For what it's worth, like a mathematician, I see no difference between existence and logical consistency and so I regard both these concepts as one and the same. Then the sentence "No object exists" can be reformulated as "No object is logically consistent", which is evidently and necessarily false. There are plenty of logically consistent objects; every object that is identical to itself is logically consistent and therefore exists (as opposed to, for example, the famous "square circle", which is a circle that is not a circle, a logically inconsistent and therefore nonexistent object).

In other words, I would have to pick out the lion first, before I have good reason to avoid it. — NotAristotle

So you pick out the lion without having a good reason and then you pass your lucky genes to your offspring. Or you don't pick out the lion and your genes go to waste. Fast-forward millions of years and virtually everyone in the gene pool automatically picks out lions.

What is your explanation for existence? — Benj96

At heart my ontology is trivial: every possible concrete thing either has no parts (and thus has the structure of the empty set) or has parts (and thus has the structure of a non-empty set). These concrete things make up all possible worlds and all possible worlds are real worlds because there is no difference between possible and real.

You do see how the assertion that 'something just happened' does not actually amount to any kind of rationale? — Wayfarer

But things do happen, and this particular thing (survival) then tended to repeat itself and become more prevalent, simply because that is what surviving entities do.

Well, I also suggested a solution to the problem of qualia, which is the hard problem.

Yes - well, when you can demonstrate a self-creating machine that follows goals, then I will accept the answer. Because machines are human artefacts, produced intentionally to deliver a result. They embody the intention of the agent who builds them. — Wayfarer

For organisms evolved by random mutations and natural selection, many goals seem to be derived from the primary goal of survival and replication. This primary goal originated when some purely unintentional (goalless) entities happened to have (by random strokes of luck) properties that sustained them in their environment, which resulted in the unsurprising fact that... they kept surviving and thus became more prevalent in the environment. And so it started to seem like they were following a "goal" of survival. Later some of these entities happened to replicate and thus kept on "surviving" in their offspring. After some time the environment was filled with entities that seemed to have the "goal" of not only surviving but also replicating. And as time went by and the surviving and replicating entities happened to acquire additional properties that made them do various things, the entities seemed to acquire additional goals, many of them supporting the primary goal of survival and replication while goals that hindered survival or replication tended to cause their unlucky carriers to die out. Sure enough, some of the new goals were more or less neutral with respect to survival or replication, and such goals were carried forward in the entities that survived and replicated.

Isn't it just lumpen materialism? You still haven't allowed for intentionality other than as a byproduct or epiphenomenon of these essentially unintentional relations. — Wayfarer

Intentionality? That seems like an easy problem, not the hard one: a machine following a goal. For example a self-driving car is "intending" to get to a destination (without running over pedestrians). Or a killer robot is "intending" to kill someone.

Maybe what makes consciousness so elusive is that we only regard elementary particles as real things. There aren't really any atoms, neurons or brains. Just elementary particles. Collections of elementary particles like atoms, neurons or brains don't seem to be real things, just useful fictions.

When you add up the masses of all elementary particles that make up a neuron, their total mass is the mass of the "neuron"; there is no additional mass provided by the "neuron" as a collection, as a whole. The absence of an additional mass provided by the "neuron" is the result of the fact that the locus of the gravitational force is only at the level of elementary particles, not at the level of their collections.

The locus of all known physical forces is at the level of elementary particles, and when you add up the forces of all elementary particles that make up a neuron, their total force is the force of the "neuron"; there is no additional force provided by the "neuron" as a collection, as a whole.

So it seems that a neuron doesn't really exist. And the same applies to collections of neurons. Consciousness seems to be somehow "generated" by collections of neurons, or seems to "emerge" somehow from collections of neurons. But what if consciousness actually is collections of neurons? What if qualia are collections of neurons? That would rid the metaphysical picture of mysterious "generation" or "emergence". But the fact remains that qualia as collections of neurons (or perhaps even as neurons themselves, which are collections of elementary particles) don't contribute their own mass and forces in addition to the masses and forces of their constituent elementary particles, and so qualia seem to be causally inert, epiphenomenal. Yet, if qualia are collections of elementary particles then qualia can exert causal influence indirectly, via their constituent elementary particles.

