You're not getting the square circle thing right, first off. The issue there isn't the shapes. It's the idea of constructing a square equal in area to a given circle. — Terrapin Station

I said nothing about the area of a circle or a square. I said a circle is a square, which is a clearly inconsistent statement. The statement "There is a unicorn on Main Street" is inconsistent too, even though it may not be obvious.

Anyway, note that I'm not claiming that someone can not have an inconsistent belief. So jumping to other examples isn't very useful. — Terrapin Station

The example about the circle is similar to the example about the unicorn, only in the unicorn example the inconsistency may not be obvious. So I wanted to show the parallels. Joe's idea is inconsistent no matter whether he believes it. If he believes it then his belief is inconsistent too.

So you would say that Joe's idea that a circle is a square is consistent?

How would you state a specific example of P & ~P re the idea? — Terrapin Station

Joe has the idea "There is a unicorn on Main Street". He may not know that there is no unicorn on Main Street, but his not knowing it doesn't make his idea consistent. He may only be aware of "There is a unicorn on Main Street" but his idea is de facto "There is a unicorn on Main Street & there is no unicorn on Main Street" (because there is in fact no unicorn on Main Street).

He might as well have the idea that a circle is a square without knowing that a circle is not a square, but his not knowing it doesn't make his idea consistent. He may only be aware of "A circle is a square" but his idea is de facto "A circle is a square & a circle is not a square" (because a circle is in fact not a square).

If Joe believes that there's an extramental/objective unicorn on Main Street, then we could say that he "defines" as his idea that there's an extramental/objective unicorn on Main Street. — Terrapin Station

But his idea is inconsistent, because it is about an inconsistent thing (a unicorn on Main Street).

It seems to leave completely empty the question of if something exists. — noAxioms

A consistent something, whether it is abstract or concrete, exists. An inconsistent "something", whether it is defined as concrete or abstract, doesn't exist (is nothing).

I own a four wheeled car with five wheels. Does my car not exist? — noAxioms

Of course it doesn't. You just defined a concrete inconsistent "thing".

Now if logical consistency is equated with ontic existence, then the unicorn exists. Does 'instantiation' also mean that same thing? — noAxioms

I am not sure what you mean by "instantiation". I mean the instatiation to be the relation between an abstract (general) thing (property) and its instance, for example between red color and a particular red thing. Both the red color and the particular red thing exist.

No one is defining a unicorn as "not being what it is" though. — Terrapin Station

If someone imagines a unicorn existing on our planet, then they define it inconsistently, even when they are not aware of the inconsistency. They define it as existing in a place where it doesn't exist, and thus as something that is what it is not.

Whenever you have an idea of a thing, you define that thing. You define what that thing looks like, its properties, its parts, its environment etc.

What would be inconsistent about that? You must be defining "inconsistent" in some unusual way. — Terrapin Station

An inconsistent idea defines something as not being what it is. For example the idea of an apple that is not an apple. That's why it has no referent in reality.

Only if you're conflating an objective unicorn with a subjective idea of a unicorn. — Terrapin Station

An inconsistent idea is a collection of thoughts/qualia that doesn't refer to anything in reality. The collection of thoughts/qualia itself is consistent and exists as a mental thing.

What doesn't exist is the extramental/objective unicorn.The idea of the unicorn is logically consistent insofar as it goes though. — Terrapin Station

If the idea requires environmental conditions that are inconsistent with the existence of a unicorn then the idea is inconsistent.

So you made no claim about a unicorn existing in external reality? Then there exists just a picture of a unicorn in your mind. It is consistent and exists as a mental thing.

You defined the unicorn as existing in external reality (according to an imagination) and at the same time you said that it doesn't exist in external reality.

First sentence is an assertion. Why should I accept that to be is the same thing as logical conherence? — Chany

Because there seems to be no fundamental difference between logical possibility and existence. All logical possibilities exist in the sense that they have an identity and therefore they are not nothing. To deny existence to selected logical possibilities would be arbitrary, without a fundamental reason. Instead we can talk about various kinds of existence - spatio-temporal, abstract, mental etc.

The concept of unicorns is logically coherent. — Chany

But if you suppose that the unicorns exist in a place, for example on our planet, where the conditions are inconsistent with their existence (the requisite genes have not evolved here), then the concept of unicorns existing on our planet is inconsistent.

If the conditions on our planet were consistent with both the existence and nonexistence of unicorns then both scenarios would exist - but in different worlds, because it would be inconsistent for these scenarios to exist in the same world.

You would have to embrace multiverse theory and say that every single possible world is a real world, as real and concrete as the actual world. — Chany

Indeed, that's what I am doing.

