On the matter of logic and the world

Constance

What do Zeno's arrow paradox, God, Einstein's theory of time space, and performative contradictions have in common? They all, and more like them, demonstrate how a perverse belief in a logically structured world can generate a false sense of paradox. Logic itself is the paradox.

Zeno's paradox: Why do we think the arrow never should reach the target? It is because logic is a quantitative delimitation of anything it applies to. The distances between the archer and the target are eternally divisible, but it is not the world that is divisible, it is the logic that imposes a principle on the world that says any given determinative distance is divisible, which is true, but in the world as an actuality, nothing is determined. Everything is indeterminate.

God: Can God create a stone so heavy that he himself cannot lift it? This sounds childish, of course, but where does such a thing come from? It comes from the standard concept of what God is, "his" omnipotence. What else can issue from Anselm's Greatest Possible Being? So when the mind takes up this concept as a serious way to think about God, we get these crude derivatives: God's omnibenevolence and omniscience? If true, why would God endure our suffering; an entirely fabricated way to deny the existence of God, which is to argue against a definition of God such that it is indefensible. Pure straw person nonsense, and all based on an overreach of logic. I mean, you take some quantification of God, here the "omni" which is simply a logical universal, and you start generating logical contradictions. so you walk away thinking you've made an important point, when all you've done worked with an abstraction, calling it "real". (The only "real" way to approach the God issue is to observe actuality, not the logic you fit it into.)

Einstein's space time: Space bending?? Nonsense. The concept of bending presupposes space. I am not a physicist, but it is an analytic certainty that if something bends, it must bend in a medium which allows things to bend IN it. Is there an implicit part of this that says there is some "absolute" space in which bending space bends? No. Because space itself is simply a geometrical abstraction that produces contradictions when applied to observing actuality. The actuality of the world is not geometrical. But what does this mean for the physics of space?It means that space time is not about the world at all. As is evidenced by the essential contradiction that arises with positing space in a quantifiable way.

Performative contradictions: Well, first, this sentence is false. And I cannot write in English. And so on. Especially the first, though: how can such a proposition every be "true"? The point I would make is simple: If logic qua logic can produce nonsense like this, then as a system of understanding the world, it is more than suspect. It is "wrong". Not only is logic incongruent with the actual world, it is self annihilating, for how can, as Wittgenstein said, all logic be tautological if it possesses just one inherent contradiction?

Just curiosities here, really. But I do not at present see any way around any of these. It does have rather staggering consequences for the way language and logic can, in empirical science, be in any way "about" the world as an actuality (and not as something already taken up in a system of assumptions).

T Clark

Unless I've misunderstood what your trying to say, this:

Einstein's space time: Space bending?? Nonsense. The concept of bending presupposes space. I am not a physicist, but it is an analytic certainty that if something bends, it must bend in a medium which allows things to bend IN it. — Constance

is a good example of this:

a perverse belief in a logically structured world can generate a false sense of paradox. — Constance

Or is that your point?

Constance

Or is that your point? — T Clark

The point? It is a diffuse point, sort of bound up in the ideas presented, each one in its own right a challenge, but the general point would be that the perversity extends from the thinking that logic can serve as a structured way to speak about the actual world. It cannot, and all of our utterances about the world are really about something else altogether. This something else is. of course, the epistemic relation we have with the world. In the traditional analysis of knowledge, S never even approaches P. Einstein's space time is not about the "actual" world, e.g. Does not "touch" the world.

180 Proof

Logic itself is the paradox. — Constance

On the contrary, misrecognized misuses (e.g. reification) of logic, or grammar, generates "paradoxes".

T Clark

The point? It is a diffuse point, sort of bound up in the ideas presented, each one in its own right a challenge, but the general point would be that the perversity extends from the thinking that logic can serve as a structured way to speak about the actual world. — Constance

I think that Zeno's arrow paradox and performative contradictions, a term I hadn't heard before, are examples of what we call paradoxes. I agree they arise from a misguided attempt to apply rigorous logic inappropriately. I think that's also true about seeming contradictions that come up when trying to talk God into a corner and yell "Gotcha!"