My point is that collections of elementary particles are not just useful fictions but real things, different from and additional to the elementary particles, even though the collections don't have a direct causal influence, only an indirect one via their parts. That may explain how qualia are seemingly nonexistent although we all know them to exist as contents of our own consciousness or parts of our own brain.

And by the way, elementary particles themselves may actually be collections of even more fundamental parts, which we have not discovered yet, or which cannot be physically probed even in principle. If collections are not real things and elementary particles are collections then even elementary particles are not real things. Then, are there any real things at all or is everything a fiction? Are only empty collections (non-composite things) real things - or would that be an arbitrary assumption?

If someone is omnipotent, they're able to do anything. If there was something they couldn't do, they wouldn't be omnipotent. — Bartricks

But a square circle is not really something. It is nothing. In mathematics it is the content of empty set.

You said if God created the world, then God created the world. Er, yes. And? — Bartricks

It's a consistent proposition. You suggest that an inconsistent proposition can be true: "If God created the world, then God didn't create the world." The point is: God's actions are parts of reality and reality must be logically consistent, which means identical to itself. If the action of God's creation of this world is a part of reality then it is so necessarily because otherwise reality would not be identical to itself. Everything that happens in reality, happens necessarily. God's free will is at best compatibilist because no other free will is coherent.

Again, you don't seem to understand what the issue is. — Bartricks

You said that this is not the best possible world. I say that even if this is not the best possible world, it may still have been created by an omnibenevolent God. Because an omnibenevolent God may have created the 10 best possible worlds and our world may be one of them. But who knows, maybe our world is the best possible one, who are we to say it isn't? How do you define the best possible world? I would imagine it's a world that somehow maximizes happiness across the whole spacetime, and so suffering at some time may enable more happiness at another time.

Yes they can. They can do anything, including things that violate the laws of logic. — Bartricks

There can't be such things. If there were, there wouldn't be.

Anyway, it's beside the point, for it is clearly not a violation of the laws of logic to refrain from creating something. — Bartricks

Right, but sometimes it would be. It is not a violation of the laws of logic for a circle to exist, but it would be a violation of the laws of logic if the circle existed in a set of triangles. Similarly, it would be a violation of the laws of logic if you refrained from doing something in a world where you don't refrain from doing it.

You've just said 'reality must be consistent......therefore God has created the world' — Bartricks

No, I didn't.

'If' God created a world, then he would create the best world. This isn't the best world, is it?! — Bartricks

I don't know. But maybe an omnibenevolent God would create top 10 best worlds and this is one of them?

But just as the wood and spring of the mouse trap in no way explain how a mouse trap could be consciousness, the laws of biology, chemistry, electricity, and quantum mechanics in no way explain consciousness—or even hint that consciousness is possible. — Art48

Come to think of it, we also don't know what mass or electrical charge is. We just know that it is something that behaves in a certain way, for example it is attracted to other things with mass or attracted to or repelled from other things with electrical charge. So there is a correlation (or association) between mass or electrical charge and a certain kind of attracting/repelling behavior. The problem with consciousness seems similar but more complicated: a conscious brain behaves in a certain way that is different than how an unconscious brain behaves but the behavior is more complex and sometimes so subtle that there seems to be no difference between the behavior of a conscious brain and the behavior of an unconscious brain. Also, consciousness doesn't seem localized on the level of elementary particles but on the level of very complex wholes. But in all these cases we can see that if there is a behavior then there must also be something that behaves. I think this is a special case of a more general truth: if there are relations then there must also be something (a non-relation) that stands in those relations.

Then he wouldn't be omnipotent. God is by definition omnipotent. So God can do anything. That includes refraining from creating a world. — Bartricks

But even an omnipotent being can't create a logically inconsistent object because such an object cannot exist, for example a square circle.

