Free will may be defined as the ability of a person to choose, the ability to have control over their future. — icosahedron

I believe I have the ability to influence/control my future. I also believe that everything I do is completely determined by factors over which I have no control. There is no contradiction between these two beliefs; it's just the compatibilist conception of free will.

I regularly spend time thinking about how to improve my own future which would make no sense in a worldview where I am not able to influence my own future (for example, in a worldview where everything is already predetermined). — icosahedron

Why would you not be able to influence your future if everything was already predetermined? Billiard ball X is able to influence billiard ball Y by bumping into it, while billiard ball X is influenced by billiard ball Z that bumps into X. So X influences Y and this influence is predetermined by Z.

5. There is no rational reason to prefer determinism over indeterminism. — icosahedron

Actually, free will needs determinism at least to some extent because if your action was not determined by your intentions then it would not be intentional and thus could not be free. (Unless you regard unintentional acts like slipping on a banana peel as freely willed.) On the other hand, if your action is determined by your intentions then it is determined by something (the intentions) you have not intentionally and thus freely created, because in order to intentionally create your intentions you would first need intentions to create those intentions. So you can do intentional and thus freely willed actions but those actions are fully predetermined by factors over which you have no control.

5) Thus, science gives human beings new powers at an ever accelerating pace.

6) Human maturity and judgment advances at an incremental pace at best, if at all.

7) To illustrate the above, imagine a car racing down the highway at ever accelerating speeds, while the driver's skill increases maybe a little bit now and then. — Hippyhead

I don't think it's so clear that there is a widening gap between human maturity and new powers afforded by science. For one thing, advances in science seem to require a maturation of the understanding of reality and of the ability to analyze and synthesize, and thus science cultivates careful reasoning, a universal outlook, honesty and cooperation. At the same time, society builds schools in which the scientists are educated not only about natural sciences but also about humanities, moral values and various aspects of the functioning of the society. Education with less focus on science is also provided for non-scientists, so the society generally is more or less educated and able to participate in beneficial application of science, including by building and respecting regulatory governments and laws.

Pressing the nuclear button may destroy the society but the fact that it hasn't happened yet shows that the modern society is a not just a collection of savages but a sophisticated system with psychological, social and technological safeguards.

Stephen Hawking doesn't "live on". — Random Name

Yeah. Woody Allen once said that he didn't want to live on in other people's hearts but in his apartment.

The best theory I've heard for the continuation of existence after "death" is the multiverse theory. Essentially, for every universe in which I've kicked the bucket, there's another universe where I didn't. — Random Name

... until your body becomes so damaged with age that it will be incompatible with life. Then there will be exactly zero parallel universes in which you continue to live.

Religions say that after the death of your physical body your consciousness continues to exist because it is sustained by another structure which appears to be more permanent than the physical body. That more permanent structure is usually called the soul or spiritual body and it supposedly uses the physical body as a kind of vehicle or virtual reality headset to be able to interact with the physical world.

The problem is how the soul could interact with the physical body or world without being detected by our scientists who have instruments sensitive enough to detect even tiny subatomic particles. I once suggested that a solution could be based on resonance (here) but needless to say it's a speculative and less than half baked idea.

nothing can’t exist, for there is no possible world at which there is no world. — Pfhorrest

Indeed. Nothingness is logically inconsistent. It can also be put in this way: if there was nothing there would be the fact that there is nothing, but a fact is something.

In your interpretation the spacetime points are coexistent, co-present, and coincide ontologically with the objects in question. I would preface that this is an intriguing interpretation as it seems to basically be a form of super-substantivalism in which an entity is exactly identical to that in which it's located at, if i'm getting at your interpretation correctly. — substantivalism

Yes, super-substantivalism seems to be a correct label for my interpretation. I just noted that in the general definition of a space in mathematics/set theory, the points of space can be any objects, so the simplest way of connecting the geometric properties of a space and the properties of matter (energy and momentum) seems to be to encode the properties of matter in the points of the space. Treating matter as a different substance than space would require introduction of a new relation of "occupation" between matter and space, the meaning of which is not clear to me but I guess we can't rule out such an additional relation and its physical distinguishability since general relativity is an incomplete theory.

