In my view, relations are what we conceive of objects when we try to make sense of objects. — L'éléphant

But that doesn't mean that relations don't exist, if that's what you were getting at. It also doesn't mean that when we make sense of an object by its relations to other objects that those other objects don't exist.

I would be inclined to hold this same view, the problem is, I see it as a circular response to ontology. — L'éléphant

Circularity doesn't bother me in ontology, it's like in mathematics where all mathematical objects are consistently interrelated and all of them exist necessarily, so they are all on the same ontological footing. I actually think that mathematics, with its concretization in set theory, is a comprehensive elaboration of logic, of the logical structure of reality.

Not to mention that it is ignoring the fact that it is our own perceptual interpretation why we see an 'apple' and not some collection of atoms. — L'éléphant

In addition to relations there are also non-relations, and particular (as opposed to universal) non-relations are collections. A collection is a non-relation that has part-whole relations to other objects that are its parts. Of course, a collection also has relations to all other objects (that are not its parts). A collection can be empty, which is an object with no parts, or non-empty, which is an object that has parts.

Theories of relation or properties do not hold that they have a being. They could only be present if objects of contemplation exist. Hence, they are not existent the way humans exist. 'Possible' is a relation or a property, not a thing or object. — L'éléphant

Relata cannot exist without their relations and relations cannot exist without their relata. Relata and relations are inseparable, and I don't see why one would be ontologically prior to the other.

Moreover, a possible object is consistently defined not only in its relations to other objects but also in relation to itself (if identity is a relation at all). If an object is identical to itself then it is a logically consistent object and thus exists. It is then also consistently related to all other objects because relations between objects are derived from the objects' identities, just as the objects' identities are derived from relations between them. All relations are similarity relations (they constitute the similarity of their relata) because they are derived from the (same and different) properties of their relata, just as the properties of the relata are derived from similarity relations between the relata.

By "possibility" I mean logical consistency, that is an object that is logically consistently defined in relations to all other possible (logically consistently defined) objects. How would you determine which of those objects are merely possible and which are real? Yes, some of those objects may be just in your mind and others out in the street. But your mind, including its contents, is part of reality too, part of everything that exists. So I say that all possible objects exist, in the way in which they are defined.

But, even in simpler terms if all possible outcomes are realized, and the determinism of the MWI is applied, then where does this leave the uncertainty principle in any reference frame? — Shawn

MWI interpretation is not deterministic in the sense that in a parallel world later events logically follow from earlier events and from the laws of physics. This lack of logical entailment means that we cannot predict (with 100% certainty) the future of our world. Yes, we can predict that all possible outcomes happen in various parallel worlds but we don't know which of those worlds is ours. This is our so-called self-locating uncertainty.

Ok, I didn't know this is used as an argument against causation. Of course in our life as humans we single out a particular cause or a small number of causes that are useful to us and help us navigate the world. Even in physics we usually don't need to consider the whole universe when predicting the future but only focus on those causes that have a significant impact on the matter at hand.

Or then we could dispense with the idea of causation completely except at scales where we humans live. If I punch you in the face and your nose bleeds, I caused the bleeding. — T Clark

You would not be the sole cause though. For example, planet Earth would participate in the causality too. If planet Earth didn't exist you would not be able to stand here, let alone punch anything. But we take it for granted, so we don't mention it.

Returning back to the question of how the nature of causality works, what are the leading theories of causality, nowadays? — Shawn

For me, the (deductive) inferential theory of causation seems the most elegant. It says that the structure of our spatio-temporal world contains regularities in the distribution of matter in spacetime called laws of physics, and that the distribution of matter in space at time t logically follows (i.e. can be deduced/computed) from the distribution of matter in space at an earlier time t-1 and from the laws of physics. The distribution of matter at time t can be called "consequences" and the distribution of matter at time t-1 can be called "causes". In this spatio-temporal structure of the world it is also possible to deduce causes from the consequences and the laws of physics; the crucial difference between causes and consequences is that causes exist at an earlier time than their consequences, so there must be an asymmetry in the time dimension of spacetime, the so-called "arrow of time", which differentiates between "earlier" and "later" moments on the time dimension. The prevailing explanation of this time asymmetry seems to be that the direction of time from the past to the future is identical with the direction of the increase of spatial entropy (disorder) of matter along the time dimension, which is in agreement with the second law of thermodynamics.

Fast-forward to the 20-21'st century, and we seem more concerned with probabilities and statistical likelihoods, as per the field of quantum mechanics. — Shawn

Quantum mechanics shows that the spatio-temporal structure of our world is not as deterministic as I have just described above. Which means that the spatial distribution of matter at time t does not logically follow (cannot be deduced/computed) from the spatial distribution of matter at time t-1 and from the laws of physics. The spatio-temporal regularities in the distribution of matter in spacetime are not strong enough for the logical entailment that is necessary for causality. Still, there are weaker regularities that enable at least the deduction of probabilities of spatial distribution of matter at time t from spatial distribution of matter at time t-1 and from the laws of physics. We could say that causality in the quantum-mechanical world is weakened.