That's flagrantly question begging. — Bartricks

Reality must be logically consistent, which means that it cannot be what it is not. God's action is a part of reality, which means that God's action cannot be what it is not, and so if God creates a world he cannot not create it.

It gets worse, not only does omnipotence not positively imply that God created the world, omnibenevolence positively implies God did not create it. — Bartricks

Then God creates the best worlds that are logically possible (consistent).

But I don't believe God created the world we live in. It doesn't look like the kind of place an all-good person would create. But Christians typically do believe that God created the world. Why? — Bartricks

Ok, I'll play God's advocate: God created this world because he couldn't have done differently. Not creating this world would be logically inconsistent because he would not have created the world he has created.

Sets exist in universes (domains of discourses) for model. The collection is a collection of models. The only things that exist in that collection are models. The set exists in the universe of one of the members of the collection. — TonesInDeepFreeze

If a set X exists in a collection (model) which exists in a collection (multiverse), I see no problem in saying that the set X exists.

What do you think set theory is?

What do you think is an inconsistent theory (You claim ZFC+CH+~CH is not an inconsistent theory, so it's clear you don't know what an inconsistent theory is.)

What do you think a model of set theory is? — TonesInDeepFreeze

Set theory is a description or explanation of sets. An axiomatized set theory is a set of axioms about sets. A model of a set theory is a set, or a collection of sets, that is described by the theory. An inconsistent set theory would be one that affirms and denies the same property to the same set.

No, you are missing the point that such a set exists in some models in the multiverse and not in other models of the multiverse. — TonesInDeepFreeze

Really, where did you get that? I said that such a set exists in a ~CH world and does not exist in a CH world.

I already told you. It a collection of models (or "worlds" informally). — TonesInDeepFreeze

Well, whether you call the multiverse a model or a collection of models, the fact remains that a set with cardinality between naturals and reals exists in this collection, although it doesn't exist in all its subcollections (models), which is fine. And the same applies to the existence of any set that is defined by a consistent axiomatized set theory; that's why I said that all logically possible (consistent) collections exist.

But there does not exist any model of ZFC+CH+~CH, since inconsistent theories do not have models. — TonesInDeepFreeze

Then the multiverse is a model of what? Or what is it?

No, he mentions that there are separate universes. That is the multiverse. The collection of separate individual universes. He doesn't combine universes all into one big clump. — TonesInDeepFreeze

"Clump"? Is that supposed to be another technical term? A multiverse is a collection of universes or worlds, that's all.

And there is no "the world of ZFC+CH" or "the world of ZFC+~CH". Rather, for each set theory, there are many non-isomorphic models. — TonesInDeepFreeze

Then there are "CH worlds" and "~CH worlds". You are missing the point, which is that a set with cardinality between naturals and reals exists in the multiverse.

Hamkins points out that we are free to work separately in different models. He doesn't say that we combine a model of ZFC+CH with a model of ZFC+~CH. — TonesInDeepFreeze

He combines the world of ZFC+CH with the world of ZFC+~CH into a multiverse. And since a set with cardinality between naturals and reals exists in the world of ZFC+~CH, it also exists in the multiverse.

The union of all axiomatized set theories does. — litewave


That is an inconsistent theory. — TonesInDeepFreeze

I suppose that you also think that a union of ZFC+CH and ZFC+~CH theories is an inconsistent theory. Yet according to Hamkins the worlds defined by these two theories are parts of a consistent multiverse.

It is as if you took these two statements:

(1) "This ball is red."

and

(2) "This ball is not red."

and concluded that these statements are contradictory. But you didn't notice that these statements are not about the same ball but about two different balls and thus there is no contradiction between them. Same with axiomatized set theories: they define different worlds and thus are not contradictory.

But if ZFC is the context of your notions, at least a kind of "base" theory for your uncountably many theories — TonesInDeepFreeze

I mentioned ZFC just as an example of axiomatized set theory.

But the more basic point is that, no matter your own views (or even Hamkins's, for that matter), it is not the case that "according to set theory, all logically possible (consistent) collections exist".