This leads to a contradiction, as it is also logically coherent (possible) that only the actual world exists and that the other possible worlds do not exist (or if they do exist, as mental objects only). — Chany

If the other worlds are consistent then they exist, and it is not possible that they do not exist. In the second part of my paper I elaborate that the principle of logical consistency entails the existence of relations between things and that there are three logically necessary relations: similarity, composition and instantiation. With these relations you can consistently define many worlds and their copies.

You're using "it" there as if the thing in question exists and has properties. It doesn't beyond something we're imagining. So it doesn't have an inconsistent set of properties a la "it exists and it doesn't." — Terrapin Station

You define the thing as "existing where it doesn't exist"; such a definition is contradictory, it defines an inconsistent thing and that's why such a thing doesn't exist. It is not that there exists a thing that has an inconsistent set of properties, it is just you attributing an inconsistent set of properties to a thing.

How can a physical object be logically anything? Logic applies to statements, not things. — T Clark

An object is logically consistent iff it is identical to itself and different from other objects.

I don't know what that means. Is a four-sided triangle not what it is or is it what it's not? — T Clark

A four-sided triangle is a triangle that is not a triangle (because a triangle has three sides). In this sense it is inconsistent.

What would it mean for the moon not to be what it is? — T Clark

It would mean for the moon not to be a moon. Of course, that's an absurdity and that's why such inconsistent "things" cannot exist.

It almost sounds like you're saying that existence is dependent on consciousness, but I don't think that's what you mean. — T Clark

Right, existence is about things, their identities.

Do abstract objects (the form of square) exist? — Chany

They are difficult to imagine/visualize and cannot be interacted with, so they are ontologically controversial. But they seem to be a necessary part of logic, and especially in mathematics they can be clearly and consistently defined, so I regard them as real entities. In my paper I regard the instantiation relation as one of the three fundamental, logically necessary relations in reality.

Do unicorns, in some ontologically relevant sense, exist? — Chany

If they are consistent, they exist. Apparently not on our planet.

I thought you had equated existence to 'logically consistent', not to 'something, not nothing', which is a weaker, circular definition. — noAxioms

That which is logically consistent has an identity and so is something. That which is logically inconsistent does not have an identity and so is nothing. We may speak of an inconsistent thing as of "something", but due to the absence of identity it is not really something or a thing.

If existence is consistency, then the consciousness is not evidence unless it can be shown to be consistent. The fact that they've named 'the hard problem of consciousness' implies that the self-consistency of it is in question. — noAxioms

Consciousness is difficult to explain but that doesn't have to mean it is inconsistent. I think qualia of consciousness could be intrinsic identities of things, as opposed to structural/relational identities of things, and that's why they are indescribable and yet related to other things (correlates of consciousness). I elaborate it in my paper An outline of reality.

Now picture two of those persons, identical, except one instantiated, and the other not. What would be the difference between the thought processes (consciousness) of the instantiated one vs. the uninstantiated one? — noAxioms

If it is consistent for a property to be instantiated in a thing then it is instantiated in that thing (because consistency = existence). If a property is not instantiated in a thing then it is inconsistent for that property to be instantiated in that thing.

Is 2+2 objectively equal to 4, or does the arithmetic require instantiation for the sum to be true/performed? — noAxioms

I think a property (abstract entity) would not be a property if it was not a property of something. In other words, uninstantiated properties are a contradiction, and so they don't exist.

Sorry, I didn't completely answer your question about properties of an inconsistent thing, but I named some of the lowest positive real number. Those properties still seem valie, even if they lead eventually to inconsistencies. If the inconsistencies are subtle enough, the nonexistence of the thing might not be so clear. — noAxioms

Yes, but whether the inconsistencies are clear to someone is ontologically irrelevant.

A couple of weeks later you ask me "can a four-sided triangle exist?" I don't say "No, a four-sided triangle can't exist." I don't say "That's inconsistent." I say "You've broken the arbitrary rules of the geometry game." — T Clark

Whatever rules you make, if they refer to reality they cannot say that something has and in the same sense doesn't have three sides.

Reality is made up of our perceptions. If we want to change our reality, we need to first change our own perceptions. Once we change our perceptions, we change our reality. — ArguingWAristotleTiff

But our perceptions are created from information that comes to our senses from external reality, no? So there is also an external reality that is the source of our perceptions.

What we imagine, exists in our minds, as thoughts or mental images. But if we imagine that some thing exists in some place in external reality where it doesn't exist, then this thing is not consistent. It may seem consistent to us because we don't know all the details of that thing or of its environment. But the thing is inconsistent, because we attribute it existence where it doesn't exist.

You might say that it would be consistent for the thing to exist under different conditions, but then you can't argue that the nonexistence of the thing under present conditions is a proof that a consistent thing can be nonexistent. Under present conditions, the thing is inconsistent - and that's why it doesn't exist.

