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Step 1: We start by believing in the bare minimum : our own subjective experience exists. This is the only thing we know to exist. The existence of other things can only be inferred. And to deny your own existence, you would have to exist in the first place. So it can't be denied

Step 2: We notice that our perceptions have a distinguishability property. For instance, we notice that distinguishable feelings of colors exist. Distinguishable feelings of sounds exist. This forms the basis of the idea of "collections" of distinguishable things.

Step 3: We start studying the rules by which our perceptions behave. We first map our distinguishable perceptions to distinguishable symbols, and then we study the rules of behavior of perceptions in terms of these symbols. This is physics. To test physics, we map these symbols back to our perceptions.

Here we also note that this map isn't information preserving. For example, we may map distinguishable colors to real numbers, and distinguishable sounds to real numbers. But there is nothing about real numbers that tells us how the perception of sounds is different from the perception of colors.

Linguistic maps only preserve the information about the distinguishability of perceptions. They lose the information about what perceptions are, which is something incommunicable using language.

Step 4: We study the behavior of other people, who so far only exist in our perceptions. We conclude that their behavior is similar to us. For example, we may find a pin-prick painful and also observe a similar behavior in other people. We may also see ourselves in a mirror to get a third person perspective of ourselves like what we have of others.

Here we take a leap and conclude that other people also have subjective perceptions like us.

Step 5: We observe other people reacting to things that are outside their bodies. For example, in the pin-prick, we can see that the pin is located outside the other person's body.

Now since we are identical to other people according to Step 4., we conclude that we are also reacting to things that are located outside our bodies. Our qualia like that of pain are correlated to outside sources.

Step 6: Then the physics that we came up with in step 3 actually describes an objective world out there. The outside world has distinguishable "objects". These objects also include peoples' brains.

The outside world is mathematical. Its nature may be a computational structure like cellular automata, or a more advanced set theoretic structure like General Relativity. We don't know the final model yet. These structures also include the human brain.

Step 7: Ever since step 3, we knew that the mathematical map was not information preserving. Qualia are the only thing whose existence we can be sure about since Step 1. The existence of other things is something we've inferred using leaps of faith.

Since the map isn't information preserving, we conclude that the mathematical structure does not encompass all that we know to exist.

So, in the end, we have two fundamental aspects of reality:

  1. Subjective experience and qualia which we know to exist since the beginning. These can't be translated into language.

  2. The objective mathematical reality, whose existence we have inferred using tiny leaps of faith.

Which steps in my argument are controversial/wrong and why?

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8 Answers 8

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Re-posting here from the other thread, I would propose a simpler argument to show the existence of an objective reality outside the subjective realm, with less leaps of faith.

I would propose the following demarcation: in your subjective experience, there are things that resist and act as obstacles to your will, or constraints on your subjective experience.

For example, no matter how hard you try, if you jump up, gravity will bring you down. Furthermore, that is the common experience of everybody else that you perceive in your experience.

Those things that resist or act as constraints on your subjective experience, we could call "objective". They appear to your subjective consciousness but they are outside the reach of active control of the subject and thus are not located within the subject. They are given to the subject as constraints, and constitute an objective reality outside the subject.

Essentially, the fact that there is any given (obstructions, blockers to your free choices) to your experience points to something outside the subject.

You could argue that those obstacles/constraints/laws are still generated by the mind of the subject. Maybe I am the only mind that exists, and for some random reason, I am creating an experience which has that gravity constraint but there is no necessity to that. Or there are several isolated minds, who each conjure up their own "reality" where different rules may apply.

A reply to that could be a probabilistic argument: there are so many coincidences in what we perceive, and so much complexity, it seems unlikely a single mind could maintain that universe, and therefore there are probably things that exist independently of our minds but manifest themselves in our experience through all those coincidences and limitations to our will. Of course, we don't know that, but it would be a probable conclusion.