If matter is a different substance than space, I would say that space is more fundamental than matter in the sense that you can define a space without matter but you can't define matter (energy and momentum) without a space (speed figures in E = mc^2, p = mv). In the paper on super-substantivalism that you linked, in footnote 26 there is a reference to theories of quantum gravity that derive spacetime as a macroscopic emergent entity from an underlying spaceless and timeless "quantum matter", but does this "quantum matter" have the properties of energy and momentum or does it acquire these properties only on the macro scale with reference to spacetime? If it doesn't have energy and momentum below the scale of spacetime maybe we should call it something else than matter. Or maybe we could regard it as an internal structure of spacetime points that encodes properties like energy and momentum which however have no meaning without reference to distances between spacetime points; this leads us back to super-substantivalism.

How does materialism even begin to explain how moving electrons across synaptic gaps in certain ways gives rise to conscious experience? — RogueAI

In principle, it doesn't seem that surprising to me that when you put together some "unconscious" stuffs you may get a stuff that is "conscious", as we know from experience that by combining stuffs we may get a different, new stuff. For example, if you mix blue and yellow paints you will get, perhaps surprisingly, a green paint.

Whether the stuffs of a brain are sufficient to constitute the stuff we call "consciousness", we don't know for sure. But we know that our brains play at least some role in it because changes in the brain correlate with changes in consciousness.

It also seems that objects that are conscious are very complex in the sense that they have many different dynamic parts that are richly dynamically interconnected (dynamic organized complexity). General anesthesia usually disrupts connections between parts of the brain and loss of consciousness follows (too much differentiation, too little connection). Epileptic seizures, on the other hand, are characterized by increased synchronization of brain processes and loss of consciousness follows (too much connection, too little differentiation). The cerebellum has four times more neurons than the cortex, but damage to the cerebellum, unlike damage to the cortex, has practically no impact on consciousness; it turns out that while there is rich differentiation and interaction in the cortex, the cerebellum has many small modules that process information locally, without much interaction with other modules.

We find a general definition of a space in mathematics: a space is a set of "points" with some added "structure". The points can be whatever but obviously they are not nothing. The structure (also called topology) is a certain collection of subsets of the underlying set of points, and this collection of subsets must satisfy certain conditions (namely, a union and an intersection of any of the subsets must belong to the collection too).

The particular kind of space in general relativity (or "spacetime", which is a 4-dimensional space with time as a special 4th dimension) is a space with a curved metric topology where the points seem to be objects with quantitative properties we call energy and momentum, and these quantitative properties of every point are related to the quantitative properties of other points via regularities across space that we call laws of physics (in general relativity, Einstein field equations).

If we regard objects possessing the properties of energy and momentum as "material" then the space in general relativity is made up of material objects. But apparently there can also be spaces with the same topology but with non-material objects as their points.

Thus begins somewhat of an inquiry as to what exactly is meant by nothingness, and the nature thereof. — CorneliusCoburn

Nothingness as the absence of all things is impossible (logically inconsistent) because if there were nothing then there would be the fact (state of affairs) that there is nothing and this fact would be something.

So there is necessarily something. What is it? For now, let's just call it entity X1. Now we can ask ourselves: Would it be possible that there is nothing in addition to entity X1? The answer is that it would not be possible, because if there were nothing in addition to entity X1 then there would be the fact that there is nothing in addition to entity X1, and this fact would be something in addition to entity X1. So there is necessarily another entity, X2.

Now we can ask ourselves: Would it be possible that there is nothing in addition to entities X1 and X2? The answer is, again, that it would not be possible, because if there were nothing in addition to entities X1 and X2 then there would be the fact that there is nothing in addition to entities X1 and X2, and this fact would be something in addition to entities X1 and X2. So there is necessarily another entity, X3.

In principle, you could go on like this until you have enumerated all possible (logically consistent) entities and concluded that they all necessarily exist. Then there would be no additional fact that there is nothing in addition to all possible entities, because this fact would already be included among the possible (and necessary) entities you have enumerated.