Well, people in history questioning their own existence (Descartes most famously) cannot start from a begging position of considering nonexistence absurd. Why ask the question if you know what the answer is going to be? — noAxioms

I never really asked myself the question if I exist - I take my existence for granted. The reason I take it for granted is that I am conscious (consciousness) and consciousness is something rather than nothing, so it exists. Regarding the existence of my body, I am not 100% sure because it might be an illusion in my consciousness and I am not totally certain that the body is necessary for my consciousness. But there seems to be a lot of sensory as well as rational converging evidence that my body exists too, and in that case the body must be logically consistent too.

An inconsistent thing doesn't exist, but it still seems to have properties, so having properties is not proof of existence. — noAxioms

How can something that doesn't exist have properties? There is nothing that would instantiate those properties.

I didn't read through it yet, but from your abstract, I disagree with taking existence and logical consistency to be identical. I'm fine with saying that existents are logically consistent with respect to how you're defining logical consistency, but I don't agree that the two are identical. — Terrapin Station

And what is the difference between a logically consistent thing that exists and a logically consistent thing that doesn't exist?

Can you be more specific? The paper addresses many things.

I didn't assert existence yet. Suppose I am self-contradictory and thus don't exist. I am not identical to myself then, but how would I know that? — noAxioms

I assert at the beginning that existing things must be consistent because it seems absurd to me that an inconsistent thing (such as a four-sided triangle) could exist. So to suppose that I am self-contradictory means to suppose that I don't exist, which is absurd.

Your statement above presumes the existence of the inconsistent thing. — noAxioms

On the contrary, I presume that inconsistent things don't exist.

If I (or my universe context) was self-contradictory, what test for that might there be? — noAxioms

I think it would be absurd if there existed something that is not identical to itself, or something that is not different from other things. So your existence is a guarantee that you are consistent with all reality, even though it is in practice impossible for you to check the consistency of your relations to all your parts, properties, and everything else.

We don't think entirely differently, do we? If no world has it, then it is logically impossible. If this is a uni-world sort of physics (non-MW interpretation), then hard-determinism is what makes the alternative with the button an impossible thing. — noAxioms

Yes. Although it doesn't seem to be inconsistent for there to be parallel worlds.

AF(F(Vulcan) <-> F(Vulcan)) is tautologous.
Therefore, Vulcan exists ??? — Owen

It depends on whether Vulcan is consistently defined. Does it have a consistent identity? If not, then it has no identity and it makes no sense to say that it is identical to itself. So we have to examine what properties the presumed Vulcan has, what parts, if any, it has, and whether these properties and parts do not contradict each other or whether they do not contradict the environment in which they presumably exist.

Wouldn't something nonexistent be identical to itself? Take the smallest postive real number, or javra's dfjsl-ajf'l, something not logically possible (mostly due to that four-sided triangle bit). — noAxioms

A nonexistent has no identity, so I don't think it makes sense to regard it as identical to itself. The definition of a four-sided triangle, for example, denies that the triangle is a triangle; it denies its identity. It refers to nothing. All contradictory definitions refer to nothing.

How about the 'like' button on this forum. It seems not to exist, but it is logically consistent, and identical to itself. Perhaps it exists, but is not present in the context of the features of this forum. Were it not to exist at all, I could not complain of the nonexistence of it in this context. — noAxioms

Maybe the existence of the 'like' button on this forum is logically consistent, but obviously its nonexistence is logically consistent too. If both scenarios are consistent then they both exist - but in different worlds (contexts), because it would be contradictory if the button existed and simultaneously didn't exist in the same world. We happen to live in a world where the button doesn't exist, but perhaps our copies in a different world (which is a copy of our world) can enjoy the button.

Interestingly, the naming of it creates it. To physics, it is all just particles and events and relations, but the grouping of them, extended in spacetime, is encapsulated by the name 'candle', which has meaning to the user of the language. — noAxioms

I wouldn't say that naming something creates it. The candle is objectively there, as a collection of atoms. Just because we find this collection interesting enough to give it a name doesn't mean we created this collection by naming it.

Thank you for this different definition, which admittedly seems not to reference a context, but is one implied? — noAxioms

Every thing must be differentiated from other things, so those other things provide a context. But I mean the word "context" in the sense of "all other things". Those other things need not be just outside a whole but also inside the whole - the parts of the whole. Because the whole is also different from its parts.

Not according the to model of spacetime which breaks down and thereby leads to the inference of a gravitational singularity. — javra

If the model is inconsistent then it is not an accurate representation of reality, because reality cannot be inconsistent. I am talking about reality, not a model. Apparently there is spacetime in reality and there is a Big Bang at the beginning of our universe.