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  • 2
    I'm sorry but the probabilistic argument has no jurisdiction here. In this context, probabilities would be rules just like the laws of physics that you invent to explain the behavior of aspects of your perceptions. In the other thread, I can accept this argument because there we are just defining "objective" and "subjective" as useful terms to refer to different parts of our experience. In this thread, we are trying to infer the existence of things independent of our experience.
    – Ryder Rude
    Commented Apr 5, 2023 at 16:07
  • @RyderRude I think it's legit though - you can argue for dualism from a probabilistic perspective. It's just another way to infer the existence of an objective reality.
    – Frank
    Commented Apr 5, 2023 at 19:00
  • @RyderRude Not sure we are speaking of the same probabilistic argument. The one I wanted to make is that it looks very improbable that all those things I'm perceiving are generated by my mind, therefore it is likely that they exist independently and somehow manifest themselves in my experience. By the way, I think Spinoza has written on that topic. For him, if I remember correctly, those manifestations in our experience that seem external are actually in the mind of God.
    – Frank
    Commented Apr 5, 2023 at 19:14
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    Your point about things resisting our will is interesting. David Deutsch makes a similar claim in defence of realism. He says that what assures us that the world is real is that when we push against it, it pushes back.
    – Bumble
    Commented Apr 5, 2023 at 20:33
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    I'll admit, while I'm not solipsist myself, I never entirely followed that argument against it. I can't even will anything I want in my own mind, I can't will myself out of depression or anxiety or the like. So why would true solipsism imply being able to will anything I want in the reality generated by my mind, that nothing in that reality would be contrary to my conscious, proactive desires?
    – Idran
    Commented Apr 5, 2023 at 21:57
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You say yourself after Step 4:

Here we take a leap and conclude that other people also have subjective perceptions like us.

You are taking a leap because the conclusions after this do not follow from the premises before. The argument, therefore, has no logical force. It is begging the question.

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Your basic argument is actually widely accepted and implemented by humans world wide. It is why children universally become dualists (See https://www2.psych.ubc.ca/~henrich/pdfs/ChudekEtAl_InutiveDualism_WorkingPaper_June2014.pdf ) and why Locke and Popper find it unproblematic to infer mind-body dualism from the subjectively inferred indirect realism intrinsic to the scientific method.

However, most philosophers today are extremely hostile to Descartes dualist thinking, and argue against one or another of your premises in order to try to avoid your conclusion.

Phenomenalism was one effort to avoid dualism -- by reducing EVERYTHING to perceptions and our inference from them, the inference to selfhood and qualia, and the inference to the outside world, were put in the same bucket. Half the logical positivists tried to make phenomenalism work to avoid dualism. Phenomenalism failed as a science project early in the last century, due to the inability of phenomenologists to be able to agree on what is nor isn't a fundamental quale, so this alternative view fell out of favor for unrelated reasons.

Direct realism -- deny that the inference to external reality is problematic. The other half of logical positivism went this route, as did Ayn Rand. Direct realism however runs directly against "scientific realism" which holds that the universe is actually wildly different from our inferred reality (IE most of what seems "solid matter" is actually empty space between atoms, what is actually real are elementary particles and forces that we can't directly perceive, etc.). Science appears to pretty explicitly refute direct realism.

Many physicalists take the phenomenalist tack, and try to put internal and external knowledge on the same footing, but with a very different take on this approach. This involves rejecting that our internal "knowledge" is direct -- IE selfhood and qualia too is arrived at by indirect inference. This is carried to its limit case in arguments that our selfhood and qualia are delusions/illusions by Daniel Dennett and the Delusionists, and also by the eliminative reductionists. The delusionists have accumulated a significant body of evidence that we CAN'T always trust our internal perceptions. This part of their case is pretty solid. The next step -- that we don't even have internal perceptions -- is a lot less solid.

Daniel Dennett has put particular effort into coming up with alternatives to your argument, and he challenges the "limits of language" claim. His argument is that with sufficient time, one can put all internal experiences into words, and that 3rd parties can then treat the description as entirely equivalent to an experience. I believe that this is easily refuted by asking anyone who makes this claim to describe a sunset, and their experience/thoughts about the sunset. Much of what we perceive and think is non-linguistic, and just translating "sunset experience" into language is a major transform task, that quickly runs into a bandwidth limit to both our translation rate, and then our ability to vocalize. Dennett has tried to address this, by then postulating infinite time to get the full data set into words, but as we never DO that (or CAN do that), then his behaviorist premise of "3rd person data can fully replace 1st person data in logic processing" is demonstrably false for humans and our world.

Holism and anti-realism and embodied mind physicalist thinking all tend to challenge that we can even have thoughts or perceptions other than as engaged with the world. They start by rejecting step 1. This is probably the most common philosophical response you will find today. This response basically argues that dualism is an artifact of philosophers engaged in an invalidly purely rationalistic thought problem speculation.