Because if such an alternative existed, it wouldn't exist. — litewave

I see a conclusion, but no premises. How and why? — Monist

It follows from the contradiction "X is not X", because from a contradiction, anything follows:

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

But even without explosion, the original assumption that an object is not what it is, is absurd enough.

Why not? — Monist

Because if such an alternative existed, it wouldn't exist.

"an apple is an apple", but why? I do not get why any certain thing called 'x', should be 'x'. — Monist

Well, what would be the alternative? A thing that is not what it is? An apple that is not an apple?

IF the quantum wave is actually saying the particle is in more than one location at the same time then why do we need probability in the first place? Simply say that the particle is in whatever location and also in another location. — TheMadFool

I see the quantum wave as an object whose mathematical (quantitative-structural) properties specify how it will interact with other objects. I don't mean that a quantum wave is less "real" than a point particle; it's just something that is there, although a different something than a point particle. The probabilistic character of the quantum wave is of course at the heart of interpretations of quantum mechanics. Currently I prefer the many-worlds interpretation because it doesn't seem to need more assumptions beyond the Schrodinger equation of the quantum wave, like wave "collapse". It just assumes that the quantum wave evolves according to the Schrodinger equation, with the mathematical consequence being that when the wave interacts with a many-particle object, parts of the wave that correspond to different possible values of a variable (for example, point position) stop interfering with each other and become separated into non-interacting parts of reality ("worlds").

A problem with the many-worlds interpretation is that an infinite number of possible values of a variable corresponds to an infinite number of worlds and it is not clear how to calculate frequentist probabilities when there is an infinite number of possibilities. Maybe a reconciliation of quantum mechanics with relativity theory will provide a solution to this problem, perhaps by limiting the number of possibilities to a finite number.

In general, history is very important. Have you heard of Richard Gregory's top-down theory of perception? — Magnus Anderson

No, but I take history into account by including in the definition of an object the object's position in spacetime.

Let's say we have two apples both of which are completely identical except in one regard: they occupy different positions. Are they identical or not? The answer depends on whether an apple's position constitutes its identity. — Magnus Anderson

We can also define the identity of an object by its relations to all other objects. The object's parts are only some of the other objects. Since the two apples have different positions relative to other objects, they have different identities. If they had the same positions relative to all other objects, they would have the same identity, which means they would be one apple, not two.

As far as I understand the quantum wave is just the probability of where a particle is located. — TheMadFool

Do you mean that the particle has a position in a point of space like the escaped convict and the quantum wave is only an expression of our incomplete knowledge of the particle's position? This idea was refuted by experimental tests of Bell's theorem: no local hidden-variable theory can be a correct description of quantum mechanics, where the hidden variable is a single point position of a particle, for example. This doesn't rule out non-local hidden-variable theories such as Bohm's but these theories seem incompatible with special relativity because they introduce superluminal speeds.

One object cannot occupy two locations in space at the same time and it is this impossibility that gives objects their identity. — TheMadFool

Yes, I would just add that this depends on how the object is defined. For example, in a sense it is true that my desk can occupy two locations in space at the same time - one leg here, another leg there! That's because the desk is defined as an object that is extended in space. But if by "location" we mean the spatial extension of the desk then it is true that the desk cannot occupy two locations in space at the same time - because it would violate the definition of the desk and so we would be talking about a different object than a desk.

This should be kept in mind when interpreting quantum mechanics. There is no point particle that occupies two points of space at the same time, but there is a quantum wave, defined as a spatially extended object, that occupies two or more points of space at the same time. Alternatively (and equivalently, if I understand it correctly), there is a point particle that occupies two points of space at the same time if the definition of the "point particle" allows the particle to move not only forward but also backward in time.

2. We know that the system (person A and the dice) is probabilistic because the experimental probability agrees with the theoretical probability which assumes the system is non-deterministic. — TheMadFool

I wouldn't say that theoretical probability assumes the system is non-deterministic. Rather, it assumes that the system has certain regularities that enable us to calculate frequencies of possible outcomes. In the example of throwing the dice, the regularities are (deterministic) laws of physics that transform initial conditions to outcomes.