General relativity is something different. GR is a theory, a model, which very effectively predicts the behavior of certain aspects of the world. Talking about space bending is a metaphor that helps people picture and understand what is happening. GR redefined what "space" means. I don't see it as a paradox at all. If you were talking about the different interpretations of quantum mechanics, I would be more likely to agree with you.

Constance

General relativity is something different. GR is a theory, a model, which very effectively predicts the behavior of certain aspects of the world. Talking about space bending is a metaphor that helps people picture and understand what is happening. GR redefined what "space" means. I don't see it as a paradox at all. If you were talking about the different interpretations of quantum mechanics, I would be more likely to agree with you. — T Clark

Space is real, and I don't think space bending is a metaphor. No mysterious force acts upon any two particles with mass that attracts them to each other; they are simply following the curvature of spacetime itself, caused due to their respective masses. Put it this way, metaphors are only as good as that which is source of the borrowed quality and that to which the quality is applied. So, I say, "He is an animal!" and the sense of it depends on the person in question and animals being both familiar. If space bending is just a metaphor, then what IS it that the metaphor is being applied to?

Constance

On the contrary, misrecognized misuses (e.g. reification) of logic, or grammar, generates "paradoxes". — 180 Proof

Yes. But then, the very structure of the performative contradiction, "this sentence is false" is very curious. It is not really a misuse, but a simple logical construction that is self contradictory, that generates contradiction where only tautologies should be allowed.
And with the others, I think there are important problems that are ignored, generally. What is God, if one ditches the Christian "misuse"? Is it wrong to think empirical science dis really not about the actualities lie before us. After all, the actual world is not a quantified presence; language and logic make it so; isn't science's claims about being about the world a hidden reification of logic?

jgill

Space is real, and I don't think space bending is a metaphor. — Constance

Usually this expression is used in reference to spacetime and depends on a certain metric. Objects, however, become distorted by gravity and speed. Length contraction, etc.

Agent Smith

On the contrary, misrecognized misuses (e.g. reification) of logic, or grammar, generates "paradoxes". — 180 Proof

Yep, blame ~~Canada~~ language. There are no (true) paradoxes and if anyone claims that there are, prove it to them that they're misusing language (semantically and/or syntactically). Is this what you're driving at? Quite an ingenious solution; saves the phenomena insofar as 1^st order logic is at stake.

Agent Smith

Logic itself is the paradox. — Constance

How?

Agreed that it can't make the case that it's rational to be rational on pain of circulus in probando. I'm telling you, I'm speaking the truth! How can you prove that, we ask? Well, I vouch for myself, I guarantee that I don't/never lie! WTFery!

The paradox is this: logic is the gold standard for proof but it can't prove itself without committing a fallacy, begging the question. I can't be trusted. Does this get an A for honesty and an F for intelligence? Logic, as it turns out, paradoxically, is a fool! The whole point to its creation and development was to build trust in a system that would always deliver the goods when it comes to truth. Yet, here we are, logic can't justify itself.

180 Proof

... isn't science's claims about being about the world a hidden reification of logic? — Constance

I don't think so, I don't see how, especially insofar as logic consists of syntact translations of tautologies and functions like scaffolding for building mathematical models of physical systems.

Constance

Usually this expression is used in reference to spacetime and depends on a certain metric. Objects, however, become distorted by gravity and speed. Length contraction, etc. — jgill

Yes, so account for distortions, what is the most elegant theory? The curvature of space. Is this an idea that makes sense, not as it is theorized about, but as a singular concept? What do you do with theory that explains things well, but is radically counterintuitive? Space bending is, as Wittgenstein put it, "an argument place" meaning it must first, to make sense at all, pass through the logic that is deployed to explain it and bring it into being, and space bending presupposes yet another space IN WHICH bending may occur, but this leads to an infinite regression of spaces. Maybe. Not clear on how positing this "second" space would make the same demands the first is subject to (that it bends, of course). At any rate, clearly, this second space would be eternity (keep in mind, we do not "see" eternity when looking up in the ight sky. This is because we are not seeing this second order of spatial existence. Interesting to note: When you do gaze into the night sky, there is this unsettling weirdness of at once facing infinity, yet not comprehending it at all. this is because what you are observing is the inside of your cranium).

