But then all you have done is claim that anything could be true. — Banno

Anything that is consistently defined and thus identical to itself.

The point is surely to sort out the way things actually are from the way things might be. — Banno

It is useful to sort out the way things are in our world from the way things are in other possible worlds.

...so an empty collection would be the simplest concrete object. — litewave

As Wayfarer impied, what is concrete about an empty set? — Banno

That it is a collection, rather than a property.

A concept/property is an object that is not a collection but it has instances in collections. — litewave

This is at odds with extensional logic, in which a property is a collection of objects; so "...is red" is the collection of red things. — Banno

I don't think that a property is a collection. Redness is not the collection of all red things but something that is had by all red things. The red things are the extension of the collection of red things as its parts, but they can also be said to be the extension the property redness as its instances. If you think that properties are collections then reality consists only of collections, which are concrete things, because properties as abstract things that have instances don't exist.

If this were so, then since in some possible world you didn't write that post; and since all possible universes exist and descriptions of all possible universes correspond to reality, you really didn't wright that post.

How will you avoid such inconsistency?

You have set the scope of "...exists" across all possible world instead of within the scope of each possible world, and that results in inconsistency. — Banno

Assuming that it is really "me" who lives in different possible worlds (which I don't think is a correct definition of "me", since my consciousness is clearly limited to only one of those worlds), I can say that I wrote the post in this world but not in some other worlds and I can also say that I wrote the post in reality as a whole, which is the collection of all possible worlds. Similar to saying that I watched Citizen Kane in Germany but I did not watch Citizen Kane in France, and I watched Citizen Kane in reality as a whole. This way inconsistency is avoided.

You appear to still be using "simples" - so you assume there is a "lowest level", and speak of "smallest parts".

But what is to count as a simple, as the atom from which you derive the world? Whatever you choose will be arbitrary - we might choose otherwise. — Banno

The smallest parts, empty sets, are obviously "simples" in the sense that they have no parts. But any collection is also a "simple" in the sense that the collection as a whole is an indivisible/unstructured thing that stands in parthood relations to other things that are its parts.

...Can you provide an indubitable account of what that "correspondence" consists in?

That's the core problem for correspondence. — Banno

A proposition describes an object by affirming that the object has certain properties. If the object really has those properties then the proposition is true - that's how a proposition corresponds to reality.

Example: Proposition "Planet Earth has approximately a spherical shape with a radius of 6,370 km" is true and thus corresponds to reality iff planet Earth has approximately a spherical shape with a radius of 6,370 km. And the properties attributed to Earth in this proposition are relational (geometric/quantitative) and thus mathematical.

Consider now a 3D object, a right cylinder with height 4 units and diameter 4 units. Depending on the angle of the light you shine on it, the shape of its shadow will change. — TheMadFool

A contradictory proposition affirms that something has and does not have the same property. But a proposition that affirms that something looks like a circle from one perspective and does not look like a circle from another perspective is not a contradiction because the property of "looking like a circle from one perspective" is not the same property as "looking like a circle from another perspective".

Sometimes it is said for emphasis that a contradictory proposition affirms that something has and does not have the same property at the same time, and/or in the same sense, but these additions can be seen as already included in the meaning of the phrase "same property".

What's impossible to you? — TheMadFool

Logically inconsistently defined objects. Objects that are not what they are. Objects that have properties they don't have.

It may not be obvious whether an object is consistently defined, because its definition, its properties include all its relations to all other objects in reality, so it must be defined consistently in relation to everything else. But at least when you interact with an object, you can know that it is consistently defined without having to check consistency of its relations to everything else, because if you interact with it it must exist and inconsistent objects cannot exist.

Perhaps surprisingly, whatever you are doing at this moment, it is impossible for you not to be doing it, at this moment. Simply because it would be a contradiction, an inconsistently defined event, if you were not doing what you are doing. For a copy of you in a different possible world it might be possible not to be doing what you are doing but not for you.

Yeah.

Isn't that begging the question? By the way if a world has to be qualified with real as you do in "...a real world", it suggests that worlds can be unreal. Care to expand and elaborate. — TheMadFool

As I said, I think that all possible worlds are just as real as our world because I don't see any ontological difference between possible and real worlds.

Every consistent description of a world corresponds to a real world.

Instead of talking of some ultimate property - which is a monistic concept - we can instead switch to seeking some ultimate relation, or form of interaction. — apokrisis

Interaction is possible only in worlds that contain a time dimension. Worlds without time seem to be possible (logically consistent) too, and since I don't see an ontological difference between a possible world and a "real" world, reality also contains worlds without time.