Set theory does not say that. — TonesInDeepFreeze

The union of all consistent axiomatized set theories does.

. Please say exactly what passages in part 7 you regard as saying that there is a set with cardinality between the naturals that is decided ('settled' in context) by the consistency of ZFC+~CH. — TonesInDeepFreeze

Hamkins regards the world defined by ZFC+~CH as equally real as the world defined by ZFC+CH and that both worlds exist in the multiverse. So that's how the continuum hypothesis is settled.

"Since we have an informed, deep understanding of how it could be that CH holds or fails, even in worlds very close to any given world, it will be difficult to regard these worlds as imaginary."

And no retraction from you that you falsely put words in my mouth by claiming that I said naive set theory must obey the axiom of regularity. — TonesInDeepFreeze

I didn't put words in your mouth. I thought that when you used the word "naively" you referred to naive set theory.

So, please quote the specific passages you contend claim that all sets exist that are "selected" by at least one consistent axiomatic set theory. Tell me the exact formulations you have in mind that Hamkins mentions in his own words. — TonesInDeepFreeze

on page 2: "In this article, I shall argue for a contrary position, the multiverse view, which holds that there are diverse distinct concepts of set, each instantiated in a corresponding set-theoretic universe, which exhibit diverse set-theoretic truths."

And please cite where Hamkins says there is a set with cardinality between the naturals and the reals and that that is decided by the fact that ZFC+~CH is consistent. — TonesInDeepFreeze

The example with CH is in part 7: "Case study: multiverse view on the continuum hypothesis". See it for yourself. I tried to express the gist of it in my previous post.

And that is not what anyone means by 'naive set theory'. So your notion is not set theory and it's not naive set theory. — TonesInDeepFreeze

Well, Wikipedia article on naive set theory just mentions the general concept of a set as a collection of objects, and related general concepts like set membership relation, equality, subset, union, intersection etc. There is no requirement that a set cannot be a member of itself or that a set must have a minimal member, which you tried to impose on naive set theory.

What are all the axiomatized set theories? There is no definitive list, and there is no conceptual limit. For that reason alone your notion is fatally vague. — TonesInDeepFreeze

Sure, the number of axiomatized set theories is uncountable. I see no reason to set any arbitrary limit to them.

And what does "included" mean? — TonesInDeepFreeze

Look at Hamkins' paper on multiverse in set theory. As an example, he talks about a world defined by axioms of ZFC + CH and a world defined by axioms of ZFC + negation of CH. He claims that both worlds exist in the set-theoretic multiverse. That means that a set with cardinality between naturals and reals doesn't exist in the (ZFC + CH) world but it exists in the (ZFC + negation of CH) world and thus exists in the multiverse. I cannot speak about set theory with the same rigor as Hamkins or you but this seems to be what I am trying to say.

since ZFC+CH is now ruled out by your requirement that there exists a set of cardinality strictly between the naturals and the reals — TonesInDeepFreeze

ZFC+CH is not "ruled out", it just defines a part of the multiverse, a part in which there is no set with cardinality between naturals and reals.

I think I can clarify a lot by addressing this part of your post:

(5) Set theory does preclude certain kinds of sets that otherwise it would be consistent to say they exist. In particular, the axiom of regularity precludes certain kinds of sets that otherwise would be consistent to say they exist.

Since you did not reply to that, I'll add: I surmise that naively (informally, intuitively) most set theorists' notion of 'set' includes that sets are not members of themselves, and that, more generally, every set has a minimal member. That is especially witnessed as the axiom of regularity is a standard axiom, which is especially relevant since you say that naive set theory is "elaborated upon" by axiomatizations such as ZFC. This is a point blank refutation of your claim that "according to set theory, all logically possible (consistent) collections exist", as indeed both the naive notion of sets and the standard axiomatizations exactly preclude the existence of certain kinds of sets that would not be inconsistent to assert their existence otherwise. That point cannot be skipped and it alone decisively refutes your claim. — TonesInDeepFreeze

As I said, by "set theory" I mean set theory in the most general sense. I supposed that this is what is commonly understood as naive set theory, but to clarify, I mean the concept of a set or collection of objects that is elaborated in all consistent axiomatized set theories together. In other words: if a set is included at least in one consistent axiomatized set theory, then such a set exists. As I said, there are uncountably many axiomatized set theories. ZFC set theory is just one of them. So I include also sets that are members of themselves and sets that don't have a minimal member, as long as these sets are consistently defined. Elsewhere you stated that there is no such thing as an inconsistent definition, so let me give you an example of an inconsistently defined set: an empty set that has one member.