To put this in simple terms, how or why does modality exist? — Shawn

I see no difference between logical consistency and existence so I think that all logical possibilities exist in reality (modal realism). This leads to the many-worlds interpretation of quantum mechanics where all possible outcomes of a measurement are realized in different worlds that are apparently causally disconnected. In the macroscopic world where we can neglect quantum indeterminism, our imaginations that our world could have different futures stem from limitations of our knowlege. Those imaginations may be accurate with respect to other possible worlds though.

That seems a lot like a definition of nothing to me. — Treatid

Empty set? Emptiness is a property, which is something. And so is that which has it.

One of the sub-threads here is that all definitions are circular. — Treatid

Is that a problem? As long as all things are consistently defined, in all relations to each other, it seems fine to me. Of course, we can never prove the consistency of all things, due to Godel's second incompleteness theorem. But that's an epistemical problem, not ontological. Consistency doesn't care whether it can be proven.

As a result axiomatic mathematics cannot define the meaning of anything. — Treatid

What do you mean by "meaning"?

What can we know with certainty? What can we describe? — Treatid

We know our own consciousness with certainty. From that we form, in our consciousness, a representation of an external reality -- not with certainty but with various degrees of certainty.

A mathematical point is a definition of nothing. We can't use 'nothing' as a building block. — Treatid

In point-set topology, a point of space can be any set. The simplest set is the empty set, which is not nothing but something that has no parts.

do you think physics describes logic? — Shawn

I don't think there is any difference between logical consistency and existence, so logic describes the whole reality. Physics describes the part of reality we live in. Mathematics, with its foundation in set theory, is an elaboration of logic.

I would say the property is less fundamental than the concept it refers to; because it presupposes it. — Bob Ross

What is the difference between property and concept? Isn't it the same general/universal entity?

The interesting thing with 'being', is that it isn't really a property: that opens up the discussion to absurd ideas, like beings which themselves contain being in their essence and other beings which do not (e.g., Spinoza's view). — Bob Ross

Why would "being" not be a property? "Being", or "existence", seems to be something general/universal that is instantiated in all existing entities, including in itself. Why would some entities have being in their essence and others not?

This pecularity indicates, by my lights, that ‘being’ is a primitive concept and, as such, is absolutely simple, unanalyzable, and (yet) still perfectly valid. — Bob Ross

Existence seems to be a property of entities that exist and as a property it can be defined by its instances, that is, by entities that exist. What is more primitive: a property or its instances? I would say neither; instances cannot exist without a property and a property cannot exist without instances.

I think there are a lot of concepts that are not decomposable, that is, you cannot break them down into component parts without losing something. Perception might be one of these things. It's easy enough to describe perception. E.g., "you see a beautiful sunset over Death Valley."

If you try to decompose the experience into what causes it though, you end up losing elements. No amount of talk of neurons or light waves, B-minimal properties, etc., no matter how informative, seems to avoid losing something. — Count Timothy von Icarus

Maybe that's because such descriptions are incomplete and even if they were complete they might be infinitely long or they might involve objects or relations that are difficult to imagine. At least neurons and light waves are 3-dimensional spatial objects so we can form some simplified picture of them, but consciousness also seems extended in time, so we might need to imagine qualia as spatiotemporal, hence 4-dimensional objects, which I don't know if anybody can. And if Gulio Tononi is right, then qualia are objects with many more dimensions in some abstract space of possible causal relations.

Right, there are some pretty good arguments out of the Thomist camp that all properties of things have to involve how they relate to other things or parts of themselves. — Count Timothy von Icarus

Trivially, all relations between any two objects can be said to be similarity relations which specify which properties the two objects have in common and which properties they don't. Thus any object (as a bundle of all its properties) is, in principle, completely defined by its (similarity) relations to all other objects.

But then what does it mean for something to simple? — Count Timothy von Icarus

Mereologically it means that it has no parts, or set-theoretically it is an empty set. But in another sense, I would say that every object, no matter whether it has parts or not, is something simple, unstructured, a monadic quality, a whole. A whole may have relations to other objects that are its parts, but it is not identical to any of its parts, it is something else than any of its parts, something in addition to its parts, which has part-whole relations to its parts.

First of all, all definitions are essentially circular, as evidence by somebody not being able to immediately glean a language simply by by being handed a dictionary. But with some ideas, the circularity of the definition becomes very short, such as in your example. — noAxioms

I think this is a good point. Every object can be defined with its relations to all other objects. We can arbitrarily take some objects as "primitive" and define other objects with relations to these "primitive" ones. However, some objects are more frequent than others, like some words are more frequent than others in a language extract. It is useful to focus on these more frequent ones, and perhaps take them as primitive (as a basis for defining others), because it makes understanding reality easier; these are the regularities or commonalities in reality, known as fundamental (most general) concepts, or fundamental (smallest) particles, or laws of nature. It is easier to define movements of planets of the solar system with their relations to the Sun than to the Earth.