T Clark

Space is real, and I don't think space bending is a metaphor. — Constance

Seems to me, most ideas refer back, or at least originally referred back, to something at human scale. That certainly makes sense with "space." Of course, there's always been space - the three-dimensional volume in a room, etc. I wonder if the development of the idea of space was changed by the development of Cartesian geometry. It certainly seems like it would have been as people learned that there were long distances between those bright things up in the sky. Science and science fiction probably changed the meaning of the word even more. General relatively just continued those changes and added another dimension. So, no. Space is not real, if by that you mean that it hasn't changed and can't change again.

And of course space bending is a metaphor. People can bend a tree branch or a piece of metal, but you can't bend air. Until, suddenly, you can.

So, I say, "He is an animal!" and the sense of it depends on the person in question and animals being both familiar. — Constance

It doesn't make any difference who the person in question is, if it's male, he is an animal. Sorry, a little cute.

As I said, I think you are caught up in the same paradox creation that you started out writing about.

T Clark

Is it wrong to think empirical science dis really not about the actualities lie before us. After all, the actual world is not a quantified presence; language and logic make it so; — Constance

If this is true, and I think it is, why can't spacetime bend?

isn't science's claims about being about the world a hidden reification of logic? — Constance

Everything put into language is a reification of something. Every word is reification. Reification and metaphor, that's all there is. I guess reification is the same thing as metaphor.

T Clark

The curvature of space. Is this an idea that makes sense, not as it is theorized about, but as a singular concept? — Constance

Yes.

What do you do with theory that explains things well, but is radically counterintuitive? — Constance

Science is all about finding out situations where our intuition is wrong. Intuition doesn't come from the great beyond, it can be changed by experience and understanding. Do you also doubt special relativity and quantum mechanics? Those theories are certainly counterintuitive.

EugeneW

What do Zeno's arrow paradox, God, Einstein's theory of time space, and performative contradictions have in common? — Constance

Zeno's arrow proves spacetime is continuous. The problem with discrete spacetime is particles moving in it and time advancing. Spacetime can't be broken up though and the nature of space remains a mystery.
Einstein's theory of spacetime showed we can actually bend space by mass. How mass informs space remains a mystery in GR.
The gods created spacetime. The reasons for their grounds remain a mystery.

That's a triplet mysteries. Performative contradiction, like I'm dead, are no mystery though.

Constance

Agreed that it can't make the case that it's rational to be rational on pain of circulus in probando. I'm telling you, I'm speaking the truth! How can you prove that, we ask? Well, I vouch for myself, I guarantee that I don't/never lie! WTFery!

The paradox is this: logic is the gold standard for proof but it can't prove itself without committing a fallacy, begging the question. I can't be trusted. Does this get an A for honesty and an F for intelligence? Logic, as it turns out, paradoxically, is a fool! The whole point to its creation and development was to build trust in a system that would always deliver the goods when it comes to truth. Yet, here we are, logic can't justify itself. — Agent Smith

Unless, on the other hand, the question begged leads to a finality that IS a finality. Put it this way, if logic were to conceive of its own generative foundation, that too would be suspect. Indeed, to question logic in this way is simply nonsense, for the asking of the question is self contradictory since the question possesses the logic form of an interrogative (and implicit assertions, negations, and so on). We only get put out because we expect logic to be something it is not. It exists, like a chair or a piano, and talk about the generative source of anything at all is nonsense.
Just to point out, logic has no point. Unless you think it is part of a divine plan, or the like. Also, when we use logic to lie, it is not logic's fault, but its use. This is different from "I am lying" or "this sentence is false." These are fashioned out of logic itself.

Agent Smith

One class of paradoxes is of particular interest to me because it seems to drive a giant wedge between rationalism and empiricism.

Zeno has a couple, one being the a priori impossibility of motion and the a posteriori actuality of motion (the dichotomy paradox).

Up until Zeno, the Parmenidean luminary, discovered these paradoxes, (Greek) thinkers must've been completely convinced of the power of lumen naturale (the light of reason) to make sense of the world - in every case, reason merely served to confirm observation or if ever the two were in conflict, reason would come out on top, an doublechecking empirical data would reveal errors, subtle and egregious.

