But apparently the known laws of physics (regularities) have been stable for billions of years. — litewave

Isn't that just the currently contingent theory, subject to revision in next week's Physical Review Letters? You have no actual evidence for such a proposition. It's an idea based on a mathematical model in a highly speculative area. It's a lot different than noticing that bowling balls fall down, isn't it? If these "known laws" -- which have become known only in the last few decades -- are changing in subtle ways, we'd be the last to know about it. Not so?

Indeed. I can't even be sure that you are not just a figment of my imagination. But I am pretty sure that whatever you are, you are what you are and not what you are not. In other words, you are a consistent object, identical to itself. To assume otherwise would be a nonsense which would lead to a logical explosion that would make discussion, science and understanding meaningless. — litewave

Agreed. We adopt scientific realism for pragmatic reasons. I suspect we are in agreement.

And FWIW, bowling balls always seem to fall down, but electrons are detected as spin up or spin down randomly. And so we invent a contingent theory to "explain" that, using an explanation that nobody really believes or understands. The 20th century was not kind to the Newtonian worldview of a consistent reality "out there," can we agree on that?

Yet in your example with objects falling down, all the historical theories from Aristotle to Einstein say that objects consistently fall down rather than up or in random directions. The later theories give more accurate predictions than earlier ones but from all of them it seems that the phenomenon of objects falling down is highly stable. How do you explain that if not by a stable regularity in the world? — litewave

If you go to the moon, the gravitational acceleration is different than on earth, And I took the trouble in my post to give the striking example of dark matter, which shows that we still don't understand gravity. If you deny that human-created physics is historically contingent, you must not be familiar with the history of science. "Bowling balls fall down" is not a law of physics, it's an empirical observation. We STILL don't fully understand the underlying law, if in fact there is one.

There are obviously persistent regularities in the world that we know have been observed for millennia and have been used to make successful predictions. — litewave

Yes indeed. The Ptolemaic system that placed the earth at the center of the solar system fit all known observations and was accepted for millennia. In fact Ptolemy's system actually fit the observed data better than the new heliocentric system of Copernicus, because Copernicus thought the orbits were circles with the sun directly at the center. Showing that "obvious persistent regularities" can be flat out wrong, and overthrown in a historical instant. Once Kepler and Newton showed up, it was all over for Ptolemy. But he had a nice 1600 year run. Made extremely successful predictions.

This doesn't mean that the regularities cannot change but they are obviously highly stable. — litewave

"Obviously" is not a scientific principle, it's an anti-scientific one. Newton's ideas were obvious. Einstein's are much less so.

Your point of view has a name, Scientific realism. It is a metaphysical stance, not an established fact.
— fishfry

Yes but I don't know of a better alternative. — litewave

That can only be because you didn't bother to read the Wiki and SEP articles I linked. Refusing to read the counterarguments then saying you don't know them doesn't prove anything except that you prefer not to learn about what you don't know.

Realism explains that our theories work because they correspond to reality while Instrumentalism offers no explanation why our theories work. — litewave

Now you're just making an argument for scientific realism. Which is fine, it's a perfectly good idea. It's just not provable. It literally lies outside of science. It's a metaphysical assumption.

I'm not arguing for the falsity of scientific realism; only noting that it's a metaphysical stance and not a scientific one. It's not even necessary to assume in order to do science. Whether there's really a consistent reality "out there" or only seems that way due to our highly limited observational experience, is not something we can know for sure. After all others have noted in this thread that the latest theories suggest that perhaps the only reason our laws of nature are the way they are is that we just happen to live in this particular branch of the multiverse; and that nature could be quite different in other ones. Even the scientists don't believe in "obvious persistent regularities" anymore, since the ones we observe are just random rolls of the dice and could have been different. You know, the famous six constants that someone linked.

Gotta go, it's feeding time in my vat.

Recently I've been thinking about why we live in a world with stable laws of physics — litewave

Do we? Aristotle said that bowling balls fall down because bowling balls are like the earth and things tend to go to like things. Fire is like air, that's why fire goes up. Good a theory as any, two thousand years worth of mindshare.

Newton said bowling balls fall down because $F = \frac{m_1 m_2}{r^2}$.

Einstein said that bowling balls fall down because spacetime is curved by mass and bowling balls are just following a geodesic in spacetime near the earth.

Multiverse theory says that bowling balls fall down because we happen to live in a universe where bowling balls fall down. In some other universe, people don't go bowling. Or something. I'm not actually sure what the multiverse says about bowling balls.

But the larger point is clear. The laws of physics are historically contingent ideas made up by people.

But perhaps by "laws of physics" you mean the "ultimate" laws of physics that our contingent theories are only approximations to. But what makes you think that (1) there are any such things; and (2) even if there are, that they don't change over time? Those are two metaphysical assumptions, not supported by empirical proof.

As a more striking example, consider dark matter. One theory of dark matter is that it's made of particles that interact with the gravitational field but not with electromagnetism, so that we can't possibly ever see them. Nevertheless they affect the rotational speed of galaxies.

Another fascinating approach to dark matter is called modified Newtonian dynamics, which is the speculative idea that we haven't got gravity quite right, and that we need to make subtle corrections to the theory to account for the observed rotational speed of galaxies.

So you say we live in a world of stable laws of physics, but that claim is highly questionable. First, if by "laws of physics" you mean our human-created theories as delineated by the likes of Aristotle, Galileo, Newton, and Einstein, those clearly are not stable, but rather change over time.

But if by laws of physics you mean some sort of ultimate rules that the world must obey, I have to ask you one, why you think there are any; and two, what makes you think they don't change all the time? I don't doubt that you could give a decent argument as to why these two things are the case; but I hope you'd at least concede that you are making metaphysical assumptions that lie far outside the limits of science.

Your point of view has a name, Scientific realism. It is a metaphysical stance, not an established fact. The Wiki link has arguments for and against it; and the SEP article has lots more.

Don't worry about that, the conversations are completely different. Luke is on a completely different plane. — Metaphysician Undercover

Maybe I should start reading the rest of this thread so we can have a free-for-all instead of a tag team.

I don't see the distinction you're trying to make here, between an inductive conclusion, and "an abstraction intended to formalize an aspect of nature". What do you mean by "formalize" other than to state an inductive conclusion. — Metaphysician Undercover

Good question, let me see if I can sharpen my explanation.

If I see 100 bowling balls fall down, "bowling balls always fall down" is an inductive conclusion. But F = ma and the law of Newtonian gravity are mathematical models from which you can derive the fact that bowling balls fall down. It's a physical law, meaning that if you assume it, you can explain (within the limits of observational technology) the thing you observe.

But this is not an important point in the overall discussion.

I see the majority of definitions as inductive conclusions. Either they are like the dictionary, giving us a formalization (inductive conclusion) of how the word is commonly used, or they are intended to say something inductive (state a formalization) about some aspect of nature. — Metaphysician Undercover

Ok. I don't think the definition of induction versus a formal model is super important here. But "bowling balls always fall down" is simply a generalization of an inductive observation, whereas the law of gravity lets you derive the fact that bowling balls fall down; and that in fact on the Moon, they'd weigh less. The latter is not evident from "bowling balls always fall down," but it is evident from the equation for gravitational force.

I think you are missing the point. If I drop a hundred bowling balls and I say, "Bowling balls fall down. That's a law of nature," then THAT is an inductive conclusion. — Metaphysician Undercover

It's not an important point, but for what it's worth, I think you are missing a major point as to the nature of science.

I think it's you who is missing the point. I do not have a firm grasp on the distinction you are trying to make, because there are no principles, or evidence to back up your claim of a difference between these two. — Metaphysician Undercover

It's not important to the larger conversation.

F=ma says something about a much broader array of things than just bowling balls. — Metaphysician Undercover

And yet it lets us derive the falling of bowling balls. After all this you DO understand the difference.

So one could not produce that generalization just from watching bowling balls, you'd have to have some information telling you that other things behave in a similar way to bowling balls. Mass is a property assigned to all things, and the statement "f=ma" indicates that a force is required to move mass. How can you not see this as an inductive conclusion? It's not just a principle dreamed up with no empirical evidence. In all cases where an object starts to move, a force is required to cause that motion. It might have been the case that "force" was a word created, thought up, or taken from some other context and handed that position, as being what is required to produce motion (acceleration), but this does not change the inductive nature of the statement. — Metaphysician Undercover

This point is not central to the main point, which is that models must necessarily omit key aspects of the thing being modeled.

As I said, I really do not understand how a "formalization" as used here, is anything other than an inductive conclusion. So I do not understand how you think my notion of induction is wrong. Perhaps you should look into what inductive reasoning is, and explain to me how you think a "formalization" is something different. I think induction is usually defined as the reasoning process whereby general principles are derived from our experiences of circumstances which are particular. — Metaphysician Undercover

Not central, let's move on.

That such things are non-physical is what I dispute. How could there be a quantity which is not physical? "Quantity" implies an amount of something, and if that something were not physical it would be nothing. "Order" implies something which is ordered, and if there was no physical things which are ordered, there would be no order. And so on, for your other terms. It makes no sense to say that properties which only exist as properties of physical things are themselves non-physical. — Metaphysician Undercover

Ok fine, then order is physical and the mathematical theory of order is an abstraction or model that necessarily misses many important real-world aspects of order yet still allows us to get some insight. That's the point of abstraction, which I already beat to death in my last post.

When you say "formalize" here, do you mean to express in a formal manner, to state in formal terms? — Metaphysician Undercover

One, to abstract, and two, to build a mathematical model of the abstraction. Or maybe those two are the aspects of the same process. I'm making a larger point, not splitting hairs.

If it is physical things in the world which have order, and mathematics seeks to express this order in a formal way, then how is this not making a generalization about the order which exists in the phyiscal world, i.e. making an inductive conclusion? — Metaphysician Undercover

Ok they are. What is your problem with this?

How can I agree with this? Chess is a game of physical pieces, and a physical board, with rules as to how one may move those physical pieces, and the results of the movements. The physical board and pieces are not "nothing at all in the real world", they are all part of the world. — Metaphysician Undercover

That's pure sophistry. There is no physical law that requires the piece to move the way they do.

What's with your motive here? Why do you insist on taking rules like those of mathematics, which clearly refer to parts of the real world, and remove them from that context, insisting that they do not refer to any part of the real world? Your analogy clearly does not work for you. The chess game is obviously a part of the world and so its rules refer to a part of the real world, just like quantity, order, shape, and symmetry are all parts of the real world, and so the rules (or formalities) of these also refer to parts of the real world. — Metaphysician Undercover

I'm explaining to you that whatever your concept of physical order is, mathematical order is an abstraction of it, which is necessarily a lie by virtue of being an abstraction or model, yet has value just as a map is not the territory yet lets us figure out how to get from here to there.

Yes, I agree with this here. Now the issue is how can you say that there is a collection of things which has no inherent order. — Metaphysician Undercover

I don't say that. Now that I understand what you mean by order, I'm happy to agree that every collection of physical things has an inherent order, namely "where every item is in time and space."

If things in the world have order, and mathematicians seek to formalize that order, then where does the idea of "no inherent order" come from? — Metaphysician Undercover

Now that I understand what you mean by inherent order, I no longer need to argue this point. Physical collections have inherent order, if by order you mean "where everything is, or how everything is arranged, in time and space."

