upon that proof?
No, I spent thirty years in searching for it.

Aint that being silly?
Nope, we can think about ourselves,
Therefore sentences can talk about themselves...
There is no paradox...only a logical error.

 

[sigurdW]

I got a problem for you, lovers of truth,,,
Maths rests on PROOF! Doesnt it?

Then please prove that sentence three below does not follow,
and mind you,you are not allowed to exclude self reference!

1 Sentence 1 is not true
2 Sentence 1 = " Sentence 1 is not true "
3 Sentence 1 is true
.

Theres more than one proof, here's the beginning of a proof.

First we note that sentence 2 is Empirically true.
If we can show that sentence 2 is Logically false
then sentence 2 is both true and false,
And sentence 3 will not correctly follow:

2 Sentence 1 = " Sentence 1 is not true " (assumption)

We have assumed that sentence 2 is true! So...what should be done next?

 

[DragonPetter]

if you believe that mathematics arises from the properties of nature, then you would be an adherent of physism. But then how would you respond to the objection that there is so much mathematics that we do that is not directly grounded in our knowledge of the physical world?

What about mathematical equations that possesses both solutions that are grounded in the physical world and solutions that would seem impossible physically? There are solutions to equations that give positive and negative energies for example, and we simply ignore/throwaway the negative roots since our laws of nature say you can't have negative energy/mass.

It seems very convenient and illogical to throw away some of the solutions as an afterthought just because they don't fit what we observe. How can we relegate them to abstraction and blissfully use their positive root siblings as physically grounded in observation? Are the equation and its supporting mathematical structure/axioms partially grounded in the physical world to where they are only partially right in describing the universe? Or is it completely abstract, and just by coincidence some of its solutions happen to be grounded in the physical world? I have a lot of other thoughts on this that I think leads me to be a realist that views mathematics as a duality of physics (mathematics can only exist if it can be expressed in our universe, and the universe is an expression of all possible mathematics), but I'm curious if someone can resolve this. I never got a good explanation from my physics teachers other than that negative solutions "don't make sense" to reality, and I am definitely not an expert in abstract algebra theory.

With regards to the negative root example: if there is a way to compute only positive roots without acknowledging the existence of negative roots to solve a physical relationship, then I think there is more flexibility of the interpretation of mathematics. We can't even make a rule that says ignore roots < 0, because that acknowledges their existence. If we cannot escape the existence of negative roots in this computation, then we have to either give some complete explanation for them not having physical grounding or call it coincidence that the abstract physically-independent math happens to have a partial duality with physical observation, and I don't think coincidence would be a sufficient answer. Also, I'm not trying to imply that what the relationship between mathematics and the universe is hinges on this negative roots thing, that's just a common example most people can relate to.

 

[apeiron]

What about mathematical equations that possesses both solutions that are grounded in the physical world and solutions that would seem impossible physically? There are solutions to equations that give positive and negative energies for example, and we simply ignore/throwaway the negative roots since our laws of nature say you can't have negative energy/mass.

Good point. The simple answer would be that the equations describe a higher symmetry which nature then breaks. So there is more to the story than the equations can tell. Further information, further constraints, have to be supplied somehow.

 

[jackmell]

I think it's other and parton me if I don't go through all the comments to see if anyone already stated it:

Mathematics is an emergent property of a survival strategy used by life on earth: the Universe is a massively non-linear dynamo. In order to survive in such a non-linear world, life adopted a likewise non-linear dynamo: brains. The brain mimics this non-linear world and part of that mimicry is mathematics: mind, mathematics, and the Universe are of the same cloth. There would be no mathematics without this synergy between biology, evolution, selection, and the non-linear nature of the Universe.

 

[DragonPetter]

Good point. The simple answer would be that the equations describe a higher symmetry which nature then breaks. So there is more to the story than the equations can tell. Further information, further constraints, have to be supplied somehow.

I never thought about the symmetry and that is something I don't know much about, as it goes deeply into theoretical physics. It definitely does sound compelling to my layman ears tho :P

In another thread I thought of the negative roots problem as a type of computational efficiency. You have to waste some computation on abstract solutions to be able to get the physically grounded solutions. Kind of like a carnot heat engine has to lose heat (nonsense/abstract ideas) that is not usable in order to produce work that is usable (real physically grounded ideas), where both types of information, abstract and physically grounded, are represented physically (and thus everything we can imagine or discuss mathematically, abstract or not, is embedded in the universe in some way).

All of the times our brains computed the negative roots as solutions, that information was imprinted into the universe through our thought processes as configurations of memory or symbols written into paper, and has some how interacted with the universe following the laws of the universe. If a Turing machine has to first consider negative root solutions to a problem before it can reject them, then those negative roots have some physical meaning, even if they don't apply to the models that we find patterns with in the positive roots. I know that is more of an artistic/philosophical and wishful thinking relation than something that any evidence points to, but I don't know of any satisfactory or rigorous explanation for such things.