Also, the example with CH may be clarifying. If there is a consistent axiomatized set theory that includes a set with cardinality between the cardinalities of the set of naturals and the set of reals, then such a set exists, simply because it is included in a consistent axiomatized set theory (that has an axiom that is the negation of CH). It's no problem that in a different axiomatized set theory, which has CH among its axioms, such a set doesn't exist. A set theory with CH as an axiom simply selects only certain sets among which a set with a cardinality between naturals and reals is not included. Every consistent axiomatized set theory selects certain sets, and by "all logically possible (consistent) collections" I mean sets or collections selected by all consistent axiomatized set theories together - that's the multiverse view in set theory. If a set is included at least in one consistent axiomatized set theory, then it exists in the set-theoretic multiverse.

Yes, a world which is called a possible world ... — Shawn

But the actual world is still necessarily identical to itself and therefore cannot be something different than it is. My actions in a merely possible world may be different than my actions in the actual world but my actions in the actual world cannot be different than my actions in the actual world.

Every day we make choices where seemingly we could have done something otherwise. — Shawn

Yes, seemingly.

Even taking your argument to the extreme, there could be a possible world where causality would have allowed for a different event cone to allow a counterfactual to arise. — Shawn

Quantum-mechanical indeterminacy could do that. But a world with a different outcome of a quantum measurement would be a different world, with a different identity, than our world. And I cannot be in both worlds, if by "I" we understand someone who is conscious of being only in one world. The "I" in the different world would be my copy, a counterpart.

Could you elaborate? — Shawn

Does Kripke believe that it is possible for us to act differently than we actually act? It seems he doesn't, because our actions are parts of spacetime and spacetime is necessarily identical to itself, which means it cannot be different than it is and so our actions cannot be different than they are.

What's posited here is that if two things are identical then they are necessarily identical. — Banno

Right, and our spacetime is necessarily what it is and could not have been different. Bye bye free will?

It is not true that according to set theory all logically possible (consistent) collections exist. — TonesInDeepFreeze

I mean "set theory" in the most general sense, also known as naive set theory. It just says that a set is a collection of objects. This general concept of set is elaborated in uncountably many axiomatized set theories, for example the famous ZFC set theory. I refer to all these axiomatized concepts of set, as long as they are consistent.

For example, it is consistent with set theory that there is a set that has cardinality strictly between the cardinality of the naturals and the cardinality of the reals, but it is not a given that it is the consensus of set theorists and philosophers that such a set exists. — TonesInDeepFreeze

For me, as long as such a set is consistently defined, it exists. In some axiomatized set theories it may exist while in others it doesn't. That's because every axiomatized set theory selects a limited collection of possible (consistently defined) sets. This is what Joel David Hamkins has called "set-theoretic multiverse".

I imagine there's a lot less to do in a merely possible world, for one thing... — busycuttingcrap

Why would there be less to do in a merely possible world? Some worlds may be simple and others more complex, whether they are merely possible or real.

And if something is logically possible, then we may also say that "there is a possible world" where that something is true or is the case. — busycuttingcrap

And what is the difference between a logically possible world and a real world?

But what is outside of spacetime? Abstract objects like thoughts and numbers. — Art48

Thoughts may actually be concrete objects (parts of a brain) and abstract objects in the sense of universals, like numbers, may actually be similarity relations among concrete objects. What is outside of spacetime then? Perhaps other concrete objects, including other spacetimes. According to theory of relativity, spacetime is actually just a special kind of space, a 4-dimensional space with one dimension (time) somewhat different from the other three. And according to topology, a space is just a special kind of collection. All mathematics seems to be reducible to concrete collections, from the empty collections (non-composite objects) to infinitely large collections (infinitely large composite objects). That's why set theory (the ultimate theory of collections) is regarded as a foundation of mathematics.