That notion of "no inherent order" is obviously not derived from any instance of order, and if mathematicians are seeking to formalize the idea of order, the idea of "no order" has no place here. It is in no way a part of the order which things have, and therefore ought not enter into the formalized idea of "order". — Metaphysician Undercover

I've conceded your point, now that I understand what you mean by inherent order.

Have you lost track of our conversation? The idea of "no inherent order" is what we are talking about, and this is what I say does not correspond with our observations of the world. — Metaphysician Undercover

Once I concede that, what else have you got?

We observe order everywhere in the world. Sets do not correspond to collections, because any collection has an inherent order, existing as the group of particular things which it is, in that particular way, therefore having that order, yet as a "set" you claim to remove that order. — Metaphysician Undercover

Now that I understand what you mean by order, I see what you are talking about and I no longer oppose your point. Simple matter of understanding what you mean by inherent order, which you could have, but inexplicably chose not to, explain many posts ago

I'll repeat. It's what we've been discussing, your idea of "a set", as a collection of things with no inherent order. Something having no inherent order is not based in, nor inspired by the real world, we don't see this anywhere in the world. We can also look at the idea of the infinite. It is not inspired by anything in the natural world. It is derived completely from the imagination. — Metaphysician Undercover

It's an abstraction that necessarily includes SOME aspects of the thing being modeled and excluces OTHER aspects. Just as a street map includes the orientation of the roads but ignores the traffic lights.

Let's try this. We'll say that a "formalism" relates to the real world in one way or another, and then we can avoid the issue of whether it is an inductive conclusion. We'll just say that it relates to the world. Now, can we make a category of ideas which do not relate to the real world? Then can we place things like "infinity", and "no order" into this category of ideas? But rules about quantifying things, and rules about chess games do relate to the real world, as formalisms. — Metaphysician Undercover

How do we make maps without drawing in the cars?

Can you see that these ideas are not formalisms, nor formalizations in any way? Because they are purely imaginary, and not grounded in any real aspects of the natural world, there is no real principles whereby we can say that they are true or false, correct or incorrect. — Metaphysician Undercover

That's right. A map is correct about some aspects of the world and incorrect about others. It's an abstraction. It's a representation of SOME ASPECTS of the thing being modeled but by necessity not ALL aspects otherwise the map would have to be an exact copy of your entire city or state. Globes would have to be as big as the earth. That they are smaller means that they are incorrect regarding size. That the oceans on a globe are not wet means they are incorrect about the wetness of the oceans.

They cannot be classed as formalizations because they do not formalize anything, they are just whimsical imaginary principles. — Metaphysician Undercover

Maps are imaginary principles and don't formalize anything? Do you see why I think you're trolling?

To use your game analogy, they are rules for a game which does not exist. People can just make up rules, and claim these are the rules to X game, but there is no such thing as X game, just a hodgepodge of rules which some people might choose to follow sometimes, and not follow other times, because they are not ever really playing game X, just choosing from a vast array of rules which people have put out there. Therefore there is nothing formal, so we cannot call these ideas formalisms or formalizations. — Metaphysician Undercover

You're just playing games now, not seriously engaging with me.

I disagree with your notion of truth. I think truth is correspondence, therefore not in the thing itself, but attributable to the accuracy of the representation of the thing. Identity is in the thing, as per the law of identity, but "true" and "false" refer to what we say about the thing. — Metaphysician Undercover

What would a true map be, in your opinion? A map of your city or town, say. Would it have to be the same size? Would the rivers and lakes have to be wet? Would the cars have to be on it?

I think this is a completely unreasonable representation of "truth", one which in no way represents how the term is commonly used. We say that a proposition is true or false, and that is a judgement we pass on the interpreted meaning of the proposition. We never say that truth is within the thing we are talking about, we say that it is a property of the talk. or a relation between the talk and the thing. — Metaphysician Undercover

Map map map map map. Engage with the point, please.

Take a look at your example. The bricks are never "orderless". They come from the factory on skids, very well ordered. Your idea of "orderless sets" in no way models our everyday notion of a collection. — Metaphysician Undercover

Map map map map map. Engage with the point, please.

The point is that orderlessness is in no way a formalization. A formalization is fundamentally, and essentially, a structure of order. Therefore you cannot start with a formalization of "no order". This is self-contradictory. As I proposed above, the idea of orderlessness, just like the idea of infinite, must be removed from the category of formalizations because it can in no way be something formal. To make it something formal is to introduce contradiction into your formalism. — Metaphysician Undercover

Why are the oceans dry on globes? Engage with the point, please.

What I'm complaining about is your attempt to represent nothing, and say that it is something. You have an idea, "no inherent order", which represents nothing real, It's not a planet, a star, or any part of the universe, it's fundamentally not real. Then you say that this nothing exists as something, a set. So this nothing idea "no inherent order" as a set. Now you have represented nothing (no inherent order), as if it is the property of something, a set. — Metaphysician Undercover

If you would engage with my examples of maps and globes, I would find that helpful.

The idea of contradictory formalisms is not at all new to me. I am very well acquainted with an abundance of them. That's why I work hard to point them out, and argue against them. — Metaphysician Undercover

If you would engage with my examples of maps and globes, I would find that helpful.

I don't see how this is analogous. Galileo represented something real, existing in the world, the motions of Jupiter's moons. What I object to is representing something which is not real, i.e. having no existence in the world, things like "no inherent order". This is not a representation, it is a fundamental assumption which does not represent anything. If a formalism is a representation, then the fundamental assumption, "no inherent order" cannot be a part of the formalism. — Metaphysician Undercover

And sets represent aspects of collections, which exist in the world. And they omit "inherent order," which for sake of argument I'll agree collections in the world have.

Consider this analogy. The idea of "no inherent order" describes nothing real, anywhere. So why is it part of the map? Obviously it's a misleading part of the map because there is nowhere out there where there is no inherent order, therefore I would not want it as part of my map. — Metaphysician Undercover

I don't think I have anything left to say. Perhaps we're done. This isn't fun and it isn't educational.

Yes, I get very frustrated when the map shows something which is not there. I look for that thing as a marker or indicator of where I am, and when i can't find it I start to feel lost. Then I realize that it was really the maker of the map who was lost. — Metaphysician Undercover

Well that has nothing to do with anything. Maps don't show things that aren't there. The question is, how do you feel when a map omits things that ARE there, like wet lakes and rivers, cars, and the size and scale of the actual territory being modeled.

sorry let me learn this forum. it'll take me a maybe like 1 more hour... — Ben Ngai

No prob it took me years to figure out the @ sign!

I really hope this is true now, because set theory is among the coolest pure math subject. And it could have vast physical applications potential? — Ben Ngai

Well in my opinion no, because it's not likely to be true that the mathematical real numbers are physical. But yes if they are, it would be a huge deal. But again, think what it would mean for the Continuum hypothesis to become a problem of physics. "Let's write a grant application to count the number of points in a meter of space and see which Aleph that is." Very unlikely. Unless some genius yet unborn figures it out.

But I think we're looking at it the wrong way. Instead of saying Math and physics are the same. We can say This universe is one of the many universes with unique properties that math can completely be derived by just a space and numbers. — Ben Ngai

Could be.

Wow, so i might have accidentally come up with the idea of the century if it turns out to be true at least even in some way or leads to an explosion of new ideas?

That's what I'm hearing? But i know that's not what you're saying.

I won't get my hopes up.

Before someone else tries to name it. I want to call this the Mathematical Theory of the Universe. if it becomes scientific cannon. — Ben Ngai

If you tag my handle I will be notified of your reply. That is, you can highlight some of my text and hit Quote, or you can simply type in an '@' sign followed by my (or anyone else's) handle in double quotes. Or you can hit the @ button above the edit window and find the handle in the search bar. This will trigger a notification to me that someone's talking to me or about me. Otherwise I might miss your reply.

Now the idea that the world is accurately modeled by the real numbers is not new, but if it someday turns out to be true it will most definitely be the idea of the century. It would be a massive mathematical and scientific revolution. As I've noted, if nothing else it would turn set theory into an experimental science. I find this most unlikely.

The idea of the mathematical universe is due to Max Tegmark. He argues that the universe is not only modeled by mathematics, but that it actually "is" mathematics. That is, the universe is literally a mathematical structure. Many people take this idea seriously; while others, myself included, regard this as a massive elementary category error that is so obviously wrong that he must be trolling.

Fish, thanks for help me bounce this outlandish idea. I was looking for someone that would help and reddit was no help. If this forum didn't exist i probably would have wrote a first draft and published a book that nobody would read then be sad and stop sharing my wild ideas due to being frustrated from being ignored. — Ben Ngai

You're welcome. I'm very happy to know that my pedantic pickiness has been useful for a change.

But you know philosophically, the idea that the physical universe is modeled by the real numbers is very common. For example in physics, time is modeled by the real numbers, even though this is very unlikely to be literally true. I don't think the physicists give this much thought, but it's an important philosophical issue.

So can you bare with me, — Ben Ngai

I will keep my clothes on if that's ok :-)

Fish, I don't think you're at odds I just presented the most crazy, outlandish idea that exists at the moment on a metaphysics forum. — Ben Ngai

Like I say, I only jumped in to correct the claim that each real number is characterized by a property. Other than that, I took no stand.

I agree with you that the idea that the real numbers might be physically real is an interesting one, full of wild implications. Sometimes I'm too picky for my own good.

Sorry Fish I misread your post. — Ben Ngai

You're replying before I'm finished typing. I'm out of breath! I don't mean to be at odds. I think the idea that the physical world is the same as the mathematical real numbers is highly unlikely, but if it ultimately turns out to be true it will be one hell of a revolution in both math and physics. Do you think the Banach-Tarski paradox would become a physical reality? Or would you reject the axiom of choice? You'd have many conceptual problems along these lines.

In any event I only popped in to point out that the statement that each real number is characterized by a property, is false. It's not right. But if you meant the natural numbers, you're right and it was only a typo.

Real analysis was the easiest subject in undergrad for me. Went to class. didn't study got A+ from chancellor professor. Made me consider grad school seriously. I skipped to measure theory my senior year and took some grad econ and stat. That was really hard and I realized grad school wasn't for me. To put it bluntly. — Ben Ngai

I notice you've changed the subject. Your ideas are muddled. Your credentials mean nothing.

Also it's been like 9 yeas since i took real analysis so... i might be confused. — Ben Ngai

Well you know there are no infinitesimals in the real numbers, right? An infinitesimal by definition is a quantity that is strictly between 0 and 1/n for any natural number n. Clearly if you claim something's an infinitesimal, I can choose n large enough to falsify your claim. There are no infinitesimals in the real numbers.

But this is less important than your speculative idea that the physical universe models the standard mathematical real numbers. I think that idea has many problems. Not that it's wrong, necessarily, but it would be a heck of a scientific revolution that would revolutionize math and physics.

I also know this is irrelevant because I only judge based on the merit of your ideas, not your formal education. But out of curiosity what did you study and how far did you get? I have a BS in mathematics and a small amount of graduate training. — Ben Ngai

You're right, it's irrelevant. You seem confused about infinitesimals, infinity, the real numbers, and a number of other things. How'd you get through real analysis?