I understand, I just meant to point out that if all possible (logically consistent/coherent) universes are equally real as the one we live in, correspondence theory of truth becomes identical to coherence theory of truth.

But an empty set is nevertheless a concrete object? — Wayfarer

By a concrete object I mean any collection, so an empty collection would be the simplest concrete object.

I know that sets (collections) are often regarded as abstract objects, but in those cases a set is meant as a concept/property (which is instantiated in concrete sets). A concept/property is an object that is not a collection but it has instances in collections.

But the original meaning of atom was literally that. Atom meant non-divisible or non-composite. The atom in modern physics doesn’t mean that, but your ‘non-composite concrete objects’ are pretty well exactly what the atom was understood to mean when the term was coined. — Wayfarer

By 'non-composite concrete objects' I mean empty sets, which have no parts by definition. No amount of empirical evidence can prove than an empty set has parts.

From then onwards, mathematicians began tinkering around with the foundational axioms of math that did correspond to reality and developed entire mathematical universes that have no real-world counterparts to correspond to. Nevertheless, physics seems to be at the forefront of applied math and I'm led to believe that many such mathematical universes seem to, intriguingly, match how reality is i.e. there's a correspondence there! — TheMadFool

Even though many descriptions of a universe by mathematicians don't correspond to our universe, they correspond to other possible universes. And what is the ontological (existential) difference between a possible universe and a "real" universe? I think none, so all possible universes exist and descriptions of all possible universes correspond to reality. There is no difference between correspondence theory of truth and coherence theory of truth.

No, atoms in physics are obviously not non-composite things.

I don't claim that truths of propositions that are joined into a longer proposition are necessarily independent from each other. To logically prove whether or not they are independent we would need to analyze the things and relations they refer to, down to the lowest level if necessary (to the smallest parts, in the case of concrete things).

So, mathematics best describes these relationships? I would agree. Yet, what's mathematical about hydrogen? Is it a 'thing', as you might say? — Shawn

Yes, the hydrogen atom is a thing with relations to other things, notably to its proton and electron and to the spacetime of which it is a part. Due to its relations it has mathematical properties such as 2 parts (proton and electron, which both have their own parts, even the electron because if the electron had no parts it would be an empty set and an empty set does not have properties such as mass or electric charge), spatial size and shape, extention in the time dimension (lifetime), value of mass/energy...

To clarify my ontology, every concrete thing is a collection of parts (the smallest collections are empty collections/sets, that is non-composite concrete objects). It is important to note that while a collection has a structure, this structure is constituted by the relations of the collection to its parts, and none of its parts is identical to the collection. So the collection as a whole is a thing too, different from its parts, and this thing is something unstructured that stands in relations to other things, notably to things that are its parts.

All possible collections are rigorously defined by set theory, which can represent all mathematical properties as collections (sets).

But, the proponents of the correspondence theory of truth lauded it as composed of logical simples, logical atomism, and even logical monads. — Shawn

Reality consists of things and relations between them. By "thing" I mean something that is not a relation, nor a structure of relations, so "thing" is something unstructured, indivisible, monadic and therefore a "qualitative stuff" (a quality). Mathematics describes the relations (quantitative, geometric, algebraic... all of these relations can be represented as structures of set membership relations, according to set theory). Mathematics does not describe things (qualities), for example colors, sounds, tastes..., only relations between things, but we have (non-mathematical) words for things too, so we can form propositions about both things and relations and iff these propositions correspond to reality they are true.

Mathematics corresponds to the structure of reality (and omits the qualities that fill the structure).

If emptiness is understood as the content of an empty set, then it is nothing. However, the empty set itself is not nothing but an object, a non-composite object, which is a part of composite objects. In this sense, concrete reality is built up from nothing.

If by "ultimate reality" you mean the most general property, that is, the property possessed by every something, it is the property called variously identity, logical consistency, or existence. If you mean the smallest concrete object, it is the non-composite object, also called the empty set; other concrete objects are constituted by combinations of empty sets into larger sets, and by combinations of those combinations, and so on. There may also be composite concrete objects that don't have empty sets "at the bottom" but infinitely differentiated parts instead, as long as their definition is logically consistent; however, that consistency, and thus their existence, may be impossible to prove due to Godel's second incompleteness theorem.

No "will" or "thought" is necessary for existence, unless by "will" or "thought" you mean logical consistency, because logical consistency is existence.