Are you saying there is no universe? — javra

If by universe you mean the collection of all existing things then there is no universe in this sense. Why? Suppose there is a collection of all existing things. Then this collection is a thing too, and another collection can be defined in which this thing is included as a part, so what you supposed to be a collection of all existing things is in fact not a collection of all existing things.

If by universe you mean all existing things then there is universe in this sense but it is not a single thing.

I didn't say 'strand'. The DNA of twins is identical, consisting only of information, not particular details of a strand, which has properties like position. — noAxioms

Then did you mean the DNA as an abstract thing? In that case, it is a single abstract thing, identical (in every way) to itself. And this abstract thing is instantiated in concrete things - in the concrete DNA strands of the twins. And each of those concrete DNA strands is identical to itself and different from the other, at least with respect to its position in spacetime. Also, each of those concrete DNA strands is different from the abstract DNA.

OK, how about the candle? Are the two states not the same candle because of the differences in lit and burnt-out, or are they one thing, identical to itself, just extended in spacetime? Even the latter has a hard time with identity if you consider MW cloning. The statement "candle is lit at time T" has no truth value if all those states are part of one identity, and only some of those states are 'lit'. — noAxioms

In the usual usage the candle is meant as a thing extended in spacetime (enduring in time). Then the statement "candle is lit at time T" means that the candle is in the lit state at time T.

Anyway, every thing is identical to itself in the sense it is defined. So "candle" as a thing extended in spacetime is identical to itself as a thing extended in spacetime. If by "candle" you mean something else, then this something else must be identical to itself too, in the sense in which it is defined. Otherwise it doesn't exist in that sense - there is no thing in that sense.

Not sure why we're nailing down the usage of identical in this topic. — noAxioms

Existence in the most general sense means being identical to oneself and different from others.

Were the gravitational singularity addressed to be ontically real, however, it of itself would have no context - no not-singularity to which it could be contrasted. Neither entities, such as cats, nor quantities, such as the number seven, would hold presence. — javra

The whole spacetime is present, with the Big Bang singularity presumably at the beginning of the time dimension. And abstract entities like numbers are present even without a spacetime.

The “cosmos” was for the purposes of the argument specifically defined as the “sum of all existents” - and not as merely a collection of things among many others. Then, to state that the context of the sum of all existents is the particular existents themselves is to equivocate both the meaning of “context” and the reasoning first quoted in my previous post. The context of a cat, for example, is not one of its ears. — javra

If by the "sum" you don't mean "collection" or "whole" but all existent things, then the "sum" is not a single thing but many things. And each of those things exists in the context of all the other things.

And if by the "sum" you mean the collection or whole of all existent things then this "sum" is different from each of its parts - because it is not identical to any of its parts, and so the sum is a thing that exists in relation to (or in the "context" of) its parts, which are other things. Anyway, there is no such greatest collection, just as there is no greatest number.

A gravitational singularity from which the Big Bang resulted (this as is modeled by todays mainstream physics) is one such instance of a given with being that is not a thing with context. — javra

If you take a more general definition of "context" you will find that the singularity of the Big Bang does have a context from which it is different. The context can be anything that is not the singularity of the Big Bang, for example my cat (which exists at a different point in spacetime) or number 7 (which transcends every spacetime).

Thus defined, I still find it justifiable to uphold that the cosmos can only exists in terms of being per se but does not exist in terms of a thing with context. — javra

A collection of things (such as a cosmos) is also different from its parts, so the parts provide a context for the collection/whole.

This doesn't help if something is logically consistent but nonexistent. I questioned that above when I cannot come up with an example of a consistent thing that nevertheless is known not to exist. — noAxioms

You cannot come up with an example of a consistent thing that is known not to exist? There is no such example. If existence is logical consistency then every logically consistent thing exists.

About identical, the word is ambiguous. Twins share identical (indistinguishable) DNA but are not the same person. A lit candle seems to share numeric identity with the burnt out stub an hour later. It is the same candle (identical), but the two states are hardly indistinguishable. — noAxioms

When I say that a thing is identical to itself I mean that it is identical in every way. The DNA strands of twins are not identical in every way - to say the least, they have different positions in spacetime, which makes them different things.

I am trying to nail down what we're claiming if we claim something exists or not. — noAxioms

I guess we can agree that every thing that exists must satisfy the criterion of logical consistency: it must be what it is and not be what it is not. In other words, it must be identical to itself and different from what it is not.

I think that in the most fundamental sense, existence is just that. Logical consistency. Then we can talk about various kinds of existence, like spatio-temporal, abstract, mental etc., but these are secondary distinctions.

Causality can be viewed as a special kind of logical relations between entities in the context of the arrow of time, where the consequences logically follow from the causes, and the causes are initial conditions and time-invariant structures known as the laws of physics.