I ment to say. Every natural number has unique properties at the very least. — Ben Ngai

Oh well nevermind then! It was a highly nontrivial typo but if you meant natural numbers then you are right.

I use the term real numbers in the mathematical sense. https://en.wikipedia.org/wiki/Real_number. — Ben Ngai

As do I. The notion that the real numbers are physically instantiated is highly problematic. Most are not first-order definable, which means most are not characterized by any finite-length string of symbols. Secondly, you'd then turn every abstract set-theoretical puzzle into a question experimental verification. Can you imagine a physics postdoc applying for a grant to count the number of zero-dimensional points in a meter of space in order to see of the Continuum hypothesis is true? I can't either.

Besides, your idea violates the Planck length, the length below which contemporary physics ceases to be meaningful.

0 can seperate itself into two infinitesimally small numbers say alpha and -alpha. — Ben Ngai

Well now you have another problem, which is that there are no infinitesimals in the real numbers. You could invoke the hyperreals of nonstandard analysis, but then you'll have other anomolies to deal with.

https://en.wikipedia.org/wiki/Hyperreal_number

now we know infinity times any positive number is infinity. — Ben Ngai

In the extended real numbers, yes.

So that means that the sum of finite alphas is infinite. — Ben Ngai

No, you said alpha is infinitesimal, so you are now working in the hyperreals, where "infinity times an infinitesimal" may be finite.

Your mathematical ideas are unclear, you keep bouncing around from the reals to the extended reals to the hyperreals without realizing it.

2) Now lets assume that positive numbers have an attractive force on the NES based on their numerical value and negative numbers have a repulsive force based on their numerical value.

Implication. Give my assumption that the universe started uniformly at a zero energy space, as natural numbers pop into existence, since the natural numbers are positive, the rest of the NES becomes ever slightly negative with positive points that are slight attractive wells. This implies that the NES expands faster over time as there is more and more average negativity in the NES almost everywhere. — Ben Ngai

This is all a little convoluted. The positive and negative integers are what they are, they're not charged particles.

as every number has a unique property — Ben Ngai

Haven't read the rest of the thread but his phrase jumped out at me, as it's false.

Almost all real numbers are neither computable nor definable. If a "property" is a predicate, a finite-length string of symbols drawn from some finite or countably infinite language. then there are only countably many properties. The set of real numbers that are characterized by a unique property has measure zero and is countably infinite. All the rest of them are noncomputable and nondefinable, and have measure 1 in the unit interval or measure infinity in the extended real numbers. So this technical point you made is wrong. As I say I don't know how that relates to the rest of your argument or whether it's materially important, but I did not want to let it pass.

FWIW the real numbers are very strange and are an abstract construction. It's extremely unlikely the universe is like the real numbers. For one thing, if they were, you'd immediately turn all highly technical mysteries of set theory, such as large cardinal axioms, into experimentally-verifiable matters of physics. For example the Continuum hypothesis would be subject to experimental verification. That seems very implausible to me.

Of course this is not a proof, only a plausibility argument. If the standard mathematical real numbers are actually physically realized in the world, that would be front-page news. For one thing it would blow all the constructivists and computationalists out of the water. It would show that the world is not a computation, and that constructive math is wrong.

Of course I could ask you, which model of the real numbers do you mean? The constructivists would complain that their model is just as good and even better, since everything is computable. And the nonstandard analysis folks would complain that you left out all the infinitesimals. These are murky waters. There's more than one model of the first-order axioms of the real numbers.

I should add that there's a subtlety here. It's true that most real numbers can NOT be characterized by any property. However, any two real numbers can indeed be distinguished by a first-order definable property. If you have two real numbers x and y, then the statement x < y is either true or false. That's the case even though we have no way of characterizing the individual numbers by properties. This shows that even the undefinable real numbers are nevertheless subject to Leibniz's identity of indiscernibles. Given any two distinct real numbers, they are always distinguishable by a first-order property.

https://en.wikipedia.org/wiki/Definable_real_number

https://en.wikipedia.org/wiki/Computable_number

https://en.wikipedia.org/wiki/Large_cardinal

https://en.wikipedia.org/wiki/Identity_of_indiscernibles

ps -- If you think the physical universe is accurately modeled by the mathematical real numbers, do you think that the Banach-Tarski paradox is physically realizable? I hope you can see that the idea that the real numbers are physical is highly problematic.

I follow this, it seems to be exactly what I've been trying to explain to Luke, so we're on the same page here. — Metaphysician Undercover

Ok good. Progress is being made. One point, I am not reading the entire thread. From your side it must seem like you're being tag-teamed by @Luke and myself, but I'm not reading his posts. I'm not aware of that half of the conversation.

These are what I would call universals, generalities produced from inductive reasoning, sometimes people call them laws, because they are meant to have a very wide application. — Metaphysician Undercover

Oh that's what you call universals. Physical laws? Ok. I'm not sure if that's standard but no matter. At least I have an idea now what you mean by that.

But "generalities produced from inductive reasoning?" I'm not sure if I agree with that. Surely F - ma is not a "generality" at all. On the contrary, Newton had to first define what he meant by force and mass. F = ma has sometimes been called a definition. It's an abstraction intended to formalize an aspect of nature. If you think it's a generalization of something, you might be missing the point. Hard to say.

As inductive conclusions they are derived from empirical observations of the physical world — Metaphysician Undercover

I think you are missing the point. If I drop a hundred bowling balls and I say, "Bowling balls fall down. That's a law of nature," then THAT is an inductive conclusion.

But if you see 100 bowling balls fall down and you go, F = ma, that is an abstraction and a mathematical formalization. You don't seem to have a firm grasp on this. Do you follow my point here?

The issue is with what you call the purely abstract. It appears to me, that you believe there are some sort of "abstractions" which are completely unrelated to the physical world. — Metaphysician Undercover

Well of course bowling balls are physical, and Newton was doing physics.

But there are non-physical parts of the world that we are interested in, such as quantity, order, shape, symmetry, and so forth. Those are the non-physical parts of the world that are formalized by math.

On the other hand, of course there are non-physical, non-part-of-the-world abstractions too. Chess, for instance. Chess is a formal game, it's its own little world, it has a self-consistent set of rules that correspond to nothing at all in the real world. Knights don't "really" move that way. Right? Say you agree. How can anyone possibly disagree?

Perhaps that's why math is special. It's a formal game, but it's a formal game that seeks to model certain aspects of the world that are themselves not quite physical. Order, quantity, shape, symmetry.

They are not generalizations, not produced from inductive reasoning, therefore not laws, or "artificial definitions", in the sense described above. — Metaphysician Undercover

But you are the one that insists that physical collections of things have an inherent order. And that's what the mathematical concept of order is intended to formalize. Things in the world have order, and we have a mathematical theory of order that seeks to formalize the idea.

Right? When mathematicians formalize numbers, they're abstracting and formalizing familiar counting and ordering. When they create abstract sets, they are formalizing the commonplace idea of collections. A bag of groceries becomes, in the formalization, a set of groceries. Surely you can see that. Why would you claim math is not based on everyday, common-sense notions of the world?

You seem to think axioms of "pure mathematics" are like this, completely unrelated to, and not derived from, the physical world. — Metaphysician Undercover

How can you say that? Some of them obviously are. Most of them are. All of math is ultimately inspired by the world, just as the fictional story of Moby Dick was inspired by a real-world incident in which a ship was sunk by a whale. All fiction is inspired by the real world in one way or another, surely you know this.

I object to the parts of these formalizations which do not correspond with our observations of the world. — Metaphysician Undercover

Like what? Can you name some of these? Sets correspond to collections. Bags of groceries, baseball teams, solar systems. Cardinal numbers correspond to quantity, ordinal numbers to order. Group theory is the study of symmetry. Crystallographers study group theory.

What mathematical ideas don't have any correspondence or at least ultimate inspiration from some aspect of the real world?

These would be faulty inductive conclusions, falsities. — Metaphysician Undercover

Your notion of induction is wrong. "All bowling balls fall down," is an inductive conclusion. F = ma is a formalization.

But again I ask you, exactly WHICH mathematical ideas are not based on or inspired by the natural world? You must have something in mind, but I am not sure what.

You claim that they do not need to correspond, that they a completely unrelated to the physical world. — Metaphysician Undercover

That's a useful mindset to have, so that we don't allow our everyday intuitions interfere with our understanding of the formalism. But of course historically, math is inspired by the real world. Even though the formalisms can indeed get way out there.

Yet when you go to describe what they are, you describe them as inductive conclusions, above, which are meant to correspond, in order that they might accurately "clarify our understanding of various aspects of the real world.". — Metaphysician Undercover

Yes exactly. You say that like it's a bad thing! That's what formalization is. We have some aspect of the world, and we invent a mathematical formalization of it that captures its important features but that is distinct from the thing itself. So that we can use math and logic to draw mathematical conclusions, and use those conclusions to get insight about the original thing were were interested in.

So I see a disconnect here, an inconsistency. — Metaphysician Undercover

You aren't making your case. Surely you don't reject all of science because science builds mathematical models of certain aspects of reality, and that those models are not identical with the aspects of reality that they model.

You describe "pure abstractions" as being related to the world in the sense of being tools, or formalizations intended to help us understand the world. — Metaphysician Undercover

Yes. As opposed to chess, say, which is a pure abstraction not intended to help us understand the world, but rather intended as an entertainment and pastime in and of itself.

Yet you insist that those who create these formalizations need not pay any attention to truth or falsity, how they correspond with the physical world, in the process of creating them. — Metaphysician Undercover

Well as you know, math consists of logical implications. IF we assume this, THEN we may conclude that. We don't necessarily assert the truth of the antecedent. I think Bertrand Russell pointed this out. Because F = ma is not "literally" true of the world, it only formally represents certain aspects of the world. You have to be willing to make that conceptual split, between what is, on the one hand, and our abstract formalization, on the other. The formalization can never be true, because it's distinct from the thing it represents. The truth is in the thing. The formalization can't be true or false, it's not a thing in the world.

And you claim that when mathematicians dream up axioms, they do not pay any attention to how these axioms correspond with the world, because they are working within some sort of realm of pure abstraction. — Metaphysician Undercover

They pay a lot of attention to the suitability of the axioms for a given purpose. But in the end, the axioms must be lies, because they are not, and CAN NOT BE, identical with the things they represent.

If I want to study the planets I put little circles on paper and draw arrows representing their motion. The truth is in the planets, not the circles and arrows. I hope you can see this and I don't know why you act like you can't.

As an example consider what we've discussed in this thread concerning " a set". It appears to me, that mathematicians have dreamed up some sort of imaginary object, a set, which has no inherent order. — Metaphysician Undercover

First, sets are intended to model our everyday notion of a collection. And in order to do a nice formalization, we like to separate ideas. So we have orderless sets, then we add in order, then we add in other stuff. If I want to put up a building, you can't complain that a brick doesn't include a staircase. First we use the bricks to build the house, then we put in the staircase. It's a process of layering.

This supposed object is inconsistent with inductive conclusions which show all existing objects as having an inherent order. — Metaphysician Undercover

The objects themselves that are in the world may well have inherent order. Our formalization begins with pure sets. It's just how this particular formalization works. I don't know why it troubles you. If I represent a planet as a circle, you don't complain that my circle doesn't have rocks and and atmosphere and little green men. I'll add those in later. Right? Do you reject representing planets as little circles on paper, devoid of features, even though the planets they represent have features? How on earth can we get science off the ground without the process of abstraction, in which we begin with only certain aspects of things, leaving other aspects out.