This, however, wasn't/isn't possible with the dichotomy paradox. Logic clearly demonstrates motion is impossible; observation, to our dismay, shows that motion is not only possible but actual (ambulando solvitur).

As you can see, a pre-Zeno reconciliation of rationalism and empiricism is impossible. We have to make a choice: believe our minds or believe our legs, but not both! We all know Zeno's preference: motion, in the Parmenidean umiverse, is an illusion. I guess this means Zeno, Parmenideans, were true blue rationalists.

That said, Zeno clearly wasn't as mathematically talented as Archimedes who had used the method of exhaustion (limits) to calculate the value of $\pi$ , presaging the advent of calculus by roughly 1.8 k years. Calculus in its full glory took off with Newton and Leibniz and it could be said that calculus (differentiation and integration) could one day bridge the rationalism vs. empiricism gulf.

Aside: Actual may not imply possible.

Constance

... isn't science's claims about being about the world a hidden reification of logic?
— Constance
I don't think so, I don't see how, especially insofar as logic consists of syntact translations of tautologies and function like scaffolding for building mathematical models of physical systems. — 180 Proof

Yeah, it works, and very well at that. But the actual "things of the world" are actualities that are not the logical forms assigned them when trying to make things work. So when the astronomer analyzes a light spectrum, the logicality of the analysis is what s/he contributes and not the visible phenomenon. This latter has nothing at all of the logicality in the description, yet science is generally confident that its work is essentially connected to the objects of its quantifications, that is, logicality (logic being essentially a quantifying utility).

Constance

Space is real, and I don't think space bending is a metaphor.
— Constance

Seems to me, most ideas refer back, or at least originally referred back, to something at human scale. That certainly makes sense with "space." Of course, there's always been space - the three-dimensional volume in a room, etc. I wonder if the development of the idea of space was changed by the development of Cartesian geometry. It certainly seems like it would have been as people learned that there were long distances between those bright things up in the sky. Science and science fiction probably changed the meaning of the word even more. General relatively just continued those changes and added another dimension. So, no. Space is not real, if by that you mean that it hasn't changed and can't change again.

And of course space bending is a metaphor. People can bend a tree branch or a piece of metal, but you can't bend air. Until, suddenly, you can. — T Clark

The idea of wind bending certainly seems unproblematic. It is not like bending something solid, but it is as determinate quantity of something, the kind of thing such that it curving here, arching there makes sense. If one can conceive of a material substance that is so hard it breaks before is bends at all, then one can still conceive of it bending given some alteration in the conditions of it doing so. That is, it is still logically possible that it can bend. The point I would make is that if the posting space "bending" is a metaphor only and not meant to be taken literally, then what IS the "literal" side of this?

Cartesian geometry had an impact on the way things were conceived and measured, I know. Important is the the basic assumption that objects are in space res extensa at all! Extension in space requires the a conceptual framework to conceive of it. The concept "extension" is a quantitative measure: to extend something has to extend to a certain degree, length, depth; and if the extension is deemed indeterminate, it is implied that determined quantifications would be possible if one knew them. The question here is, Is the world a quantified presence that when encountered we "read off" from its presence what it already has. Or, is the world altogether without quantification, and the quantifying is done by us in our efforts to systematically make use of it?

Constance

Is it wrong to think empirical science dis really not about the actualities lie before us. After all, the actual world is not a quantified presence; language and logic make it so;
— Constance

If this is true, and I think it is, why can't spacetime bend?

isn't science's claims about being about the world a hidden reification of logic?
— Constance

Everything put into language is a reification of something. Every word is reification. Reification and metaphor, that's all there is. I guess reification is the same thing as metaphor. — T Clark

As I see it, to bend absolutely requires a medium in which a thing can bend. Bending is a contingent idea.
Reification is the same thing as metaphor? An intriguing idea. How so?