 

[apeiron]

In another thread I thought of the negative roots problem as a type of computational efficiency. You have to waste some computation on abstract solutions to be able to get the physically grounded solutions.

I see the analogy. But in the context of the OP - whether maths is generally Platonic or utilitarian - the Platonic claim would seem to be that it is not the computation that is the issue. The answers would "exist" regardless of whether some human calculated them.

The difficulty comes only at the point of chosing one computation to be real, and discarding the other one as unphysical. And this seems a non-mathematical decision. The maths itself does not offer the grounds for making the choice.

All of the times our brains computed the negative roots as solutions, that information was imprinted into the universe through our thought processes as configurations of memory or symbols written into paper, and has some how interacted with the universe following the laws of the universe.

But how is there any interaction apart from that we create ourselves? This is where the utilitarian part of the story comes in. To the universe, any symbols scribbled out on paper are just noise - meaningless entropy. It is only to our minds that the symbols are information - one root being the definitely true, the other being the definitely false. And our minds decide this through further measurement - we observe the world and make the distinction.

 

[DragonPetter]

I see the analogy. But in the context of the OP - whether maths is generally Platonic or utilitarian - the Platonic claim would seem to be that it is not the computation that is the issue. The answers would "exist" regardless of whether some human calculated them.

Well, I only use human computation as the example. I am talking purely computational in the generic sense, like a Turing machine. A computer has no mind or existence, it is an object, and yet it can compute math based on what the laws of the universe allow it do. It might take infinitely long for it to reach some results, but it is still only able to get results that the laws of the universe let it reach.

I suppose it might still be debatable that if everything a human mind can do, a Turing machine can do too, but if that is true then anything our minds think up has to be processed in adherence to the laws of physics just like for a Turing machine. If you write a computer program to find the roots of a solution to give you an answer that matches physical reality, the throw away roots are still processed. At some point we make a decision to stop finding roots or throw away roots, which costs energy and creates heat by the computer, and so I think it might be more than just an analogy.

The difficulty comes only at the point of chosing one computation to be real, and discarding the other one as unphysical. And this seems a non-mathematical decision. The maths itself does not offer the grounds for making the choice.

Yes, I agree to a certain degree. I am taking the step to say that the universe's rules makes the choice automatically, but the universe's rules also allowed for the existence of the negative root solution as well, even if it has no other physical grounding to the world than its own existence. Perhaps, by the universe's rules, you cannot generate some solutions without creating an abstract "waste" solution. That's why I am confused/annoyed/interested that we think we can make such non-mathematical decisions about a purely mathematical result. We break away from the math at the last minute, even though part of its result is what we want, and then we go on happily using the math that works (ya, I'm trying to stress that analogy) for us. But if what you suggested is the case, that the universe breaks symmetry from math, then the universe is not purely mathematical or does not include all math. If that is the case, I would guess that we should not even be aware of these abstract ideas.

But how is there any interaction apart from that we create ourselves? This is where the utilitarian part of the story comes in. To the universe, any symbols scribbled out on paper are just noise - meaningless entropy. It is only to our minds that the symbols are information - one root being the definitely true, the other being the definitely false. And our minds decide this through further measurement - we observe the world and make the distinction.

To the first question: Our brains are part of the universe, and so the interaction is with parts of the universe. The neurons exchange signals, consume energy, generate heat, organize synapses to form ideas, etc. This is all physically governed by the laws of the universe. If the laws of the universe don't allow our brains to do something, then there is no possibility for it to exist in our thoughts. Likewise, if our brains can process the information that generates abstract mathematical logic, then its only because it is built into the interaction of the universe's laws.

Also, I don't see the organization of those symbols as noise if there is no brain around to interpret them. That organization of symbols still exists, regardless of anyone to interpret it. I don't know for sure though :P

 

[Pythagorean]

From a science perspective, when doing mathematics, really getting into a problem... pages of derivation, especially based in physics... it's really easy to slip into a platonist mind set. Perhaps even advantageous.

When you actually go and try to apply models to the real world and do experiments, and raise all the caveats that come from a complex and rich world, physism/formalism emerges.

 

[apeiron]

If you write a computer program to find the roots of a solution to give you an answer that matches physical reality, the throw away roots are still processed. At some point we make a decision to stop finding roots or throw away roots, which costs energy and creates heat by the computer, and so I think it might be more than just an analogy.

Yes, all actual computation will generate entropy (putting aside http://en.wikipedia.org/wiki/Landauer's_principle for the moment). But the central trick of computation is precisely that it minimises any interaction with the world - so as to put itself into a "Platonic" realm.