You act like all this is new to you. Why?

You seem to think, that's fine so long as this formalized mathematical system helps us to understand the world. I would agree that falsities, such as the use of counterfactuals, may help us to understand the world in some instances. — Metaphysician Undercover

I refer you to Galileo's sketch of Jupiter's moons. With this picture he started a scientific and philosophical revolution. Yet anyone can see that these little circles are not planets! There are no rocks, no craters, no gaseous Jovian atmosphere. Why do you pretend to be mystified by this obvious point?

If Galileo showed you this diagram would you complain that it's a lie because it doesn't show the features of Jupiter? It is "true" insofar as it faithfully represents the small aspect of reality that it's trying to model. The fact that Jupiter has moons was a huge, massive, world-changing discovery. That's what was important here. You reject this line of thinking entirely? When you go to the planetarium do you complain that those aren't the real planets, that the models are made of plastic and are too small and are therefore lies?

You can't be this obtuse. Are you trolling?

But if we do not keep a clear demarcation between premises which are factual, and premises which are counterfactual, then the use of such falsities will produce a blurred or vague boundary between understanding and misunderstanding, where we have no principles to distinguish one from the other. — Metaphysician Undercover

We are usually perfectly clear about these demarcations. When we look at a globe of the earth, we see the oceans but the oceans are not wet. We say to ourselves, "The real ocean is wet, but the ocean on the globe is made of hard plastic. It's a lie, but it's a lie in the service of the truth." Nobody in the world is confused by this but you!

If axioms, as the premises for logical formalizations are allowed to be false, then how do we maintain sound conclusions? — Metaphysician Undercover

Do you feel the same way about maps? Ever use a map? The map is not the territory. Yet the map shows us true things about certain aspects of the territory, like the street names and where the freeway is.

Tell me this, @Meta. When you see a map, do you raise all these issues? "The rivers aren't wet. The streets aren't filled with cars. It's made of paper." Well ok I can't remember the last time I saw a paper map. But you get the idea. A map is a representation of some aspects of the world that we find of interest. Maps are lies, of course. In fact maps ARE lies, since maps are flat and the earth is a sphere. The projection's all off. You know this, right?

Do you rail at maps, at planetariums. at Galileo's crude drawings that changed the world? Darwin draws a finch, and you say, "It doesn't cheep. It doesn't lay eggs. It doesn't eat worms. It's only a pencil sketch. It's a lie, it's a lie I tell you!" Do you do this? Frankly I doubt it. You only act this way to play a character on this site.

Bottom line: Abstraction is a process of capturing the essence of some aspects of a thing of interest, by leaving out all other aspects. Abstractions are necessarily lies because they must leave important things out. Yet from them, we discern truth.

Regarding the implications of a God programming this world, I remain agnostic — Gnomon

Why do you so studiously avoid the only substantive thing on which we disagree and that I have a definite opinion on?

When I talk about Turing's limits on computation, and why God and the Programmer are two distinct things, and that a Great Programmer is distinctly weaker than God, do you know what I'm talking about? It's an important point. You need to understand it for your own work whether you talk to me about it or not. Penrose has made the argument that the mind is not computable, and he's speculated that quantum effects in the physical structures of the brain might be what allows us to transcend the limits of computability. It's very important for you to know about this stuff. You say the implications of "God programming this world," showing that you do not comprehend this subject. When you say God programs the world, you are placing massive restrictions on what God can do. God, by definition omnipotent, is not restricted by computability or programming. I see you don't get this but -- again, for your OWN work -- it's imperative that you do. Not for me, for you.

But again, if you are agnostic, why did something I said get you to respond to me with such ... well, interest, passion, anger, whatever word you like. I said something that triggered you. Why else would you repeatedly say I don't belong on this forum, only in the end to completely agree with everything I said? What was it all about?

Anyway God is not limited by computation, and the sooner you spend an afternoon Googling around about the subject, the sooner your own work will become sharper. As long as you think the world is programmed, you are making a powerful metaphysical assumption without even realizing it. The world might be created by God, the world might be programmed by God, or there might be no God. That is three things, not two. I suspect that you still don't get that.

When I said order is spatial and temporal, you claimed a completely "abstract order", which I didn't understand, and still don't understand because you haven't yet explained this in a coherent way. — Metaphysician Undercover

Ok. This is a good starting point.

The question is, are you interested in understanding mathematical order in a coherent way? The idea, as with anything else mathematical, is that we have some aspect of the real world, in this case "order"; and we create a mathematical formalism that can be used to study it. And like many mathematical formalisms, it often seems funny or strange compared to our everyday understanding of the aspect of the world we're trying to formally model.

So if you're interested, I can explain that. Or frankly the Wiki article can do the same. If you're interested. If not, not.

After all bowling balls fall down, and the moon orbits the earth. To help us understand why, Newton said things like $F = ma$, and $F = \frac{m_1 m_2} {r^2}$. And $E = \frac{1}{2} mv^2$, and things like that. And you could just as easily say, "Well this doesn't seem to be about bowling balls. These are highly artificial definitions that Newton just made up." And you'd essentially be right, while at the same time totally missing the point of how we use formalized mathematical models in order to clarify our understanding of various aspects of the real world.

So if you can see the difference between a real world thing like order, on the one hand; and how mathematicians formalize it, on the other; and if you are interested in the latter, if for no other reason than to be better able to throw rocks at it, I'm at your service.

And it's helpful to remember that the mathematical formalisms are not supposed to be reality. Nobody is saying they are. It's like chess. You don't complain about how the knight moves, because you understand that chess is a formal game that must be taken on its own terms.

That's the mindset for understanding how math works. You seem to object to math because it's a formalized model and not the thing itself, but that's how formal models and formal systems like chess work. They are not supposed to be reality and it's no knock agains them that they are not reality. They're formal systems. If you can see your way to taking math on its own terms, you'd be in a better position to understand it. And like I say, for no other reason than to have better arguments when you want to throw rocks at it.

What did you interpret as an ad hominem? Is "missed the distinction" a personal attack? I'll have to be more careful in stating any disagreement, to avoid cracking your "thin shell". Ooops! There I go again. :joke: — Gnomon

You typed in a lot of words so you deserve a response. Since (looking ahead) you regard this as friendly sparring, I'll respond in kind. Just up front I need to reiterate two things, to provide some context.

* Regarding the ultimate nature of the world, I have no opinion, no beliefs, and little philosophical interest. That is, I am ignorant and apathetic. I don't know and I don't care. That's why this conversation is puzzling to me. You have strong feelings about this subject, so surely you'd have more fun talking to someone who has equally strong but perhaps different opinions. What's the fun arguing football with someone who doesn't follow football, right? Ok.

* I do have one strong opinion in this regard; which is that whether or not God exists, I'm certain that a Great Programmer doesn't exist. Why? Because the world is not computable. I've mentioned this to you a couple of times and you haven't responded, so perhaps you are not sure what I mean. I'll talk about it more as I go on. That's something I do know a bit about and do have definite and strong opinions about.

Now, what did I regard as an insult? You said I don't belong on a philosophy forum if I don't care much about the ultimate nature of reality. Well "don't care" is a little strong. It's just not one of my top five or ten interests in life. Now when you said I don't belong on this forum because of that, I took it as a personal attack. But of course Hanlon's razor says: Never attribute to malice that which is adequately explained by stupidity. And I believe that's what applies here. Philosophy includes things like ethics, philosophy of math and science, political philosophy, philosophy of art, and so forth. Those are just some of the section headings on this very website. Clearly one can care about some of those topics without having a high interest in metaphysics. So you are just ignorant of philosophy, and imagining that what little philosophy you know is all of philosophy. I should have taken that into account.

Ok I sparred a little by calling you stupid and ignorant, but I must say to you, my heart really isn't in it. I have no idea why you're even talking to me about this stuff, about which you have a high interest and I don't. But I'll soldier on, apparently by your request. I do hope I've made my point that there are many interesting areas of philosophy that do not involve the "why" of the world.

First, according to modern Science, the knowable universe cannot be infinite, since it had a specific origin. — Gnomon

I'm perfectly well aware of that. That's why I distinguished between God, who is infinite, and the contingent world, which is (most likely) not. And in the end, you completely agree. Yet you seem to be arguing that I've got it wrong. Again, your conversational style leaves me baffled. I say something you're in perfect agreement with and you argue with me strenuously.

Any speculations about an a priori infinite Multiverse are just that : conjectures with no evidence. So my conjecture of a pre-existing Programmer is just as valid as any other. — Gnomon

Yes this is perfectly true. I never said otherwise. On the contrary, I was completely agreeing with you. The world is finite, and God, whether existent or not, is certainly infinity. I made that distinction. Which you agree with. And now want to "correct" me on. I don't get it.

But I do need to once again call attention to your technical error. God and the Great Programmer are factually distinct. The Programmer is restricted to implementing that which is computable. And computable things are a tiny subset of all the things there are. Turing made this point in 1936 and it's still well-understood today. Perhaps you are not conversant with this distinction. God can solve the Halting problem. The Great Programmer can not. So your speculation that the world may be the work of a Programmer carries a hidden assumption, one that you do not seem to be conversant with: namely, the claim that the world is computable. I hold the opposite, and THAT is something on which I can argue with passion.

A popular question asked of Astronomers is "what existed prior to the Big Bang?". And their guess is usually "more of the same". Which is not a conclusive answer, but a "turtles all the way down" non-conclusion. Simply "being there" does not explain why the world works as it does, and gives no hint of where it's going. — Gnomon

Not sure what this refers to or what I'm intended to take from it.

Second, did our universe write its own program? Do, you think the Chance + Choice evolutionary algorithm was an accident? If not, does the self-existent universe do what it does with an intended goal in mind, or is its evolution totally random? It's the signs of teleology that allow me to infer the necessity for a Programmer. — Gnomon

But I am on record as an agnostic. I don't imagine I'm clever enough to know or even make a good guess at the ultimate nature of the world. Of course for religious people, cleverness is not needed, only faith. I haven't got that either. I'm an agnostic. Does that trouble you? If so, why?

Additionally I am not very passionate about my agnosticism. The religious zealot and the professional atheists (Sam Harris et. al.) have passion. Agnostics mostly don't, I imagine. Surely I don't. Again, you think this disqualifies me from philosophy. Not so. I can argue passionately about math or politics. Just not metaphysics.

If you're interested, those "signs" are discussed in the Enformationism thesis and in the BothAnd Blog. :nerd: — Gnomon

Well that's my point. You have a personal metaphysics and a blog. I commend you your discipline, focus, and passion. But then I must be a very disappointing conversational partner. I have no convictions and little interest. Not even a blog.

And when someone uses the phrase, "close to infinite," I know I'm in the presence of someone who hasn't given five minutes thought to their own words.
— fishfry
Ouch! Was that remark an ad hominem? "Let he who is without sin cast the first stone". :gasp: — Gnomon

Nice deflection. I'll repeat the question I asked you. Can you name a quantity or a thing that is "close to infinite?" I claim the phrase is incoherent. A big number like a million or a billion or a zillionty-zillion is still a finite number. Collections that are bijectively equivalent to a proper subset of themselves are infinite; all others are finite. "Close to infinite" is like a little pregnant. You either are or you aren't. There's no "close to" possible. Would you care to justify or retract your usage of the phrase? All in the interest of intellectually honest sparring, I hope.