Constance

Science is all about finding out situations where our intuition is wrong. Intuition doesn't come from the great beyond, it can be changed by experience and understanding. Do you also doubt special relativity and quantum mechanics? Those theories are certainly counter-intuitive. — T Clark

I think quantum physicists "doubt" quantum mechanics, meaning they really don't understand it because it itself is not clear...yet. By counterintuitive is simply mean that space bending makes no sense as a logical concept. It is apriori nonsense: One cannot even imagine something bending without a medium in which it bends. I said space is real, and I mean space is not an abstract concept. I wave my hand through ???? It is not nothing. The physical concept of nothing requires space to be nothing IN. This is how it is with bending, or curving, arching, rounding out, and so on: these are spatial terms. They presuppose space. Space bending is like saying logic implying: to imply is to USE logic. It cannot be its own presupposition.

Constance

Zeno's arrow proves spacetime is continuous. The problem with discrete spacetime is particles moving in it and time advancing. Spacetime can't be broken up though and the nature of space remains a mystery.
Einstein's theory of spacetime showed we can actually bend space by mass. How mass informs space remains a mystery in GR.
The gods created spacetime. The reasons for their grounds remain a mystery.

That's a triplet mysteries. Performative contradiction, like I'm dead, are no mystery though. — EugeneW

Well, just note that you had to bring god into it. If you do your explaining of something with this kind of talk, then you must realize you have gone metaphysical. Is space time a metaphysical concept? It is. Of course, measurements of speed, mass, relative values for these and so on, this is not metaphysical at all. Very clear ( I have read how it is clear, that is. Not the actual physics). But space time IS. For in order for it to make sense one must posit something entirely inconceivable: that IN which space bends.

the gods created spacetime? No, I think not. We created it in a system of pragmatic utility to "deal with" what the "gods made". Quantitative measurement is a logical function. If you think we are the gods, then fine. Maybe we are.

But at last, I agree, it is a mystery. But the mystery has consequences. How about acceleration as a concept? Acceleration occurs in spacetime, and this is the mystery. How about any quantification AT ALL vis a vis the empirical world?

Constance

This, however, wasn't/isn't possible with the dichotomy paradox. Logic clearly demonstrates motion is impossible; observation, to our dismay, shows that motion is not only possible but actual (ambulando solvitur).

As you can see, a pre-Zeno reconciliation of rationalism and empiricism is impossible. We have to make a choice: believe our minds or believe our legs, but not both! We all know Zeno's preference: motion, in the Parmenidean umiverse, is an illusion. I guess this means Zeno, Parmenideans, were true blue rationalists. — Agent Smith

Bring Parmenides and Heraclitus together and you have Plato, essentially. It seems Parmenides won the argument in Plato, the latter insisting the what what truly real was the idea, not the palpable phenomenon. By my thinking, Heraclitus wins out, though it gets pretty complicated, because while the desire to yield to an ontology of a palpable world over what is merely a conception of it, concepts are in their own way, just as palpable: No concepts, no singularities.

Slippery. The trick is, obviously, to reconcile the conceptuality with the irrational yet imposing and really impossible world (impossible because it is not contained categorically. It qualitatively "exceeds" categorical thinking. Sui generis).

EugeneW

Is space time a metaphysical concept — Constance

It's a physical concept. Our perception of space is like it really is. We can move in it. Objects can move in it. It's the sauce between matter. It's the stuff objects can move in.

T Clark

As I see it, to bend absolutely requires a medium in which a thing can bend. — Constance

People used to think that there must be a luminiferous aether because they thought that electromagnetic waves had to have a medium to propagate through. Turns out they were wrong. I don't see how your inability to conceive of space bending without any outside space to bend in is any different.

I think quantum physicists "doubt" quantum mechanics, meaning they really don't understand it because it itself is not clear...yet. — Constance

I don't think that any reputable physicist doubts quantum mechanics at all. They may argue about the interpretation, but I think that is a metaphysical argument, not a scientific one. Fact is, it works. As they say, shut up and calculate. It doesn't make any difference if you can understand why. Science isn't about understanding why things happen, it's about understanding how things happen. Your "...yet" is a bit too cute for my taste. Most physicists don't think further study will make QM any less counterintuitive. The world is not obligated to arrange itself in a way that fits into your way of thinking about it. You can't change the world, but you can change your thinking.