So according to set theory, all logically possible (consistent) collections exist, from the empty collections to infinite collections, and they, or relations between/among them, constitute all known mathematical objects, relations or structures. Note that all of this exists necessarily/automatically because nothingness constitutes the content of empty collections and empty collections constitute the content of larger collections, and larger collections constitute the content of even larger collections, and so on. And a spacetime is one of those collections and we are collections that are parts of a spacetime.

So is everything math? Well, there seems to be something about collections that is extra-mathematical. There is a composition relation (or set membership relation) between a collection and a larger collection that includes it. So collections are somethings (not nothing, as there can be no relations between nothing), but mathematics doesn't tell you more about these somethings than that one something includes another something. Mathematics is just about relations between these somethings and these relations are reducible to the composition relation. These somethings are not relations; they are what stands in composition relations. These non-relations might be called "things" or "qualities".

This does not address the question, wherein alternatives to choose among occur. — javra

What question do you mean?

For example, your intent is to learn about subject X; how does this intent of itself establish whether you choose a) to read a book about X or b) to see a documentary about X? — javra

I may stumble upon a good book review and then the information from the review together with my intent to learn about subject X create in me the intent to read the book about X and this intent drives me to read the book. Where is free will?

Is he not his ingrained predispositions? — NOS4A2

Yes, you could say that the agent is his ingrained predispositions (as well as his experiences in the course of his life). So the agent has free will even though all his actions are completely determined by his ingrained predispositions?

What I’m suggesting is that there isn’t a strict logical dichotomy between “completely determined (hence no free will)” and “completely undetermined (hence no intentionality)”; that there logically can very well occur something in-between, a “partly determined and hence partly undetermined” state of being that (partly) defines us as agents; and that our free will - if real - would necessarily be of the latter state of affairs: e.g., always partly determined by intents (among other possible factors), but never completely determined. — javra

Then our actions are partly intended and therefore partly unfree, and also partly unintended and therefore partly unfree too. So they are wholly unfree.

Its a variant of compatibilism, though I take it you're not much enamored with the prospect of compatibilism. — javra

I think compatibilist version of free will has some merit because it says that we have free will if we can do want we want. But it also admits that our actions may still be completely determined by factors that are ultimately out of our control (we do what we want but our wants are ultimately ingrained in us), which seems to conflict with what we usually mean by free will when we bother to talk about it: a free will that gives us ultimate control and moral responsibility that can override all circumstances.

Are you saying that the agent can act freely even though all his actions are completely determined by his ingrained predispositions?

Slipping, falling, colliding with the ground, and breaking one’s arm are not the “free acts” of the agent because those are the actions he is trying to avoid. — NOS4A2

Can the agent choose not to avoid those actions? If he cannot, is he acting freely?

Either way, be it something you’ve previously chosen for yourself of something ingrained that is beyond your choosing, it does not nullify the logical possibility of free will in the choices you do make at any given juncture. — javra

Even if your choice is driven by a goal you chose previously, the choice of that goal itself was driven by something ingrained in you or by another goal which however must ultimately be driven by something ingrained in you too because you cannot have an infinite regress of goals. So ultimately all your choices are completely determined by factors that are out of your control or maybe are partially undetermined, which precludes your control too.

Nor would the occurrence of free will necessitate that causal determinacy does not take place in the world - it would only necessitate that the world is not one of (complete) causal determinism. — javra

To the extent that your action is not determined by your (ultimately ingrained) goals, it is unintended and therefore unfree. Indeterminacy doesn't save free will, it just makes you do things you don't intend to or hampers your ability to do things you intend to.

But you are not isolated from your environment. You cannot think freely without breathing oxygen and you cannot walk freely without having a ground to walk on. So why is that slip on a banana peel not your free act?