My buttons are hard to push, because my emotions are well-balanced. My intention here is to share opinions. And I enjoy having my ideas challenged. — Gnomon

Ahem. "Wouldn't you at least have to have some ideas?" he said half-heartedly. With a straight line like that, my response was practically compulsory. And frankly you haven't expressed any specific ideas other than the one you're clearly wrong about, the Programmer. May I ask you, do you understand my point about the difference between God and the Programmer? It's rather important, because it affects simulation theory and "mind uploading" and other related trendy ideas floating around among the "artificial intelligensia" in somebody's immortal phrase.

That's what philosophy is all about. — Gnomon

So YOU say. But philosophy of math, philosophy of art, philosophy of science, of literature, of ethics, etc., are not about metaphysics. Are you committing the fallacy of thinking that the only things that matter are the things you know and care about?

But in a text only format, it's all to easy to offend others by challenging their certainty. — Gnomon

Would it be harder to offend others if you posted pictures? The site allows for the uploading of images, you can do that if you're so inclined. But even here you're wrong, it's easy to offend with pictures. Don't you agree? What are you saying here, it doesn't even make sense.

That's why I use a lot of smilies & emojis : to indicate that I mean no offense. — Gnomon

I was noting that you always seem to use a different one. At some point you must run out and you'll be forced to repeat. That's a thing in math called the pigeonhole principle.

If I step on your toes, it's either because they were in the wrong place at the right time, or because I'm clumsy, but not malicious. :blush: — Gnomon

Awwww shucks. I take that as a conciliatory gesture. Much appreciated. LOL.

Yes. You seem to be playing rope-a-dope, by making evasive maneuvers. — Gnomon

No not at all. I'm responding to you directly. But I have little interest in metaphysics, and no hard opinions. That must obviously be frustrating to you. I can see that.

But I get that a lot, from those who have no answers to hard questions. — Gnomon

The True Believers and the professional atheists must hate hate hate the agnostics. "Um, I guess I really don't know what is the ultimate nature of the world." What an absolutely terrible thing to say, right?

But you know, you have several times avoided the question I've asked you. Do you understand the distinction between God and the Programmer, and can you justify your believe that the world is programmable? That's actually the only metaphysical topic I have a strong opinion on.

Besides, I'm not boxing with you, but merely using you as a sparring partner to develop my own skills. As long as you're willing to play the game, I can do this all day. :wink: — Gnomon

Well here I am. But seriously, you haven't said much.

Rope-a-dope : a boxing tactic of pretending to be trapped against the ropes, goading an opponent to throw tiring ineffective punches. — Gnomon

Ah the great Rumble in the Jungle match between Ali and Foreman. Except that Foreman could hit hard. You are just kind of slapping at me. I don't even need to rope-a-dope. I don't see anything to argue with.

Apparently, you don't understand the purpose of a philosophy forum. — Gnomon

I think we've established that YOU are the one to whom that applies. They call that projection.

It's not intended to reinforce your own beliefs & biases, but to have them tested by others, who don't share your point of view. — Gnomon

But that's the problem here. It's not only that I don't share your point of view. It's that I can't figure out your point of view; and secondly, I don't have much interest in metaphysics. I truly don't know whether there's a God. I'm pretty sure there can be no Programmer. And, this being the single subtopic on which I have an opinion, I wish you'd engage with it.

I don't have any religion to convert you to. And I don't think the Programmer will send you to Hell if you don't believe as I do. — Gnomon

Sending to Hell is not computable. The Programmer couldn't do that even if they existed.

Site Guidelines :Don't start a new discussion unless you are:
a) Genuinely interested in the topic you've begun and are willing to engage those who engage you. — Gnomon

Ahhhhhhhhh. Enlightenment. I see your problem. I see your problem! You know how when you're puzzled by something you don't understand, and it suddenly all becomes clear? I just had such a moment.

Sit down, take a deep breath, and read carefully:

I am not the OP

Perhaps you think I am, and that's why you're complaining that I don't have a strong interest in the topic. But you see, I am not the OP. Did you make a little mistake here?

It's several pages ago, but I seem to remember that I made some minor, offhand remark to the OP, and you have read into that much more than what was on the page. But I could be wrong, I did not go back to check. I do know that I did not start the thread, hence what you quoted does not apply to me in any way.

but your own passion for ... something or other ... is blinding you to the points I'm making, and upsetting you besides.
— fishfry
I could say the same about you. — Gnomon

You could not. I have no passion for metaphysics. I am honestly -- I am not joking or being snarky -- I am honestly confused by this conversation. I've been perfectly honest about my beliefs and interests.

But I won't. I do indeed have a "passion" for my personal worldview, and like to share it with others. — Gnomon

I get that. If you'd state your worldview perhaps I could whip up a little intelligent conversation at my end. After all this I still don't get your point, except to note that you don't seem to understand the limitations of a Programmer, restricted to that which is computable.

That's why I responded to the OP : "In other words, and here's where it gets interesting, mindless evolution through random mutation is exactly what a mind which is as intelligent as us would do given the way things were, are, will probably be." — Gnomon

Yes ok. And you understand I am not the OP. I probably didn't read your post. How did we get here?

The "intelligent mind" behind the evolutionary algorithm is what I call "The Programmer". — Gnomon

Yes and this is a technical error because computability is distinctly limited.

But, obviously, you take exception to any suggestion of intelligence in Evolution. — Gnomon

I'm just floored, man. What have I ever said on this site to give you such an impression?

In fact last week on this site, or maybe a couple of weeks ago, I enumerated the arguments against Darwinian evolution. I named-checked Michael Behe, Stephen Meyer, and David Berlinski. I am familiar with the argument of irreducible complexity. I am all over the miraculous bacterial flagellum. I don't believe or disbelieve in intelligent evolution, but I'm actually more familiar than most people with the arguments for it, and the arguments against classical Darwinian evolution.

What on earth are you talking about? Excuse my French but you are just making shit up. You have decided that I have a certain set of beliefs and you are arguing with me about them, but they are not my beliefs. You're just making all this up.

Preferring instead to believe that this world is a cosmic accident. Is that true, or another ad hominem? :yum: — Gnomon

It's just another belief of yours about things you think I believe but don't. You know, you are not making any points with me by going off in these directions, attributing to me beliefs I've never expressed.

I did say that I do not find "God did it" helpful in the least, because it explains nothing.
— fishfry
Do you have another answer to the "why" of our existence, that explains everything? — Gnomon

No, I have no answer. And I am generally puzzled at those who think they do. I find both the religious believers and the militant professional atheists equally baffling. What makes them so certain? At least the religious types can sometimes invoke their own personal experience of faith. What do the atheists have? Is that a faith-base position too?

I'm agnostic. I don't know. I truly don't know. But as it happens I DO know a bit about the arguments on each side. The arguments interest me. The anti-Darwinists interest me.

Or do you prefer the attitude of Nihilism? "It just is, and always has been", explains nothing. — Gnomon

That's not what nihilism is. I'd call that a humble and self-aware recognition that I have no idea what is the ultimate nature of the world. My interests seem to lie in the are of pointing out the logical flaws of those who think they do. The God squad, the atheists, the Simulationists and Uploaders. People who are so very sure about things that nobody can possibly be sure about.

How would you describe your personal worldview? — Gnomon

As it happens there is a name for what I believe. New mysterianism.

New mysterianism—or commonly just mysterianism—is a philosophical position proposing that the hard problem of consciousness cannot be resolved by humans. The unresolvable problem is how to explain the existence of qualia (individual instances of subjective, conscious experience). In terms of the various schools of philosophy of mind, mysterianism is a form of nonreductive physicalism. Some "mysterians" state their case uncompromisingly (Colin McGinn has said that consciousness is "a mystery that human intelligence will never unravel"); others believe merely that consciousness is not within the grasp of present human understanding, but may be comprehensible to future advances of science and technology.

I apply this to the mind and to the universe. I think such knowledge is above our pay grade. Like a caterpillar on a leaf on a branch on a tree in a forest. The caterpillar knows night from day, things it likes to eat from things that like to eat it. It knows, deep in its genes, that someday it will ascend to become a beautiful butterfly. It has a metaphysics. But it can't know what we know. Its brain and nervous system are limited by nature. As is ours. The universe is vast, we live on a small rock and crawled out of caves only 100,000 years ago. We don't know the ultimate nature of the world and we cannot know and we will never know.

That is my belief. Thanks for asking.

If you would be less evasive, and more forthcoming, perhaps I could avoid stepping on your toes. — Gnomon

I have not been evasive in the least. You just don't like my answers.

If you are not interested in "why" questions, why are you posting on a Philosophy Forum? — Gnomon

Philosophy of math, philosophy of science, political philosophy, philosophy of art, ethics, philosophy of language ... and those are just some of the topic headings on this site. Will you please stop showing how little you know about philosophy? It's amazing that you'd make such a weak point. You're right, I originally felt personally insulted, but now I realize that you simply have so little understanding of most of philosophy that you just can't help yourself.

Do you take this point? That philosophy encompasses so much more than metaphysics? And that you are confusing your own interests with the totality of everything? Why are you making such an elementary error?

Philosophy "explains nothing" about the physical world, but focuses on understanding the meta-physical aspects of the world. :cool: — Gnomon

Then it's an abject failure. Because we can not understand the metaphysical aspects of the world. I'm perpetually baffled by those who think we can, and by those who actually believe that they do. That's ignorance and arrogance wrapped up in a dangerous package.

"The problems that metaphysics attempts to solve are existential, essential, and origin-al. But philosophy covers these and more. . . . We could say: metaphysics ⊆ philosophy, but vice versa is not true." ___ Quora — Gnomon

Quora? Jeez that's scraping the bottom of the metaphysical barrel. Have you been to Quora lately? But now at last I see that you have agreed with my point. Metaphysics is a proper subset of philosophy. Why, then, should someone with a not-very-strong interest in metaphysics not nevertheless be on a philosophy forum? After all this, you see my point.

If I may ask ... why did you make this elementary rhetorical error? To claim that someone doesn't belong on a philosophy forum if they are uninterested in metaphysics; only to finally agree that metaphysics is only a part of philosophy?

I'll score this round for me. Remember, Ali knocked Foreman senseless. But then again, Foreman went on to successfully market a line of kitchen grilling gadgets. So there's that.

Sigh. I've always believed that each of us has so many keystrokes in our fingers, and this was a mighty load to little effect.

I say again honestly, I have no idea what this is about. Except that you are wrong about the Programmer. If there is a God, and I am agnostic on whether there is or isn't; but if there is, God can not possibly be only a Programmer. Because the world is not computable. In fact the most interesting parts of the world are not computable. Mind, for one. Roger Penrose agrees with me on that.

poor post quality — StreetlightX

Jeez who'd be left if you uniformly enforced that?

The way you described sets in this thread, a set is something which cannot have an identity because it has no inherent order. — Metaphysician Undercover

Well this is just nonsense, but it relates to the reason I didn't reply to the last post you wrote to me regarding the subject of order. It finally became clear that by order you mean "where everything is in time and space," so that for example a collection of spatial points or a collection of school kids does have an inherent order.