I think nothing in the most general sense can be defined as an "object" that is logically inconsistently defined. For example: a circle that is not a circle. There are objects that are circles and there are objects that are not circles, but there is no object that both is and isn't a circle. That's why I put the word object into scare quotes in the first sentence; there is no such object, and the inconsistent definition as a whole has no referent.

I think the IIT theory might be a very good theory of identity - every system that integrates information is a conscious individual. But as a theory of consciousness I think it fails, as it gives no reason to suppose that the integration of information couldn't happen, as it were 'in the dark'. — bert1

I don't know whether Tononi's specific approach to quantifying the intensity of consciousness is correct but the general idea of associating the intensity of consciousness with organized complexity is supported by neuroscience and also seems to make intuitive sense to me. More specifically, it is organized complexity in a dynamic form, based on processes of differentiation and integration, or repulsive and attractive forces between the parts of a whole. Intrinsic properties of parts are "subsumed" in the intrinsic property of their whole (collection). Differentiation of parts may intensify the intrinsic property of the whole by giving it different contributions but may also weaken the intrinsic property of the whole by fragmenting it. Conversely, integration of parts may intensify the intrinsic property of the whole by concentrating them but it may also weaken the intrinsic property of the whole by losing their different contributions. So there would be intrinsic properties of different intensity on different levels of composition of structure: for example, there may be weak intrinsic properties on the level of atoms, intense intrinsic properties on the level of neural networks, and weak intrinsic properties on the level of a group of people. By intrinsic properties I mean non-relational, non-structural, monadic, qualitative properties, some or all of which may be identical to qualia of consciousness.

Either way it seems arbitrary to me to confine experiences to neural structures, which in the most general reductionist sense is just a certain configuration of atoms. — TheHorselessHeadman

Why stop at atoms? Atoms consist of electrons, protons and neutrons, and protons and neutrons consist of quarks...

it just "seems strange to me", that an entirely new phenomenon could arise in the universe, (suddenly blue exists), because atoms acquired a certain combination of molecules and ions in the brain. — TheHorselessHeadman

In my view, the new phenomenon is the combination of atoms, molecules, cells etc., and so it is necessarily there if the atoms, molecules and cells are there. It may seem strange to regard a combination of objects as an object in its own right; if somebody showed you an apple and an orange and asked you how many objects there are, you would probably say two, and not three, where the third object would be the combination (or collection) of the apple and the orange. But then again, apples and oranges are combinations too, because they consist of atoms, and atoms consist of subatomic particles, etc. It seems tempting to conclude that the only "real" objects are the smallest, indivisible objects at the bottom and everything else is "just" combinations of them without any new intrinsic or uncomputable properties. But why would it be so? There are actually also holistic views of the universe - for example a version of panpsychism called cosmopsychism - according to which the universe as a whole is the only "real" object, and everything else is "just" de-combinations from it. These two views seem to be special cases of a more general view according to which all combinations (collections) are "real" objects, not just the empty combinations or an all-encompassing combination.

So in the example of general anesthesia I would probably view it in the same way as bert1 expressed, as the anesthesia disrupting the unification of the experiences, and maybe pain as an example isn't a fundamental conscious property but an amalgam of different kinds. — TheHorselessHeadman

Yes, but if the anesthesia disrupts the unity of human consciousness, then the specific combination of neurons we experience as pain no longer exists, and so there is no consciousness of pain.

Now let me return to something you said earlier:

Then there's just the question of why we don't experience everything all at once then, why my consciousness doesn't stretch to include the rest of my brain, and out through my skull, into the air and across the globe and include yours as well ;D So it appears that there are some boundaries. — TheHorselessHeadman