They presuppose space. Space bending is like saying logic implying: to imply is to USE logic. It cannot be its own presupposition. — Constance

I'll say this one more time, then I promise I won't say it again - You've fallen into the same trap of mistaking the words for the world that you identify in the OP.

EugeneW

If you think we are the gods, then fine. Maybe we are. — Constance

I dont think we are the gods. I think they made us. They had good reason. There are as many gods as creatures in the universe. We just play the game they played already eternally. From virus gods to hominid gods. The god story will be revealed shortly... Exclusively here on Teeee...Peee...Eeeef!

Constance

It's a physical concept. Our perception of space is like it really is. We can move in it. Objects can move in it. It's the sauce between matter. It's the stuff objects can move in. — EugeneW

Of course it is, that is, until you get to the part where it is bending. Then you have to explain this. When you reach an explanatory threshold like this, you have to concede that though the idea works to explain one thing, it creates a problem that also needs explaining, like a rug's wrinkle that is flattened out here, but rises up again over there. In this case the wrinkle is a metaphysical one.

The real problem? This lies not in the world, but in the conditions of its observation. To observe at all is to condition the object. Language and logic are not these "transparencies" that record the conditions of the world around us. They are "opacities" if you will, that are an independent existence.

EugeneW

To observe at all is to condition the object — Constance

Of course. But we also have to condition the subject, i.e, us. There is no such thing as "an observation". Thats already a theoretical claim. How and what we observe is not theory-laden but a theory, a story on its own. Space can have an objective existence, like the bending of it. A bend space(time) is a physical reality. The GW hunters at LIGO don't wanna chase metaphysical ghosts!

Constance

People used to think that there must be a luminiferous aether because they thought that electromagnetic waves had to have a medium to propagate through. Turns out they were wrong. I don't see how your inability to conceive of space bending without any outside space to bend in is any different. — T Clark

Think of it as an apriori problem, not an empirical one. What if someone theorized in a way that violated the principle of causality? Putting aside that someone has in fact done this, ask your self how well this sits with your understanding. It is a blatant absurdity, apodictically impossible. Rejecting the aether theory of light propagation was not like this at all since aether had no apriori status.

I don't think that any reputable physicist doubts quantum mechanics at all. They may argue about the interpretation, but I think that is a metaphysical argument, not a scientific one. Fact is, it works. As they say, shut up and calculate. It doesn't make any difference if you can understand why. Science isn't about understanding why things happen, it's about understanding how things happen. Your "...yet" is a bit too cute for my taste. Most physicists don't think further study will make QM any less counterintuitive. The world is not obligated to arrange itself in a way that fits into your way of thinking about it. You can't change the world, but you can change your thinking. — T Clark

Richard Feynman: "I think I can say that nobody understands QM." Not that I am fond of quoting authority to argue a point, but in my own limited exposure to this idea, I can say with confidence that it is not something people understand. When I say "doubt" I mean just this. They don't doubt the repeatability of the evidence; they doubt it can be understood. A bit like understanding rockets go up, escape the atmosphere and so on, but not having a clue as to how. How that cat can both dead and alive. Unless you have something I never heard of.

But as to, "The world is not obligated to arrange itself in a way that fits into your way of thinking about it." If you think the world is so "radically contingent" that anything could happen because nothing constrained by the "laws" of physics, I think you are right. There are no laws like this sitting out there among things. This is our doing, and it sounds like you agree with this. But are you willing to agree with the what follows from this? It is not the indeterminacy of a handful of problematic ideas. It is all that comes before us: To know at all is to take up the world AS this knowledge claim is expressed. Taken APART from the knowledge claim, pure metaphysics. The cup on the table, e.g. is qua cup, a cup, but qua a palpable presence not a cup at all.

Constance

I dont think we are the gods. I think they made us. They had good reason. There are as many gods as creatures in the universe. We just play the game they played already eternally. From virus gods to hominid gods. The god story will be revealed shortly... Exclusively herd on Peee Eees Eeeef! — EugeneW

I will be listening for the god story, looking for a clue to something profound. Hint: I don't think they made us. Nor did we make them. It is a conspiracy and we are both in on it.

On the matter of logic and the world

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