However, the universality of dualism among toddlers worldwide -- dramatically refutes this dismissal and turns it on its head. Your list, and dualism, is how basically all of us think. And it is only philosophers casting about for some rationalizations to dismiss this pragmatic approach to thinking because they don't like the implications from it, who are engaged in esoteric rationalizing.

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  • wow I knew about Solipsism in infants, as they don't understand object permanence. But I didn't know that dualism was universal in children too. Perhaps we can take the transition from Solipsism to Dualism as a gradual application of something similar to these steps by children. That infants start with no object permanence is a great clue that they start with something like Step 1.
    – Ryder Rude
    Commented Apr 7, 2023 at 19:27
  • Nice explanation. It always irks me when people say that some folks couldn't agree on something. Figure it out!
    – Scott Rowe
    Commented Apr 7, 2023 at 23:50
  • Note I give Delusionists half marks. The evidence they have accumulated against "we can know our internal states with absolute certainty" is quite extensive. That leaves internal knowledge ALSO an inference, and uncertain. But still, DIFFERENT from external knowledge.
    – Dcleve
    Commented Apr 8, 2023 at 0:03
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Re. Step 1: We start by believing in the bare minimum : our own subjective experience exists.

the reduction to the pure ego and to the solipsistic sphere of the mine, in the sense that Husserl understands it, is forbidden by the very structure of Dasein, that an ego without world and without others is never given to us, and that my relation to the other is not established by an Einfühlung [empathy] bridging two subjectivities but has always already come about.

So the problem with step 1 is that the premise, an isolated ego, is a misconception. For Dasein, the ego — the I — is one thing amongst others: the I, the you, the table. Each thing is managed according to what it is but at no stage is there only an I.

Quote is from Jacques Derrida's Heidegger: The Question of Being and History - pages 120-121

Continuation

So, in the end, we have two fundamental aspects of reality: 1. Subjective experience and qualia which we know to exist since the beginning. 2. The objective mathematical reality, whose existence we have inferred using tiny leaps of faith.

Re 1. Experience is being-in-the-world from the beginning, amongst all the phenomena at hand. The subject owns the experience; the self/not-self distinction develops gradually, understanding of phenomena is refined. Discovery of things in-the-world like mathematical constants are still in-the-world. (That was re 2.)

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  • I would argue that Step 1 of OP is not exactly a "reduction to the pure ego". In a heideggerian context, speaking of "subjective experience" does sound risky but what OP seems to ultimately want for this first step is not something like the ego but on the contrary the world (in the heideggerian sense) as projected by the Dasein.
    – Johan
    Commented Apr 5, 2023 at 18:24
  • @Johan Good comment. Replying from B&T [116]: "Dasein is in each case mine, and this is its constitution; but what if this should be the very reason why, proximally and for the most part, Dasein is not itself?" Perhaps Dasein is world, or existence. (I'm still reading about it.) Commented Apr 5, 2023 at 19:21
  • @Johan This quote at H.116 is in the section that Derrida leads on from in page 120-121. Commented Apr 5, 2023 at 21:55
  • Seems like begging the question: merely asserting that things beyond subjective experience exist, as an axiom. Descartes's first principle asserts/assumes much less. Commented Apr 7, 2023 at 19:16
  • 1
    Also I'm not sure that step 1 is actually a necessary prerequisite for the rest of the argument. Commented Apr 7, 2023 at 19:18
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Here we also note that this map isn't information preserving. For example, we may map distinguishable colors to real numbers, and distinguishable sounds to real numbers.

You may not, in fact, do this. You may map colours to ℝ³ (or ℝ⁴, if you're a tetrachromat), and distinguishable sounds to ℝ→ℝ, though. Humans don't perceive zero-size points in the perceptive space, so we'll have to use a structure-preserving map of some kind. Alternatively, since human perception has a finite resolution, we can quantise our perceptions to give a finite representation.

A hole identified, but it's very easily closed.

Linguistic maps only preserve the information about the distinguishability of perceptions. They lose the information about what perceptions are, which is something incommunicable using language.

Therefore, map colours to ("the colour", ℝ³), and sounds to ("the sound", ℝ→ℝ). Hurrah! We have an information-preserving map, by combining the powers of both description and encoding. (This technique is used by your computer.)