On the basis of study of neural correlates of our consciousness it appears that the "intensity" or "level" of consciousness possessed by an object is positively correlated with organized complexity of the object. High organized complexity means that the object has many different parts which are also richly integrated/connected (as opposed to high unorganized complexity, which means that the object has many different but independent parts). General anesthesia usually seems to reduce organized complexity of brain processes by disrupting their connections, thus reducing consciousness of the brain to a negligible level. On the other hand, when a person is in a deep, dreamless, natural sleep, organized complexity of brain processes is reduced by the presence of long delta waves that homogenize the brain processes, so there is too much connection and too little differentiation in the brain. Similarly, loss of consciousness during an epileptic seizure correlates with increased synchronization of brain waves. The cerebellum has four times more neurons than the cortex, but damage to cerebellum, unlike damage to cortex, has practically no impact on consciousness; it turns out that while there is rich differentiation and interaction in the cortex, the cerebellum has many small modules that process information locally, without much interaction with other modules. Giulio Tononi has proposed a measure of organized complexity for the determination of the level of consciousness called "integrated information."

But who then experienced the pain? Are we not talking about the same thing?

How do you know it is consciousness that is switched off, rather than unitary identity that is disrupted? — bert1

I am not sure what you mean by unitary identity, but I think my consciousness was switched off during general anesthesia because I don't remember any experiences from that time. I guess I can't rule out that I actually experienced the pain of a lancet cutting into my body or a fantastic orgasm or whatever and then forgot it, but that kind of begs the question.

And it doesn't mean that I believe that individual atoms are having complicated experiences as we do. But that different atoms, just as they have different measurable chemical properties they might also have different types of experiences. It sounds completely nuts, but maybe some type of atom (let's say all carbon atoms) just experiences the color green, and others experience what we identify as pressure, another as what we identify as warmth. — TheHorselessHeadman

Do you think that the atoms of a dead human body have these experiences? Such experiences probably exist on the level of neural structures, not atoms, and can be temporarily switched off by general anesthesia.

Everything just appears, and I might think "Hey, no, I can control things. I can snap my fingers anytime I want." But those words also just arrived. — TheHorselessHeadman

Yes, we can act intentionally only when the intention pops up in our mind. If nothing pops up, tough luck. So much for libertarian free will. On the other hand, if we are lucky enough and the intention appears, it often seems to have causal power that drives our intentional actions. Maybe consciousness is a particular causal mechanism.

conscious experience could just be a side-effect, like smoke rising from a train-engine and which has no bearing on the train itself. — TheHorselessHeadman

Or it could be like the engine itself. Consciousness could be a particular kind of matter, or both consciousness and matter could be particular kinds of "stuff", for lack of a better word.

A never-ending life does not necessarily entail repetition. Moreover, more complex bodies or mental structures may hold qualia we can't even imagine yet.

A Big Crunch doesn't seem likely from current data. Expansion of our universe is currently accelerating and the most likely scenario is that it will expand forever but at some point it will end up in heat death where all stuff is homogenously distributed in space and thus supports no life. Maybe an extremely intelligent civilization evolved over billions of years will be able to manipulate some parameters of the universe to ensure endless continuation of life.

What I see our friend saying is that he seeks gnosis as described in this link.

https://www.youtube.com/watch?v=_9QI3nlinYQ — Gnostic Christian Bishop

Well, I'm curious about general aspects of reality and existence. I also think it would suck if I bit the dust at the end of this life and that was it.

So your perspective is that our greater complexity is just a pointless extension of our basic animal nature - and there is no real point in self-reflection at all, let alone revising our behaviour patterns or seeking information, except perhaps to increase chances of ‘survival’ in a losing game...? — Possibility

Survival instinct must arise somewhere at the start of evolution, unless you assume an intelligent creator who can create living beings without a survival instinct and then can keep them in a safe place where they can live and evolve - which doesn't seem to be our world, although we may already be becoming such intelligent designers by applying genetic engineering or cybernetics.

That said, we don't need to always act with the conscious intention to survive or reproduce, even when our actions do promote our survival or reproduction: we can simply enjoy food or sex. And complex beings like today's humans can also indulge in activities that don't directly satisfy their survival or reproductive needs; they can even afford to indulge in activities that are detrimental to their survival or reproduction, as long as they have the means to reverse or mitigate such detrimental effects (for example pharmaceuticals, surgeries, etc.). As I said in the previous post, love (or similar feelings like happiness) seems to accompany accepting behaviors, so theoretically an organism can develop love for things that are beneficial or detrimental or neutral to its survival or reproduction - by accepting the things (as opposed to resisting them).