If nothing existed, there would be the fact that nothing exists, but a fact is something. Or, in other words, there would be the property of "there being nothing", but a property is something. So the idea of nothingness is logically inconsistent. However, the idea of nothingness is logically consistent if it refers to a part of reality, instead of whole reality: there can be nothing in a part of reality. Such a part of reality can be called an "empty world" or "empty set". Combinations of empty sets into larger sets and combinations of those larger sets into even larger sets, and so on, constitute the structures of all possible composite objects and thus all possible worlds.

Therefore, not only is it logically necessary that something exists, it is also logically necessary that all possible worlds exist.

Ok, but the apple would still fall down every time we drop it, no? So the regularity would still exist even if we took our blinders off and the question would remain why the regularity persists.

Because our sciences substitute idealized abstractions for a more immediate and intricate experiencing of our world. — Joshs

So if our sciences didn't do this, we would not experience the apple as falling down every time we drop it?

An explanations consists of descriptions but a "better, general" description is not an explanation. — 180 Proof

I usually understand "explanation" as a derivation of something particular from something more general. Like, why does the apple fall down? Because of the law of gravity.

Isn't this just Hume's problem of induction? — fishfry

Yes. I wonder why Solomonoff's solution to the problem of induction is not mentioned in that article.

As far as we know the "constants" are constant (our physics breaks down at various edge cases already mentioned), but I agree insofar as better explanations, not merely more precise descriptions, have been found. — 180 Proof

In other words, better general descriptions from which more detailed descriptions can be derived. This is possible when there is an even more general/universal regularity than the ones we knew before.

Isn't that just the currently contingent theory, subject to revision in next week's Physical Review Letters? — fishfry

I guess physicists have a lot of evidence that points to the stability of the known laws?

Still, there are exceptions: the Big Bang and Black Holes. Things break down at these levels. — Manuel

We don't know what is going on in these special cases but outside of them the regularities seem stable.

Later physical theories consist of better, more comprehensive, less ad hoc explanations than earlier physical theories. From this comes more precise predictions — 180 Proof

Right. But apparently the regularities of the world have not changed much, if at all. Scientists just found more accurate descriptions of them.

These laws were different immediately at and immediately after the Big Bang. They also have problems inside black holes. And who knows if they apply to all of the universe? — Manuel

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

The physicist Lee Smolin thinks that physics, its laws, and constants evolve: https://blogs.scientificamerican.com/cross-check/troublemaker-lee-smolin-says-physics-8211-and-its-laws-8211-must-evolve/ — Fooloso4

Smolin has a theory of cosmological natural selection in which the laws or constants may change when a new universe is born from a black hole in the preceding universe. So if I understand him right, he doesn't propose that such a change has happened in our universe since it was born.

If you go to the moon, the gravitational acceleration is different than on earth — fishfry

Still, the apple falls down on Earth, similarly like it did 2000 years ago.

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. — fishfry

Do you expect that once we understand dark matter the apple will stop falling down on Earth?

If you deny that human-created physics is historically contingent, you must not be familiar with the history of science. — fishfry

I really don't know why the apple falling down on Earth would be a historically contingent, human-made regularity.

The Ptolemaic system that placed the earth at the center of the solar system fit all known observations and was accepted for millennia. — fishfry

The planets were moving with the same regularity at the time of Ptolemy as they are now. Ptolemy just invented a very cumbersome way of describing their motions, by choosing to describe them in relation to Earth. Copernicus later found that it was much more simple to describe them in relation to the Sun, Kepler found it was more accurate to approximate their orbits with ellipses rather than circles, Newton postulated a universal law of gravity, from which the elliptical orbits followed as a logical consequence, and Einstein improved the accuracy of description by introducing a curved spacetime. Still, the planets were moving with the same regularity at the time of Ptolemy as they are now.

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

Obviously the apple falls down on Earth like it did 2000 years ago. The planets move in the same way too.

That can only be because you didn't bother to read the Wiki and SEP articles I linked. — fishfry

Actually I gave a look at the Wikipedia article, which confirmed that realism offers a sensible explanation of why our theories work while instrumentalism offers none.

I'm not arguing for the falsity of scientific realism; only noting that it's a metaphysical stance and not a scientific one. — fishfry

Ok.

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. — fishfry

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.

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. — fishfry

Sure, that was also the basis of my OP.