This invalidates step 7, thus the argument. This doesn't seem recoverable.


Here we take a leap and conclude that other people also have subjective perceptions like us.

You can't "take a leap" without some justification for taking that leap, and then generalise; lest you accidentally generalise in a way incompatible with justifications for that leap (exploding your argument).


Now since we are identical to other people according to Step 4., we conclude that we are also reacting to things that are located outside our bodies. Our qualia like that of pain are correlated to outside sources.

So far, we have only established that these people exist in the world that produces our perceptions: we haven't shown that this world is outside, in any sense. If we're making leaps, you might as well make the "things I perceive exist outside my mind" leap here and now, skipping steps 4 and 5 entirely. (I don't think this hurts your argument.)


The outside world is mathematical.

Depending on what you mean by this, it's either a HUGE leap, or vacuous. I like to think that the universe is fundamentally mathematical, but to the extent I believe that, I take it as an article of faith: I have no proof of it.

Your argument doesn't demonstrate that (say) water is mindless. Perhaps water behaves as it does because it has a mind, and wants to do what it does? Perhaps the entire universe, including people, is made of mental soul thoughtstuff, and that's the direction in which it's non-dualist?

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  • Thanks for the criticism. You say we can map the sound to $(Sound, R)$. Is the "Sound" in the ordered pair supposed to refer to the feeling of the sound? If yes, then this isn't a linguistic map, as you haven't translated the feeling of the sound to a mathematical structure. I am okay with the idea of the brain computably mapping mathematical structures to non-mathematical structures that exist. I did infer that: 1. The brain is a part of the mathematical reality. 2. Qualia are correlated to the things that exist out there.
    – Ryder Rude
    Commented Apr 6, 2023 at 2:48
  • Sorry, I misunderstood you. This kind of distinction between sounds and colors is already present in physics, as the models describe, say, the time evolution of air pressure waves and EM waves differently. What I meant is that the information about the subjective feelings of colors and sounds is not present in the mathematical map. When we map colors to numbers, we are diluting what exactly we know about colors to a mere "colors are dinstinguishable". This diluted description of what we know is what physics deals with.
    – Ryder Rude
    Commented Apr 6, 2023 at 4:08
  • I'm saying that when we map feelings to set-theoretic structures, the map doesn't preserve the information because there are undescribable aspects of feelings. You can map different colors to different real numbers. Colors are distinguishable and so are real numbers. But distinguishability is just one aspect of colors. If you postulate that the math is all that exists, you don't get colors out of it, but we all have direct evidence of colors.......I do know linear algebra. You are perhaps speaking of invertible transformations. That's not the problem I mean here.
    – Ryder Rude
    Commented Apr 6, 2023 at 13:31
  • I'm saying that mathematical structures are a way to describe the properties that we can speak of qualia. If one cannot speak of something, that doesn't mean it doesn't exist. In our experience, we know that there is more to the difference between the "feeling of sound", "feeling of pain", and " feeling of colors", than : "they're just different things". You don't see sounds. You don't hear colors. The information describing "seeing" and "hearing" is missing in the math
    – Ryder Rude
    Commented Apr 6, 2023 at 13:34
  • 1
    Let us continue this discussion in chat.
    – Ryder Rude
    Commented Apr 6, 2023 at 14:05
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Two aspects of reality?

Subjective experience and qualia which we know to exist since the beginning. These can't be translated into language... The objective mathematical reality, whose existence we have inferred using tiny leaps of faith.

They blend nicely into a single aspect called intersubjectivity. It may surprise you to learn, since it is often a pillar of Western philosophy, that there are some famous mathematicians who reject that mathematics is objective and that apriorticity is somewhat meaningless. Such mathematicians such as Charles Sanders Pierce and L.E.J. Brouwer consider mathematics an empirical and constructivist activity that start with subjective considerations. In fact, mathematical constructivism while unpopular among professional mathematicians has many advantages over the Platonic, the most important of which is that to deny the claim that math exists independent of people as a class. Ideas may exist independent of any one person, but what ideas existing independent of all people? It seems silly, really, if you employ scientific notions of physical existence to things that are obviously not physically extant, like numbers. One famous philosopher, Quine, thought a great deal about what an abstract object (SEP) might be.