By the way, I don't argue that we are purely extensions of our animal nature. Who knows, we may have started our evolution in a spiritual/non-material world, perhaps even with an intervention of an intelligent creator, and arrived here later. My argument is about evolution and feelings like hate and love in general.

Hate seems to be a quale that accompanies a behavior where we resist something (it is also closely related to qualia like pain and fear). On the other hand, love seems to be a quale that accompanies a behavior where we accept something (and is closely related to qualia like happiness and trust). Evolution by random mutations and natural selection tends to cause that we hate (resist) and love (accept) the "right" things, that is such things our hate or love of which improves our chances of survival and/or reproduction. The unfortunate organisms that happen to hate things that are beneficial to them or love things that are detrimental to them tend to fall out of the gene pool in the long run. Evolution by random mutations and natural selection is of course a crude and long-term mechanism but it does seem to cause in the long run that organisms hate at least the most important things that are detrimental to their survival and/or reproduction and love at least the most important things that are beneficial to their survival and/or reproduction. In more complex organisms this basic hate and love are transferred also to more sophisticated things that may not be directly related to survival and/or reproduction, for example love of biologically important information may transfer to love of science or philosophy (that is, love of science or philosophy is driven, through complex cognitive structures, by the more primitive love of seeking and understanding biologically important information). On the other hand, hate of information overload may transfer to hate of science or philosophy.

Memory’s ideas recall the last heard tone;
Sensation savors what is presently known;
Imagination anticipates coming sounds;
The delight is such that none could produce alone. — PoeticUniverse

Nicely put. Unfortunately, delights are sometimes replaced by horrors. My comforting hope is that the horrors as a learning experience will facilitate prevention of future horrors.

Yes, for while there isn't anything as temporary that is identical to itself over time, there needs to be a Permanence to make the events possible. — PoeticUniverse

In a sense, everything is permanent, because its existence is logical consistency and logical consistency is timeless; a logically consistent object cannot not be logically consistent and thus it cannot not exist; time just falls out of the picture. But how do we reconcile this timeless permanence of all objects with our experience of the passage of time and the evolution of our identity over time?

Well, theory of relativity describes time as a special kind of space: in addition to the three "normal" spatial dimensions there is a fourth spatial dimension that is mathematically a bit different and can be usefully regarded as time. A spacetime, then, is a kind of 4-dimensional geometrical object that exists timelessly and this object has a certain structure that constitutes objects in spacetime and has regularities that we know as laws of physics.

Our conscious selves are some of the objects in spacetime which are extended not only in the three "normal" spatial dimensions but also in the time dimension; their extension in the time dimension measures on the order of tens of milliseconds (that's the temporal span of human conscious experience). My conscious self at this moment and my conscious self a few tens of milliseconds further are different objects in spacetime which are however closely connected through laws of physics and their character is such that a certain representation of a prior self is contained in the later self and the later self experiences this representation as a memory. The later self also contains a certain representation of an even later self and this representation is usually less specified than a memory and is experienced as an anticipation. The experience of memories and anticipations together with the overall experience of the self that contains them seems to constitute the experience of the passage of time.

I used to be amazed by the question of why there exists something rather than nothing. I am still amazed by it but I experienced some resolution when I asked myself what "existence" actually means. What does it mean that something "exists"?

My answer is that "existence" in the most general sense is logical consistency: something "exists" if it is logically consistent; or in other words, if it is what it is and is not what it is not; or if it is identical to itself and different from what it is not. This is the most general definition of existence because anything that exists must satisfy this condition of logical consistency or identity. It is actually the definition of existence in mathematics.

You may agree that anything that exists must be identical to itself and still disagree that anything that is identical to itself exists. But that would just narrow the definition of existence: you would pick a subset of objects from the set of all objects that exist under the most general definition of existence. The reason why the objects of this particular subset exist is the same reason why all objects exist (logical consistency); the objects in this particular subset just have some particular interesting property, for example they are part of an object that in physics is called "spacetime" and thus they are subject to laws of physics and can be interacted with. We could also say that the objects of the particular subset exist in a particular way.