But this is a total equivocation of the way I defined mathematical order to you, as a binary relation on a set that is reflexive, antisymmetric, and transitive.

Now I gave you that definition several times. So you could (and should) have said something like,

"I don't understand what the words reflexive, antisymmetric, and transitive mean," or "I don't know what you mean by binary relation," or, "I see you're giving the mathematical definition, but I am using the more general definition of "where things are in time and space,"".

But you didn't say any of those things. Instead you just accepted the mathematical definition I repeatedly gave you, and then kept arguing from your own private definition. When I finally figured out what you were doing, I was literally shocked by your bad faith and disingenuousness. I'm willing to have you explain yourself, or put your deliberate confusion-inducing equivocation into context, but failing that I no longer believe you are arguing in good faith at all. You have no interest in communication, but rather prefer to waste people's time by deliberately inducing confusion.

I'm perfectly willing to have you explain yourself. But once I repeatedly gave the mathematical definition of order, and instead of saying, "Oh that's not how I define order," but rather kept arguing from your own private definition without acknowledging that you were doing so, I believe you were arguing in bad faith and I have lost interest in conversing with you further. Like I say I'm perfectly willing to hear your side of this, but I can't tell you how dismayed I was to finally realize what you meant by order, and to realize that you deliberately didn't bother to explain that you were ignoring the mathematical definition. You never said, "No that is not the definition I use." My frustration with this your conversational style is terminal at this point.

Therefore I cannot agree that the set {0,1,2,3,4} is identical to the set {0,1,2,3,4}. — Metaphysician Undercover

Yeah right, whatever.

It seems like a set is an abstraction, — Metaphysician Undercover

Uh ... what the hell else could it be? I've told you a dozen times a set is a mathematical abstraction.

a universal, rather than a particular, and therefore does not have an identity as a "thing". — Metaphysician Undercover

Yeah ok. We could have a conversation around this, but I don't believe you're interested in communication, only obfuscation.

It is particulars, individual things, which have identity according to the law of identity. Notice that the law of identity says something about things, a thing is the same as itself. — Metaphysician Undercover

You just denied a set is equal to itself.

The law of identity is intended to make that category separation between particular things, and abstractions which are universals, so that we can avoid the category mistake of thinking that abstractions are things. "The set {0,1,2,3,4}" refers to something with no inherent order, so it does not have an identity and is therefore not a thing, by the law of identity, To say that it is a thing with an identity is to violate the law of identity.[/quote

I'm sorry, this is just no longer of interest to me.
— Metaphysician Undercover

This is the whole point of the law of identity, to distinguish an abstract concept from a thing, so that we have a solid principle whereby we can avoid the category mistake of thinking of concepts as if they are things. A thing has an identity which means that it has a form proper to itself as a particular. To have a form is to have an order, because every part of the thing must be in the required order for the thing to have the form that it has. So to talk about something with no inherent order, is to talk about something without a form, and this is to talk about something without an identity, and this is therefore not a thing. — Metaphysician Undercover

Word salad. Which I don't mind. But you've convinced me you're not conversating in good faith.

The problem is not that I don't think a thing is the same as itself. That is the law of identity, which I adhere to. The problem is that you make the category mistake of believing that abstract conceptions are things. Because you will not admit that a concept is not a thing, you make great effort to show that two distinct concepts, like what "2+3" means, and what "5" means, which have equal quantitative value, refer to the same "thing". Obviously though, "2+3" refers to a completely different concept from "5". — Metaphysician Undercover

When you put those in quotes of course that is correct, but that has never been the subject of the conversation. More obvious bad faith and sophistry.

If you would just recognize the very simple, easy to understand, fact, that "2+3" does not mean the same thing as "5" does, you would understand that the two expressions do not refer to the same concept. — Metaphysician Undercover

I think any reader following this thread can perfectly well see that the quotation marks have never been the subject of the conversation. I think you genuinely argue in bad faith and like to waste people's time. You're a troll.

So even if concepts were things, we could not say that "2+3" refers to the same thing as "5", because they each have different associated concepts. And it's futile to argue as you do, that the law of identity is upheld in your practice of saying that they refer to the same "mathematical object", because all you are doing is assuming something else, something beyond the concepts of "2+3", and "5", as your "mathematical object". This supposed "object" is not a particular, nor a universal concept, but something conjured up for the sake of saying that there is a thing referred to. But there is no basis for this object. It is not the concept of "2+3" nor is it the concept of "5", it is just a fiction, a false premise you produce for the sake of begging the question in your claim that the law of identity is not violated. — Metaphysician Undercover

I'd be more inclined to respond if you hadn't been deliberately obfuscatory about your different use of the word order, after I'd given you the mathematical definition several times. Absent a clear explanation of why you did that, knowing how much confusion you were causing, I don't want to play.

That helps me. Thanks — Gregory

Glad I could help. You're welcome :-)

I get what you are saying. However a point has no dimensions, so how can it have any relation to space except as a limit. — Gregory

Do you mean physical space, as in the real world? No relation at all. Dimensionless points are purely a mathematical abstraction. For example a point on the x-y plane that we call, say, (2,3), meaning the point at x = 2 and y = 3, has mathematical existence as a pair of real numbers. But there are no dimensionless points in the real world. They're purely conceptual mathematical entities. Physicists find them useful when building mathematical models of the world, but they are not real (as far as we know, of course). They're only mathematical. Does that make sense?

If it helps to think about it this way, math is a complete, total fiction that just happens to be useful to people. But that's not unusual. The novel Moby Dick is a work of fiction, but it teaches us not to follow our obsessions to our doom. So works of fiction can be highly useful. Sometimes it's helpful to think about math that way. I'm not necessarily saying math IS this way, but that it often helps to THINK about it this way.

So: Math is fiction; fiction can sometimes be useful, so we need not believe that math is true in order to use it. Think Moby Dick.

I
An infinitesimal is what comes closest to zero — Gregory

There are no infinitesimals in the real numbers. We can work out mathematical systems that have infinitesimals, but I'm not sure how that helps us in the present conversation. If there are no dimensionless points in the real world, it's likewise unlikely that there are infinitesimals. I think that if you would separate math and physics in your mind it would be helpful.

but that's an infinite region and is infinite. — Gregory

Infinitesimals are not infinite. I'm not sure what you're saying.

Infinite infinities equal finite space? How? — Gregory

If you're asking how infinitely many dimensionless points can make up a region that has size, even mathematically, it's just the way it is. Nobody knows the answer to that.For example the unit interval consisting of all the real numbers between 0 and 1 has length 1, but it's made up of uncountably many dimensionless points. Just how it is. The concept goes back to Euclid., , although I don't think he talked about infinity. There's no explanation for how it works, if that's what you mean.

I mentally divide objects though. I don't think if this is intuition or imagination, but flexing the segment infinitely than bringing it back like a slinky to the finite aspect of the segment, which certainly seems to require an extra thought in logic in order to accomplish because the slinky would stretch to infinity in both directions — Gregory

Do you see that no matter how many times you cut an object and its subparts in half, there are always finitely many parts? And that their area always sums up to exactly the original size?

Stretching a slinky is a little different. I take this as your noting that we can stretch the unit interval (0,1) to the entire real line? It's interesting that we can do that. The tangent function from high school trigonometry class does that very nicely, it maps the interval (-pi/2, pi/2) to the real line. The key point is that length is not a topological property. We can stretch things, even to infinity, while preserving all topological relationships.

Can we visualize this? Yes. Imagine a straight line through the origin of the x-y plane. Its slope at any point is actually the tangent of the angle it makes with the positive x-axis. When the line is nearly vertical going from lower left to upper right, its slope gets larger and larger, approaching infinity. When the line is nearly vertical going from upper left to lower right, its slope is smaller and smaller, approaching minus infinity. So as the line sweeps out an arc from going straight down to straight up. it corresponds every angle from -pi/2 to -pi/2, exclusive of the endpoints. to every real number. Literally easy to see.

Or just take the function 1/x. That maps (0,1) to (0, infinity). In this case we're only stretching half the slinky to infinity. Mathematically it's trivial, 1/x is one of the basic high school functions.

I may not be understanding the point you're making. The math is at high school level, it's very simple. Topological stretching does not preserve length, so we can stretch things arbitrarily, even to infinity.

Of course this is math, not physics. Nobody knows if these infinite stretching operations have physical meaning. You can't arbitrarily divide or stretch physical objects.

Apparently, you missed the distinction between a random accidental event as the beginning of our world, and a programmed intentional act of creation. If that makes "no difference" to you, then you are wasting your time with science & philosophy. You'd do better to just "eat, drink, and be merry . . . for tomorrow we die". For me, it's the difference between a meaningless absurd universe, and a world that grows & matures like a living organism. — Gnomon

When the ad hominems start I always know I'm in the presence of a superior mind. Teach me, oh wise one.

As for the "short-lived" creation, I must ask, relative to what? — Gnomon

Finite compared to infinite. Was the Great Programmer always there? How's that any different from a universe that's always there?

Compared to your individual life, the span of the universe is close to infinite. — Gnomon

And when someone uses the phrase, "close to infinite," I know I'm in the presence of someone who hasn't given five minutes thought to their own words. Can you name me a finite quantity that is "close to infinite?" A quantity is either infinite or not. The concept of "close to infinite" is incoherent. We often see it used by physicists who likewise have not given the matter sufficient thought.

But when compared to a timeless Creator, this experiment in living & thinking is a mere momentary blip in eternity. — Gnomon

Well then you PERFECTLY WELL AGREE with my phrasing of "relatively short-lived." You argue yourself into a huff and finally end up agreeing with exactly what I said.

You are worked up about something I said, and I'm not sure what. I'm on record as one, being agnostic about God; and two, being highly non-passionate about the subject. It's something that registers near zero on my interest and emotion scale. You are the only one worked up about this.

However please do note that the Great Programmer is distinctly more restricted than God, because the GP, if I can call him/her that, is limited to writing algorithms; and as Turing showed us, algorithms can solve a very small subset of the overall collection of problems. All simulation theories are flawed in this way. God can solve the Halting problem but the GP can not.

↪180 Proof mentioned the "rejection of transcendence by Absurdists". They must have been appalled by the new science of Quantum Theory, which seemed absurd compared to the intuitive Classical worldview. But those who actually study, and engage with, the Quantum realm are excited by the opportunity to explore "strange new worlds". Instead of retreating into pessimism, they view this opportunity almost like a vacation trip to exotic locales. It allows us to momentarily "transcend" our mundane classical reality, and to experience a "higher" ideality. Does String Theory seem realistic to you? :joke: — Gnomon

I don't know. I don't even feel like I'm in this conversation. Something I said pushed your buttons, and that was not my intention. I only stated my opinions. I don't even have a thesis to argue. I have very little interest in the topic except to explain to simulationists that algorithms are severely limited in what they can do. See Turing 1936, he laid it all out.

I suppose then, that you do have an idea of "what most mathematicians believe". You claim to know that "most give the matter no thought at all". Does that defect make you feel superior to B. Russell and A.N. Whitehead? — Gnomon

Statistically very few mathematicians work in foundations. A group theorist or topologist generally feels like they are working on group theory or topology. They don't typically tend to reflect much on whether these things are "real." Russell and Whitehead are long gone, and even foundations have advanced far beyond 1900.