Interestingly, your model of dualism based on the subject and the objective is just a restatement of classical notions of dualism like Cartesian dualism. Indeed, modern analytical philosophers are uneasy with dualism because intuitively, there seems like there should be something in common between mind and brain. You are right to note that we think dualistically, but it is also intuitive to believe in mental causation (SEP) which on closer inspection seems to be an illusion.

Your argument is relatively sophisticated (most people give this stuff no thought), but you'll find there are a great deal of arguments that might unseat the details of your claims. For instance, if you believe in evolution, how would a mind come to be if it has no survival value? Clearly a mind has survival value, but since natural selection operates on genes and not ideas, the existence of the mind as a control system seems to suggest some fundamental connection to the brain. Additionally, if the brain is damaged, doesn't it affect the mind? Indubitably. So what's the connection? And if you find yourself believing in that connection, then there seems to be something common to the mind and body, and therefore you're not strictly speaking a dualist any more. That's why thinkers like Chalmer's have devised arguments to argue that your dualism is not true dualism, but only property dualism instead which is a form of physical reductionism. There are some clever thinkers on this forum which reject with some measure of persuasiveness physical reductionism, and some classical philosophical positions like Berkeley's subjective idealism that once were very popular.

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  • +1 I've been considering that mathematical structures of physics are just a property of qualia. So, in this sense, these two unify into some sort of monism. We know the concepts of "distinguishability" and "collections" based on properties of our qualia. These concepts form the basis of set theory, which later builds mathematics. So it all seems to have been derived from qualia alone. But at the same time, it is very tempting to believe in an objective world too. Maybe we can then say that the objective reality is comprised of the "substance of the mind" which also has mathematical properties.
    – Ryder Rude
    Commented Apr 7, 2023 at 19:52
  • At the moment, I practice epoche on this matter. I see quantum probability functions as purely linguistic structures so in that regard I'm a nominalist. Qualia are properties of phenomena, so that is to say they are aspects of the objects of our conscious mind. That we have language to conduct conversation in a domain of discourse precedes any set theory historically, so presumably cognitively. That we are aware of phenomena that are empirical and external seems certain. Any "substance" is rooted in linguistic intuition that tries to make sense of physical intuition, sure...
    – J D
    Commented Apr 8, 2023 at 14:24
  • To me, the question of monism or dualism or something more align with Chalmers where he has a monism of dualism which seems akin to Kant's transcendental idealism, is still vague in my mind. For the time being, I suspect that any attempts to resolve monism versus dualism will wind up with something similar to Kant's transcendental idealism, and I have a hunch that I'm trying to flesh out. I think Chalmers' hard problem is essentially a statement of this.
    – J D
    Commented Apr 8, 2023 at 14:27
  • @RyderRude My primary philosophical drive at the moment is to pursue the philosophy of language in the spirit of linguistic turn. I'm a firm believer that reflecting on language and linguistics is the key to making sense of philosophy as a whole. The problem is finding people to carry out that sort of discourse.
    – J D
    Commented Apr 8, 2023 at 14:30
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"Here we also note that this map [of our distinguishable perceptions to distinguishable symbols] isn't information preserving"

I don't really follow your logic for saying this.

I do think accepting this is reasonable though. We have a limited understanding of (what we perceive as) reality and of our own minds, so naturally some information would be lost in trying to interpret these things. Regardless of how accurate our understanding of objective reality is, or whether one's mind exists in a void, we don't know this, which means we have a limited understanding of reality.

"Here we take a leap and conclude that other people also have subjective perceptions like us"

This is quite the leap. The main problem is that you haven't proven that other people exist. All you have is your perception of other people reacting to things outside their body.

This invalidates the justification for concluding that we are also reacting to things that are located outside our bodies.

"Then the physics that we came up with in step 3 actually describes an objective world out there"

This is also invalidated by the above.

Additionally, this may be invalidated by step 3. If our map of our distinguishable perceptions to distinguishable symbols (that you call physics) isn't information preserving, then the question would be how much information is lost and thus how accurate this mapping is, and what it's actually mapped to.

"The existence of other things is something we've inferred using leaps of faith"

Not quite. It does seem like the simplest explanation for our perception, which I would argue is thus the most reasonable conclusion and it should be accepted based on that. This would not be a "leap of faith".