I'm baffled by your reply. What else did you think I said? And where yet did you say anything useful about the nature of this "energy density" which you have to go off and measure? — apokrisis

I said that energy is mathematically related to the acceleration that the space point imparts to another space point during an interaction. It means that energy can do work.

You said some posts back that energy and dynamics cannot be explained only by math; that we also need a "material principle". I don't understand what you mean by the material principle, and I just outlined how energy and dynamics (acceleration during interaction) can be explained by mathematical relations and how they are related to spacetime curvature, a geometric property of the mathematical object called spacetime.

The kind of existence of an abstract object (property) is such that the object has instances. And the kind of existence of a concrete object is such that the object has no instances.

If you are trying to imagine where objectively existing abstract objects would exist, one answer could be: nowhere. Just as the universe exists nowhere, as there is no underlying space for it.

Another answer could be: in the collection of all possible objects, which are related by the relations of similarity, composition and instantiation. Some of those objects form topological or metric spaces, including the one in which we live.

Perhaps, but do abstract objects exist independently of their being thought, and if so, how would that "existence" look? — Janus

Yes, I think they exist independently of being thought because they are properties that different objects have in common; they are ways in which different objects are similar; they are conditions that different objects satisfy if they are of a particular kind. But I don't think we can visualize abstract objects, because they are not objects in space. (We may be able to visualize their particular instances or a typical instance.) But apparently we can inductively infer their existence by noticing in what ways different things are similar.

So what exists as "an object" is completely arbitrary, and dependent only on the way that human beings assign properties. if someone assigns properties, there is an object there. — Metaphysician Undercover

No, an object has properties even if no one assigns them to it. Planet Earth is round no matter whether someone assigns roundness to it. It was also round before anyone believed it was round, or before anyone even existed.

So an object is identified as something individual, particular, and unique, while a subject is identified as something specific. One is a particular, the other a universal. — Metaphysician Undercover

Huh? An object is a particular and a subject is a universal? Where did you get this terminology?

We could say that biology and physics are distinct subjects within the subject of natural science, just like Euclidean space and non-Euclidean space are distinct subjects within the subject mathematics. However, we cannot allow that biology and physics proceed from contradictory axioms, because this would signify incoherency within the subject of natural science. — Metaphysician Undercover

But biology is part of physics; properties of biological objects are physical properties. Curved space is not part of flat space and flat space is not part of curved space.

Any mathematical object can be regarded as a "possible world".

Curvature is a geometric property of spacetime and is related by Einstein's field equation to energy. Spacetime curvature and energy determine each other through Einstein's field equation.

First, I see no definition of "object". Second, you say "axioms are properties of an object". Third, opposing axioms may describe different objects. Why this is totally confused is that you have no principle to differentiate one object from another object because you have no definition of "object" — Metaphysician Undercover

Object is something that has properties.

In other words, we could make up an endless number of random axioms, each describing a different object, therefore mathematics would consist of an endless supply of random objects, each with its own axiom. — Metaphysician Undercover

Yes. That's the most general idea of mathematics.

Now, let's get logical. Within logic we have subjects. You cannot attribute to the same subject, opposing predicates, without contradiction. — Metaphysician Undercover

Is there any difference between object and subject?

Mathematics is a subject, so we cannot attribute to mathematics, opposing hypotheses, without contradiction. — Metaphysician Undercover

We don't attribute opposing axioms to the whole mathematical world, only to its parts (objects in the mathematical world). For example, zero curvature of space does not hold in the whole mathematical world but only in Euclidean spaces. And non-zero curvature of space does not hold in the whole mathematical world but only in non-Euclidean spaces.

Is it just that? The claim would be that it is some quantity of something. So the structuralism of the maths still leaves open the question of how to understand the material part of reality’s equation. — apokrisis

Maybe we could say that energy density is a mapping (defined by Einstein's field equation) from spacetime curvature to real numbers at a given point in spacetime? This mapping is in turn mathematically related to acceleration that this point can impart to another point during an interaction as the energy does work.