I always worry that the anthropic principle explains nothing by explaining too much. The reason the world is just-so is because, if it weren't, then we wouldn't exist. — Cuthbert

It only makes sense to invoke the anthropic principle for properties that are necessary for the existence of human life and that vary across a collection of different possible worlds (the so-called fine-tuning for human life), and it may be difficult to identify such properties or their combinations. It may be a very general principle that can't describe a detailed structure of our world since there may be many different worlds that can support human life. And while it may explain why the laws of physics have been stable for a long time it doesn't seem able to explain why we should expect that they will remain stable in the future.

Nah, it's probably you that has changed, not the law of gravity.

Even random things have reasons. What would make a randomly selected value for c change to another randomly selected value of c? — Kenosha Kid

Ultimately, the reason for anything to exist is the same: that it is possible (logically consistent). But some properties are simpler and therefore more likely than others. A world where the speed of light randomly changes is less simple than a world where it is constant (all other laws and initial conditions being equal).

A change in a law would raise the question, what changed it? In all other things, inertia is a sign of being left the hell alone: change suggests something driving that change. — Kenosha Kid

I am not sure we can view it this way. If the structure of a world is random instead of deterministic does it mean that the world is not being "left alone"? It does mean that randomness increases (Kolmogorov) complexity of a world.

"Physical laws" are features of physical models and not the universe itself. Our physical models are stable, therefore "physical laws" are stable. If in current scientific terms new observations indicate that aspects of the universe have changed, then, in order to account for such changes, we will have to reformulate our current (or conjecture new) physical models which might entail changes to current (or wholly different) "physical laws". E.g. Aristotlean teleology —> Newtonian gravity —> Einsteinian relativity. — 180 Proof

Still, all these theories describe a stable phenomenon of objects falling down (rather than up or in random directions), although later theories give more accurate predictions than earlier ones.

The laws of nature are simply patterns in the way matter & energy interact and that they've been as they are now for quite some time — TheMadFool

That seems explained by the anthropic principle: we could have evolved only in a world where the laws have been stable for a long time.

So, take a deep breath, strap yourselves in because the so-called laws of nature (the order/ the pattern) could devolve into utter chaos at any time. — TheMadFool

Solomonoff induction seems to show that this is very unlikely.

The first question I have is whether the 'plethora of possible worlds' is simply a figment of the imagination. — Wayfarer

I agree that theories supported by sensory evidence are more convincing and useful than theories supported by logic alone but one might also ask whether sensory experiences are not simply figments of the imagination. My reason for taking other possible worlds as real is that I don't know a difference between "real" and "possible" worlds. I can't even imagine what such a difference could be. The only way to show that a world is not real would be to show that it is not logically consistent, but such a world would not be possible either.

That there might be 'other worlds' or 'other universes' seems like the most idle of idle speculation - what light does it cast, what explanatory advantages does it provide? — Wayfarer

It can provide a clear logical explanation why some properties of our world are the way they are when it seems that they could have been different, for example the stability of the laws of physics or the values of some constants that seem fine tuned for the existence of living organisms. There may be no other explanation than that we happen to live or are likely to live or necessarily live in one of those worlds that have certain properties.

And what evidence could there ever be for it? — Wayfarer

I don't know. If any interaction with other worlds is in principle impossible then we can never have direct observational evidence of such worlds. But we may get indirect supportive observational evidence if we observe things in our world that can be better explained or predicted by a theory that assumes the existence of other worlds.

Why is that such speculation is regarded as scientifically respectable, when, for instance, speculation about any form of higher intelligence is inevitably dismissed as creationist? — Wayfarer

Multiverse theories are more logically transparent than obscure theories of God, and their more limited versions are also closely connected with theories of physics that are well supported by observational evidence, for example theories that postulate that there are worlds beyond the horizon of our observable universe (beyond the Hubble volume) but still within our universe, inflationary multiverse, string theory multiverse, or quantum mechanical multiverse.

Second point is to consider that the stability of the laws of physics are conditions for the existence of anything whatever, and questioning them is tantamount to questioning why two plus two equals four, and not an elephant. They are simply so, in order that anything might exist whatever. — Wayfarer

Something can exist also in a world with unstable laws of physics, namely the unstable laws themselves and various unstable or random objects that are compatible with those laws.

As is well-known, there are a small number of fundamental constants that seemed to be poised according to minute tolerances, in the absence of which a Universe would not have been formed in the first place (per Lloyd Rees, Just Six Numbers.) — Wayfarer

A world without these constants would be very different from ours but that doesn't mean it would be nothing. Worlds without time seem to be possible too, basically any consistent mathematical structure, and in the extreme also completely empty worlds that are identical to an empty set.