What do you know that they didn't, a century ago? What novel philosophical insights to reality are revealed in non-linear or differential geometry? Have you found a topological path around the roadblock of the Incompleteness and Uncertainty principles? If not, what's your point? :chin: — Gnomon

You're gonna blow a gasket, man. Do you understand you're arguing with someone who's not arguing back?

Apparently, you think Meta-Physics is a perverse attempt to "explain" the mechanisms of Matter. But Aristotle's purpose in his second volume, was not to explain Physics, but to set out some principles of Logic & Reason, in order to explain the mysterious workings of the human mind. Now 2500 years later, physical science has made great progress in inventing gadgets like Cell Phones and Nuclear Weapons. But the Quantum Leap from objective neurons to subjective consciousness remains a "hard question". Aristotle's Physics is completely out-of-date. But his Meta-Physics is still debated by scientists and philosophers. Science is good at explaining the mundane Mechanisms of things, but not so much for explaining the sublime Meaning of inter-relationships. — Gnomon

Ok. What of it, exactly? I've surely never expressed any such sentiments on this site.

You admit that "In the end science itself tells us what but not why". But, if you are not interested in "why" questions, why are you posting on a feckless philosophy forum, instead of discussing Physics and Formulas? :nerd: — Gnomon

You're going to wear out your smiley button.

If you are only interested in measurable "how" explanations, this is the wrong forum for you. Can science measure Morality? Can it predict the overthrow of US Democracy by a mendacious Autocrat? Can physics explain why people fall for Fascism? Maybe a better understanding of the human mind can help us to understand the "whys" & "wherefores" of this crazy mixed-up world. But then, the simple notion of a Programmer of this Cosmos will not explain all of our questions. But if we can understand better how & why the "Program" works as it does, we may alleviate some of our existential angst. :cool: — Gnomon

How many times can you do this before your smileys repeat? Pigeonhole principle I think.

PS___I'm currently reading a book by physicist Carlo Rovelli, Helgoland. And he takes a rather metaphysical approach to understanding the apparent absurdities of Quantum Physics. He advocates a different path to explaining its counter-intuitive aspects in terms of "the relational interpretation of quantum theory". And that is exactly the point of the Enformationism thesis. What's philosophically important is not physical objects but the metaphysical relations between them. — Gnomon

I"m happy for you. Nice chatting with you, all the best. I wish I could have a more interesting conversation with you, but your own passion for ... something or other ... is blinding you to the points I'm making, and upsetting you besides. I hope you can find peace in this life that doesn't involve converting me to a point of view that you're not articulating very well.

ps -- Ok let me see if I can shed a little bit of light. You wrote:

You admit that "In the end science itself tells us what but not why". But, if you are not interested in "why" questions, why are you posting on a feckless philosophy forum, instead of discussing Physics and Formulas? — Gnomon

Now first, I have often made the point myself that science tells us what but not why. I know this, and I've explained it to others many times.

Then you say that I am not interested in the why. If you can find anywhere I've ever said that, please find it and quote it. Because I never did.

I did say that I do not find "God did it" helpful in the least, because it explains nothing. And I find "The Great Programmer did it" even LESS persuasive, because algorithms are severely limited in their problem solving capabilities.

From those opinions of mine, you have extrapolated things I never said, and accused me of all manner of things, such as being in interested in eating, drinking, and being merry. Are you some sort of ascetic? I think you are way off the mark in almost every word you wrote in your most recent post to me.

Well as I've mentioned to you before, I don't see how you can slice through a geometric object forever, creating infinite little pieces that keep dividing, while the whole remains finite — Gregory

Suppose I cut a circular disk (that includes the boundary and the enclosed region) in half. How many pieces do you have? 2. Finite or infinite? Finite.

Cut the halves in half. Total pieces, 4. Finite. Cut them in half. Pieces 8, finite. Again. Pieces 16, finite.

You can always cut the pieces in half, and you always have finitely many pieces.

At no time is there ever an infinite number of pieces. Your intuition is fooling you. There are always finitely many pieces, whose area adds up to the size of the original circle.

@TheMadFool :up: :up: :up: :up: :up: :up:

So you are saying the cardinality vs density distinction applies in geometry? — Gregory

I'm not sure how you got that from anything I wrote. I pointed out that there's a one-to-one correspondence between the points of any two circles, and that your use of the word area was off the mark.

I was trying to think if there was a density or measure argument regarding the set of lines through and not through a point, but I couldn't think of anything useful.

ps -- There is a dimension argument. The lines through a point are parameterized by a single real number, the slope of the line through the point. The lines not through the point require two points to specify their slope and y-intercept.

I think there are too many problems with abstract geometry in this regard. I have always wonder if I could go off in one direction in space forever until a friend told me I would simply return to where I started. — Gregory

That's a question of physics, not math. But it's a good question. You'd laugh at someone with a fat ass, then realize it's yourself. :-) Or rear end your own car and send your insurance company into an infinite loop.

This blow my mind. Then recently I realized this applies too, perhaps, to the infinite divisibility thing. If I divide an object too much I will come back to the surface area. This makes sense to me as a looped curve — Gregory

I don't think I can visualize that at all. If you take the unit interval and divide it into lengths 1/2, 1/4, 1/8, 1/16, etc., you don't get back to the unit interval. On the other hand, each subinterval is topologically the same as the original one. So if you're an ant on the real line, you have no way to know the scale of the points around you unless they're marked. In fact any open interval (an interval that omits its endpoints) is topologically equivalent to the entire infinitely long real line. I've always thought that's kind of interesting. Even if the universe is infinite in extent, it might really be finite, and the laws of physics just make you slow down as you reach the boundary. Mathematically it would amount to the same thing.

As per the quotes above, from Wikipedia, the mathematical notion of identical , as equal, is not consistent with the philosophical notion of identity, described by the law of identity. — Metaphysician Undercover

You're factually wrong.

Is the set {0,1,2,3,4} identical to the set {0,1,2,3,4}? I have to assume you'd say yes.

But 2 + 3 and 5 are both representations of the set {0,1,2,3,4}. So they're identical.

In other words, mathematicians violate the law of identity to apply a different concept of identity, making two things of equal value mathematically identical. — Metaphysician Undercover

I just showed (as I have probably a hundred times before) that you are wrong about this. Mathematicians call two things identical when those things are identical.

Now I will concede that there are subtle counterexamples. For example the natural number 5 and the real number 5 are distinct as sets. Nevertheless they are identical when viewed structurally. If you wanted to say they are equal but not identical that would be arguable, but it's a subtle point, and could be argued either way.

You might accept this, and we could move on to visit the possible consequences of what I believe is an ontological failure of mathematics, or you could continue to deny that mathematicians violate this principle. — Metaphysician Undercover

Well, math does not violate this principle. 2 + 3 and 5 are identical. They are both representations of the set represented by {0,1,2,3,4}, which of course is not actually "the" set, but is rather yet another representation of that abstract concept of 5.

The latter is rather pointless. — Metaphysician Undercover

Only to the extent that you don't seem to think a thing is identical to itself. Because when mathematicians use equality, they mean identity, and this is provable from first principles. They either mean identity as sets; which is easy to show; or, they often mean identical structurally. This is a more subtle philosophical point.

I stand instructed. — tim wood

That's ok, maybe I'll say something on one of the political threads and then you can throw rocks :-)

ps. Ball. I had to look that up, which means I'm starting to forget things I used to know. A solid sphere, including the enclosed region, is a ball.

Perhaps Gregory you mean that their points can be placed into one-to-one correspondence, as evidenced by drawing rays from the center, each ray passing through exactly one point of each circle or sphere.
— fishfry
Am I misreading or do you mean one point on on each circumference or surface? — tim wood

Not sure what you mean. Unless you are interpreting circle and sphere as including their enclosed regions. In math the convention is that a circle is just the points on the circumference, likewise for a sphere. Is that what you meant?

That is, the unit circle is the set of points whose distance is exactly one from the origin. The set of points less than or equal to one is a disk. Not sure what's the corresponding term for a sphere, but the sphere itself is just the points on the surface. It's a 2-dimensional manifold.

A sphere within a sphere has the same infinity of area as the one that contains it. — Gregory

Thanks Gregory, but I didn't understand the sphere example. Can you please explain it? — anon123

Uh yeah, me too. Take the example in two dimensions. You have two concentric circles, one with radius 1 and the other with radius 2. Surely they have different circumferences; and surely if they are spheres they have different surface areas.

Perhaps @Gregory you mean that their points can be placed into one-to-one correspondence, as evidenced by drawing rays from the center, each ray passing through exactly one point of each circle or sphere.

Now the thing is there are infinitely many lines in a plane. Also there are infinitely many lines which pass through a point. So does it mean that no such line exists? Of course not because practically it does. I just need a proof of the same. — anon123

Here's a proof. Take the two-dimensional plane. Put the usual x-y rectangular coordinate system on it. One point's as good as another, so take your point to be the origin (0,0). You want to find lines that don't go through it. How about all the horizontal lines y = k for all nonzero k? That's infinitely many lines that don't go through the origin.

Of course infinitely many lines do go through the origin.

We can in fact make meaningful statements comparing these two quantities. We can in fact show that we can put the lines through the origin into one-to-one correspondence with the lines that don't go through the origin.

It's not much different than noting that we can put all the even numbers into one-to-one correspondence with the odd numbers, even though there are infinitely many of each. Every even number of the form 2n is paired up with an odd number of the form 2n + 1. So we can in fact make meaningful comparisons between two infinite quantities.

Before the Big Bang theory became accepted by physicists and cosmologists -- including Einstein -- their unproven assumption was that the physical world had always existed in some form. One theory was the Steady-State or Continuous Creation postulation, in which new energy & matter was constantly emerging to replace that lost to Entropy. But when astronomers proved conclusively that the whole universe was expanding like a balloon, from a single point of space & time, the notion of a sudden creation act was no longer scientifically deniable. Ironically, the best alternative to the Big Bang theory is the various versions of Multiverse theories, which are merely updates to the old Continuous Creation concept. Moreover, just like the creation myth in Genesis, the Multiverse Myth has to be taken on faith, because there is no physical evidence to support it. — Gnomon

Nothing you said was responsive to my point. There is no difference between an eternal universe and an eternal creator that creates a short-lived universe. No philosophical difference. Name-checking various contingent physical theories is irrelevant IMO.

Perhaps, "most assume without question" would suit you better, than "most believe". It's true, that Russell and Whitehead attempted to validate mathematical axioms once & for all. But then their dream of certainty was undermined by Goedel's Incompleteness Theorem, among other Uncertainty principles. Math is supposed to be the bedrock foundation of Science. Yet we now know, but prefer not to accept, that all of our knowledge is conditional. And that includes both Physical and Meta-Physical knowledge. — Gnomon

You have no idea what "most mathematicians" believe. And if R & W are your idea of mathematicians, you are making the same mistake made by many philosophers, which is to imagine that mathematics is what philosophers of math were doing in 1900. Or even 1930. "Most assume without question?" No. Most give the matter no thought at all, not even enough to assume anything without question. You are simply making a statement without evidence and without knowledge of what most mathematicians do. It should be noted that out of all mathematicians, the percentage that have ever given foundational questions the slightest thought must be well less than 1%.