But also, this statement of yours contradict the rest of your argument. If the existence of other things is something we've inferred using leaps of faith (or even if it's a reasonable conclusion given the evidence), it cannot also be the case that we've concluded that the existence of other things exist through logic alone, as per step 4 and 5.

"Since the map isn't information preserving, we conclude that the mathematical structure does not encompass all that we know to exist"

I'm unsure what you're trying to conclude here.

If you mean the "mathematical structure" of the objective reality doesn't encompass all we know to exist, because the mapping of our perception to symbols/understanding isn't information preserving, then you may swapping things around here. If our understanding has less information than our perception, this says nothing about how much information objective reality has. Objective reality can encompass both our perception and our understanding regardless of whether our understanding has more or less information than our perception.

If you mean the "mathematical structure" of the objective reality encompasses more than what we know to exist, this is probably reasonable to say, but it seems to follow somewhat trivially from our understanding not being information preserving.

If you didn't mean either of those things, you'll have to clarify what you meant.

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  • Thanks for the criticism. 1 I didn't say that steps 4 and 5 were "logical reasoning". The leap is explicitly mentioned in step 4. 2 The mathematical structure of objective reality encompasses less than what we know to exist because the mathematical structures corresponding to qualia are a dilution from what we know about qualia, as I showed in step 3. This is why the universe's ontology cannot be purely mathematical.
    – Ryder Rude
    Commented Apr 6, 2023 at 9:49
  • What I have concluded are two aspects of reality. Of course, both of them combined encompass everything we know. But the mathematical aspect that we have inferred (or concluded using reasonable leaps) does not encompass everything we know about our existence.
    – Ryder Rude
    Commented Apr 6, 2023 at 10:03
  • @RyderRude It seems like you're equivocating. You have a "mathematical structure" on one side which is believed to be objective reality, and you have the mathematical structure that is our understanding of the universe on the other, with our perception in the middle, connecting the two. The structure of our understanding is a subset of our perception, and you seem to be saying that the structure of objective reality is a subset of our perception, which doesn't follow (if anything, I'd say our perception is a subset of reality).
    – NotThatGuy
    Commented Apr 6, 2023 at 12:11
  • I'm sorry. Any ambiguity was not intended from my end....Your assumption that "all that exists" is a mathematical reality is unjustified. We should stick to what we know. What we know is that : 1. We have subjective experiences 2. We have a mathematical structure that is born out of a information non-preserving map from qualia to language. I'm defining "all that exists" to be the "union of these two". I don't know if there's anything else that exists. Of course, this union could be a subset of "all that exists", but I have no reason of assuming that "all that exists" is mathematics.....
    – Ryder Rude
    Commented Apr 6, 2023 at 13:01
  • 1
    @RyderRude "Your assumption that 'all that exists' is a mathematical reality is unjustified" - I thought that was what you were saying. "I'm defining 'all [we know] that exists' to be the 'union of these two'" - that's fine, but both are in the mind, which wouldn't be "2 fundamental aspects of reality", as mentioned in your question, and then you wouldn't have concluded a dualist reality (also, your question mentions a lot about "objective" reality and existence external to an individual, which would be misleading phrasing if referring merely to our understanding of our perception of reality).
    – NotThatGuy
    Commented Apr 6, 2023 at 16:56
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Notably, your dual reality somehow does not include the one and only objective Reality.

I think many people struggle with this concept because they only look at it from their own perspective -- and to them, their perspective become indistinguishable from the Reality itself. That's where the belief that everyone has their own reality and their own truth, originates form -- again, mistaking individual perspectives of the Reality for individual realities.

How can we see the Reality itself then? -- through the power of our imagination. We can visualize how it looks from different angles, and, indeed, to see ourselves from the outside.1 This, by the way, is the only way to see the boundary separating our minds from the Reality outside.

Oh, and, of course, we can't know for sure that our perceptions reflect the actual Reality outside, and not something else. There are however, practical reasons why we should assume that what we perceive is the one and only objective Reality, which everyone belongs to, even though it itself does not belong to anyone.

Specifically, assuming the objective Reality gives us the concept of truth: true means it's real. And we need to know what is real from what isn't in order to know our options; to be able to choose consciously between them; and, therefore, to have agency! This is how the truth makes us free.

1 The way Galileo could visualize the Earth being just another planet orbiting Sun. He too have trouble persuading his distinguished opponents who were struggling to visualize in their imagination what Galileo so clearly saw in his.

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