A sequential symbol processing computer - a Turing machine - executes any individual step with exactly the same heat dissipation. So as far as the world knows (as far as the second law cares), calculating nonsense looks the same as calulating mentally-significant results. Inside the machine, spitting out a positive or negative answer is still a symmetric situation as the entropic cost is precisely the same.

The real impact on the world only comes from the actions people take based on what they believe. Some further choice has to be made as to which answer is the correct one. Further energy is required to break the entropic symmetry of the computational result, even if some entropic effort was required to produce that result - get things to the stage of a choice between a positive and negative root in your example.

I am taking the step to say that the universe's rules makes the choice automatically, but the universe's rules also allowed for the existence of the negative root solution as well, even if it has no other physical grounding to the world than its own existence.

But the laws of physics are a human invention. They may certainly encode some regularity, some generality, that describes nature. But it is falling back into the confusion of Platonism to mistake our models of reality with reality itself.

So here it is our model (expressed in mathematical statements) that allows for a symmetric pair of choices. The Universe just does what it does and if our model can't predict that, then this is just a sign of its incompleteness.

It is the model that has rules. And it is the rules themselves which create the appearance of choice. The Universe by contrast exists in time and has locked in its critical "choices". (See http://en.wikipedia.org/wiki/Loschmidt's_paradox).

But if what you suggested is the case, that the universe breaks symmetry from math, then the universe is not purely mathematical or does not include all math. If that is the case, I would guess that we should not even be aware of these abstract ideas.

No, my argument is that we create math (or rather, our mathematical descriptions of material reality) by stepping back from the current broken symmetry we see all around to recover the original symmetry that must have been the Universe's initial state.

We are modellers, so there is no problem with being aware of our own created abstractions.

To the first question: Our brains are part of the universe, and so the interaction is with parts of the universe. The neurons exchange signals, consume energy, generate heat, organize synapses to form ideas, etc. This is all physically governed by the laws of the universe. If the laws of the universe don't allow our brains to do something, then there is no possibility for it to exist in our thoughts. Likewise, if our brains can process the information that generates abstract mathematical logic, then its only because it is built into the interaction of the universe's laws.

Humans cannot ultimately escape the second law of thermodynamics (the relevant law here). But again, the whole point about computation (and modelling in general) is that it allows for the kind of temporary escape available to life/mind as an order-creating dissipative structure - http://merkury.orconhosting.net.nz/lifeas.pdf

So computation must create heat in practice. But it is useful because it demands so little energy compared to the amount of energy it allows us to harness. And the energy consumption is the same regardless of whether we are computing sense or nonsense - which is what gives us free choice about what to compute, what results to generate.

So the second law can't effectively see what we are doing inside our heads, or computing inside our computers. We have created a private Platonic realm of pure thought and choice. On the larger scale of course, the second law does rule. We have to eat to think, plug in our computers to compute. But that still leaves us a fantastic amount of Platonic freedom to play around in.

Also, I don't see the organization of those symbols as noise if there is no brain around to interpret them. That organization of symbols still exists, regardless of anyone to interpret it. I don't know for sure though :P

This is the symbol grounding problem. And quite clearly symbols require interpreters.

Information theory can be used to model an observerless reality. But that is just another of our useful modern abstractions that should not be mistaken as the deep truth of reality.

Bits are just entropy - countable states. To be "orderly", they have to also be placed within an interpretive context. Someone has to care enough to count.

 

[Noja888]

If we could measure all components of a human mind can we predict what choices will be made by that mind? - Or - I like to think we end up at such small scales that quantum mechanics plays a role. The turing machine becomes the incorrect anology perhaps. A quantum turing machine, where the outcome always has some degree of uncertaincy. The act of measurement disturbs the system, our freewill is a manifestation of this concept in someway perhaps. By studying someones likes and dislikes you can reasonabliy predict how they will act in a particular situation. But until they make their choice you cannot say for certain the outcome. To me atleast freewill seems linked to the uncertaincy princeable in quantum mechanics. has anyone heard of someone theorise a strong AI system with quantum computing? IBM seems a few years off from creating a quantum computer. Would be great to see if that is possible. On a sidenote I believe any mathematical construct has an application because it was created in this universe

 

[chiro]

Noja888: You might want to consider whether the information is even local or not: what are you going to do when it isn't local?

As an interesting thing to ponder: consider the idea of the "soul".

A lot of people when they tried to find the soul, cut up the body and were looking for this thing called the soul and unsurprisingly, no one could find a single element that they called the soul.

You might laugh at this, but in a large sense, we still analyze in this exact same way: we isolate and divide in a way where we segregate things into mutually exclusive parts and consider that the totality of the system and its context is within some sort of isolated boundary.

But how are you going to even find the information if most of it doesn't even exist within the boundary?

 

[Evo]

This thread should have been locked a LONG time ago.