It's an eternal problem on any philosophy forum that discussions of math are invariably about foundational issues; and even then, only foundational issues as they were understood before 1950, say. Before Category theory started taking over algebra, logic, and geometry. But 99% of working mathematicians don't do foundations. Nobody ever talks about group theory here, or differential geometry, or the Riemann hypothesis. If there was more discussion of those topics, this would be a math forum and not a philosophy forum. But at least nobody would accuse differential geometers of making assumptions about Russell and Whitehead.

I don't necessarily regard myself as a materialist, but I don't find non-material explanations satisfying.
— fishfry
I apologize, if my descriptive, not pejorative, label offended you. — Gnomon

Oh not at all. I took it as descriptive and probably accurate. And funny.

Some on this forum prefer the label "Physicalist". But most of us are Materialists in practical matters. We assume that the wooden table in front of us is solid matter. But Quantum Physics asks us to believe that 99% of that table is empty space, and even the atoms of wood are in constant motion. The reason you find Meta-physical explanations un-satisfying is that the evidence is purely subjective. But then, your personal subjective mental image of reality is the only reality you have any direct experience of. Most of the "objective facts" presented by Science -- especially those of Quantum "reality" -- must be taken on faith in the abstruse "knowledge" of the researchers. I've never seen a Quark, have you? :joke: — Gnomon

Why would you be asking a short-sighted materialist such a question? :-) Of course there are tables and chairs. And quantum physicists. That the world can contain both is evidence of Walt Whitman's point: "Very well then I contradict myself, (I am large, I contain multitudes.)"

I find metaphysical explanations unsatisfying is because they don't explain anything. Why do bowling balls fall down? God did it. That's unsatisfying. Of course to be fair, Newton's law of gravity was criticized on exactly the same grounds. He could describe gravity, but he could not explain it. In the end science itself tells us what but not why. Maybe God and the quantum field are two names for the same thing.

But science has one big advantage: It makes specific, measurable predictions. That makes science preferable to God as an explanation.

You ask if I think quarks exist. Yes I do. They exist in the sense that we can do experiments that confirm our mathematical theories that posit them. That's what existence ultimately comes down to. We do an experiment, we invent a conceptual and mathematical model that involves an atom or an electron or a quark, we do more experiments that confirm the theory. That's physical existence. And even a carpenter knows that chairs aren't really chairs. You have to cut up a tree and shape the wood into something you call a chair. You don't even need quantum fields to make the point that everyday objects aren't "really" that object, but rather assemblages of more primitive objects.

We'd have no excuse not to get our act together.... — Tom Storm

We'd have every excuse. It's mortality that makes us get our butts in gear. "I'll do it next millennium."

Which way is better? — Wheatley

I regularly read the math-oriented subreddits on Reddit. There's a steady stream of people trying to learn math at their own at literally every level, from adults who never learned math as kids trying to pick up what they missed at the grade school level, to former math majors now in other careers trying to self-learn graduate level math.

I think it's a very hard way to go. It's a method that works for geniuses. Galileo was a college dropout, and Newton made his most brilliant discoveries while away from school during London's plague year.

But for most of us mortals, having a teacher is essential. In theory you can pick up a math book and start grinding through the definition/theorem/proof exposition and work hard on the problem sets. In reality, a good teacher makes all the difference. It's very difficult to go it alone.

Suppose that science have achieve immortality for humans (whatever the mean for this).

What would be philosophical consequence? — John Pingo

Great old Twilight Zone. Guy sells his soul to the Devil for immortality. He is allowed to live as long as he wants, and he can die and turn over his soul any time he says so. Of course he thinks he never will.

He engages in risky behavior, jumps in front of subway trains, drinks ammonia. Nothing happens to him. He gets bored. He fights with his wife and throws her off the roof of a building. Of course he's not worried, he's going to get the death penalty and they can't kill him. Instead he gets a lawyer intent on saving him, and he gets life in prison. As he's sitting there in his cell contemplating spending eternity in his miserable prison cell, he summons the Devil and asks to die.

As I've explained to you already, the idea that 2+3 is mathematically the same as 5, is simply a misunderstanding of the difference between equality and identity. — Metaphysician Undercover

On the contrary. 2 + 3 and 5 are mathematically identical. There is not the slightest question, controversy, or doubt about that.

They are equal, but equal is distinct from identity. I've told you this numerous times before, but you do not listen. — Metaphysician Undercover

I listen very well, but the problem is that you are factually wrong. Wrong on the facts. 2 + 3 and 5 are mathematically identical. They represent the same thing. The identical thing. There is one single thing, and it has two names, 2 + 3 and 5. It has many other names as well, such as, "The cardinality of the vertices of a pentagon." If you kept telling me the sun rises in the west and I disagreed and you accused me of not listening, that would be an unfair statement on your part, would it not? Likewise 2 + 3.

Nor do you seem to pay any attention to my references, only repeating your misunderstanding in ignorance.[/quote = 5. — Metaphysician Undercover

You did in fact give me a reference, the very first one you've given me in three years, after I've asked you many times for references. And it turned out to be only a reference to another thread on this board, and not a reference to the work of any reputable or even disreputable philosopher. And when I read the reference, I did not find anything that shows that 2 + 3 is anything at all other than 5.

There are numerous philosophers who argue against the law of identity as stated by Aristotle, Hegel opposed it, as is evident here: https://thephilosophyforum.com/discussion/9078/hegel-versus-aristotle-and-the-law-of-identity/p1 — Metaphysician Undercover

Appreciate the reference.

What I see as an issue which arises from rejecting the idea that each particular object has its own unique identity (law of identity), is a failure of the other two interrelated laws, non-contradiction, and excluded middle. Some philosophers in the Hegelian tradition, like dialectical materialists, and dialetheists, openly reject the the law of non-contradiction. When the law of identity is dismissed, and a thing does not have an identity inherent to itself, the law of non-contradiction loses its applicability because things, or "objects" are imaginary, and physical reality has no bearing on how we conceive of objects.

There are specific issues with the nature of the physical world that we observe with our senses, which make aspects of it appear to be unintelligible. There must be a reason why aspects of it appear as unintelligible. We can assume that unintelligibility inheres within the object itself, it violates those fundamental laws of intelligibility, or we can assume that our approach to understanding it is making it appear.as unintelligible. I argue that the latter is the only rational choice, and I look for faults in mathematical axioms, and theories of physics, to account for the reason why aspects appear as unintelligible. I believe this is the only rational choice, because if we take the other option, and assume that there is nothing which distinguishes a thing as itself, making it distinct from everything else (aspects of reality violate the law of identity), or that the same thing has contradictory properties at the same time (aspects of reality violate the law of non-contradiction), we actually assume that it is impossible to understand these aspects of reality. So I say it is the irrational choice, because if we start from the assumption that it is impossible to understand certain aspects of reality, we will not attempt to understand them, even though it may be the case that the appearance of unintelligibility is actually caused by the application of faulty principles. Therefore it is our duty subject all fundamental principles to skeptical practices, to first rule out that possibility before we can conclude that unintelligibility inheres within the object.

Aristotle devised principles whereby the third fundamental law, excluded middle would be suspended under certain circumstances, to account for the appearance of unintelligibility. Ontologically, there is a very big difference between violating the law of excluded middle, and violating the law of non-contradiction. When we allow that excluded middle is violated we admit that the object has not been adequately identified by us. When we allow that non-contradiction is violated we assume that the object has been adequately identified, and it simply is unintelligible. — Metaphysician Undercover

Not a word of this is even on topic relative to whether 2 + 3 and 5 are identical. Since mathematically they are, and as a mathematical expression it must necessarily be interpreted in terms of mathematics, nothing you say can make the slightest difference. Excluded middle? Did Aristotle anticipate intuitionism? That's interesting.

But the most reasonable solution to the eternal "regress problem" is to assume that the Programmer is self-existent. — Gnomon

Well then why can't the world be self-existent without the need for the Great Programmer?

Sorry I'm not qualified to comment on the rest of your post, which clearly you've given a lot of thought to. It just seems to me that if you say the world didn't create itself but it was created by something that created itself, you haven't actually told me anything meaningful.

That is a typical short-sighted Materialist response to any notion of Transcendence. I — Gnomon

I don't necessarily regard myself as a materialist, but I don't find non-material explanations satisfying. Perhaps I am a materialist. Maybe short sighted too. I'm certainly near sighted, but that's a correctible refractive error. Maybe I need some philosophical spectacles.

That's why materialist Multiverse proponents must assume, without evidence, that the Forces and Rules-for-their-application logically pre-exist any functioning world or mini-verse. — Gnomon

A criticism I myself have leveled at the physicists.

In fact, most mathematicians assume that the axioms of their trade are timeless. — Gnomon

On the contrary, the modern axiomitization of set theory dates to Zermelo in 1908 and revised in 1922. And the categorical foundations are as recent as the 1940's. It's funny that many non-mathematicians believe that mathematicians think their discipline is flawless and eternal; while the mathematicians themselves, at least the small minority who have ever given the matter any thought, don't feel that way at all. Except for the ones who do. But your "most believe" formulation is surely false, since most haven't given the matter a moment's thought.

http://blog-glossary.enformationism.info/page10.html — Gnomon

I'll take a look, but I must admit most of these kinds of philosophical expositions make my eyes glaze. I think perhaps I am a short-sighted materialist. It's a perfectly sensible position to take in an otherwise inexplicable universe.

@Metaphysician Undercover I just happened to run across an article in Philosophy Now called, A Justification of Empirical Thinking by Arnold Zuboff, whom Wiki describes as, "an American philosopher who has worked on topics such as personal identity, philosophy of mind, ethics, metaphysics, epistemology and the philosophy of probability.[1] He is the original formulator of the Sleeping Beauty Problem[2] and a view analogous to open individualism—the position that there is one subject of experience, who is everyone—which he calls "universalism.""

So, a professional philosopher. At one point in the article he says: "We are indeed rationally justified in thinking 2 plus 3 will always be 5, because 2 plus 3 is not distinct from but rather identical with 5." My emphasis. So at least one professional philosopher would object to your claim that they are not identical.

The "mechanism" of evolution is viewed as something like a program written by a Programmer — Gnomon

Who created the Great Programmer? All creation myths that depend on an 'original intelligence" have a regress problem.

And secondly, as I pointed out, God or the Great Programmer doesn't explain anything. Say God did it. Ok, so what? Does that mean we stop doing science? Of course not. We do science to understand how the world works; or, as Newton would have put it, to better understand the glory of God's creation.

Religion and science are two separate subjects; two non-overlapping magesteria. Religion tells you how to live your life. Science tells you why bowling balls fall down. I just don't see any conflict between them.

And finally, as I can never resist pointing out, a programmatic explanation of the world is terribly restrictive. Programs, or algorithms, are quite limited in what they can do. A program can never solve the Halting problem; whereas God certainly can. Given a Turing machine and a given input, there is absolutely a fact of the matter as to whether that TM halts on that input. No computer program could ever determine the answer; yet the answer exists.

All simulation arguments fail for this reason. There's no reason to believe that the universe is computable. Some people think it is, but there's no proof, nor is it even clear what such a proof would look like. Why should the creator of the universe be constrained by the limitations of algorithms?