How could that be? I am definitely not conscious of my experience 10 minutes ago. Either I am, or I am not; there is no in between. And the fact is, at some point I was, but I no longer am. That's change. — Ø implies everything

You can have different experiences simultaneously, like hearing a sound, seeing something, experiencing a memory and an anticipation, and having the feeling of passage of time. Some of these experiences may feel more salient while others may feel vague or subconscious.

That still necessitates change; the change from experiencing a moment subconsciously to experiencing it consciously. — Ø implies everything

Maybe not. The conscious and subconscious experiences may be simultaneous, the subconscious in the background. Transition from moment to moment may be just an impression, a feeling.

But I think I've ruled out eternalism as self-contradictory, which means there must be real change. — Ø implies everything

I am not sure it is self-contradictory.

However, eternalism is itself very problematic, philosophically. How do you explain our changing experience? — Ø implies everything

I don't have our experience of passing time figured out, honestly it seems like a major mindfuck. I imagine myself as being extended not only in space but also in time, as having many temporal parts in different moments of time, in continuous sequence. Each temporal part od myself experiences only its moment but my whole temporal self somehow (subconsciously?) experiences itself as a whole too, which perhaps provides the impression that the different experiences at different moments belong to me as to a single object. The arrow of time according to physics seems to be provided by the rising entropy along the time dimension (2nd law of thermodynamics), which perhaps creates the impression of irreversible progression of moments from the past to the future, along with impressions of memories and anticipations.

I don't think that works, because it introduces the choice again. Since both worlds already existed separately, then they were two separate objects (despite their identicality). Thus, a paralogical choice is made between which of the two worlds gets a banana and which gets an apple. — Ø implies everything

But such a choice is never made because the apple and the banana are part of the identity of each world and the identity of an object can never be different than it is, because that would constitute a logical inconsistency. So, the world that has the apple has the apple necessarily; it is logically impossible for the world to be different.

You seem to be thinking of objects as changing in the passage of time but time is structurally (mathematically) a special kind of space, and space doesn't pass; it just exists. What appears in our experience as the future already exists, just like the past, and it exists the way it is and cannot be different, because that would constitute a logical inconsistency.

If one simply answers that the original sentience is no longer present, and two new sentiences were born (both having access to the original sentience's memories, and experiencing their birth as continuous extension of the original sentience's experience), then you have answered the question. — Ø implies everything

I think you can put it that way. Another possibility might be that there were two worlds with two sentiences where everything was the same up to a moment when an apple appeared in one world and a banana in the other world.

There can be two sentiences - one experiencing the world with an apple and one experiencing the world with a banana. After all, a sentience is just an object, like anything that exists. There can be many objects.

I don't see any mystery in why one sentience experiences this world and another sentience experiences another world. Location and experience are part of the identity of each sentience. Each sentience (each object) is what it is, and cannot be what it is not because that would constitute logical inconsistency.

Okay, now we are getting somewhere. This splitting of worlds; has it happened after sentience entered the picture? — Ø implies everything

I don't know what sentience has to do with this. This is about logical consistency: each world is identical to itself. Each world is what it is and is not what it is not. That's all.

Edit: By the way, the principle of logical consistency or identity does not pertain only to "worlds" but to any object. For example, one object cannot be both an apple and a banana because that would be a logically inconsistent object. But there can be two logically consistent objects - an apple and a banana.

Okay, let me take this step-by-step:

1. First moment in time, there is just being (I don't claim you believe this, but you have to deny it).
2. For this moment in time, due to the lack of any laws or anything specific, it would be logically consistent that a banana spawns at coordinates x,y,z.
3. By the same logic, it would also be logically consistent that an apple spawns at coordinates x,y,z.

So, in the next moment in time, what happens? Do both spawn? Well, each spawning is separately consistent, but together, they are inconsistent. — Ø implies everything

Then there are two logically consistent worlds - one in which an apple spawns and one in which a banana spawns. Both worlds exist because they are logically consistent.

Sure, but in the real world, a banana and an apple cannot exist with their centers overlapping. — Ø implies everything

Because such a world would be logically inconsistent, with respect to the laws that characterize its structure. So I state again: all logically consistent objects exist because there is no difference between logical consistency and existence.

But then everything would have popped into existence simultaneously, and contradictions would have arisen. How did the universe remove these contradictions? How did it choose one thing over the other? — Ø implies everything

In mathematics all logically consistent objects exist simultaneously and there is no contradiction.

The purely logical donkey, when faced with two equally voluptuous hay stacks, starves to death. — Ø implies everything

So what? There is nothing logically inconsistent about starving to death.

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.