As for the Idea of infinity - residing in the world of Platonic Forms - I dunno what that would look like. What is the Form of infinity? — Agent Smith

I don't know that Plato had much to say about "infinity" per se.. But his Forms are essentially definitions of possible or potential things. So the Form of Infinity would be something like : 1. spacelessness, or 2. a number greater than any assignable quantity or countable number. Anyway, I suppose "Infinity" would look like nothingness, but with the potential for something. :smile:

Plato on the Infinite :
Plato therefore will locate the infinite in the world of change, but since the world we experience is a dependent and deficient, ‘less real’, world, Plato can be seen to continue in the ancient Greek tradition of rejecting the actual or transcendent and fully real infinite.
https://infinityonline.valzorex.com/plato.html

. So, some physicists will confidently assert that a VP is just as "real" as an ordinary particle. I guess they mean that a non-physical bit of mind-stuff is mathematically interchangeable with a physical speck of matter. — Gnomon

If you mean that a VP is a non-physical bit of mind stuff I disagree. The real and virtual particle are just as real. Every real particle is a virtual particle is part of a virtual particle that propagates forward in time with well defined momentum and energy (obeying the relativistic energy-momentum relation). I think the mind stuff is not the particle but that what's inside of it.

Our first meeting with infinity — Agent Smith

Can we meet infinity? If we've reached it we can always walk further. It will always stay ahead of us. That's why the female mind comes close to infinity.

I don't think one has to be an infinite being to simply understand the idea of "no end"

Agent Smith is a lot brighter than he seems at times. Humor him. :roll:

If you mean that a VP is a non-physical bit of mind stuff I disagree. The real and virtual particle are just as real — EugeneW

OK. I won't argue with you about your personal opinion, or that of a particle physicist. FWIW, in my opinion is there's an important difference between Objective Reality and Virtual Reality. When I look into a VR headset, I'm aware that what I'm seeing is a crude imitation of reality : an artificial model of reality. For me, that mental construct is a non-physical thought, not a physical thing. Similarly, a VP is an imaginary simulation of a real particle. :smile:

Virtual reality (VR) is a simulated experience that can be similar to or completely different from the real world.
https://en.wikipedia.org/wiki/Virtual_reality

Simulated :
1 : to give or assume the appearance or effect of often with the intent to deceive : imitate.

The Form of infinity can perhaps be deduced from its definition: nonterminating, endless. Basically, infinity is that which can't be completed, from a task standpoint.

I didn't know Plato had rejected infinity. Why did he do that, may I ask? One reason, according to an article I read, for why infinity was avoided like the plague by most mathematicians & philosophers for much of history was because it generates paradoxes, one of which is part = whole e.g. the set of odd numbers (a part) = the set of natural numbers (the whole).

One way of avoiding infinity is to use arbitrarily large but finite numbers; so, for example, if you find yourself having to do caclulations with infinity, you could instead use a googol or a googolplex. So says a book on philosophy on math I read last month.

Agent Smith is a lot brighter than he seems at times. Humor him. :roll: — jgill

Hey! :smile: You didn't answer my question. So, yeah.

I don't think one has to be an infinite being to simply understand the idea of "no end" — Gregory

You have a point. Hadn't thought of it that way. Nevertheless, it does strike me as odd that the brain/mind can conceive of something (infinity) that isn't physically instantiated (implications in re empiricism). Infinity is arrived at via pure deduction (rationalism & knowledge).

A VP is an imaginary simulation of a real particle. :smile: — Gnomon

So is a real particle... :wink:

It's their behavior in time and their energy-momentum relation that's pretty virtual. But still real...

And if they are just mathematical constructs (integrals over 4-momentum of e^ip, a virtual propagator), consider the mathematical structures real.

I didn't know Plato had rejected infinity. Why did he do that, may I ask? — Agent Smith

I don't think Plato "rejected infinity". As you noted, his concept of a realm of Forms is functionally infinite in a Potential sense. However, Aristotle, as a realist, may have rejected the notion of "actual Infinity" as impossible in the real world of constant beginnings & endings. However. mathematics is not inherently realistic, so it can accommodate Ideal concepts.

Modern mathematics has been forced to become comfortable with the paradoxes of infinities. So, it has developed workarounds to deal with them. The easiest dodge is to define "infinity" as a large-but-countable number. Scientists though, typically prefer to avoid Infinities for practical reasons, such as the tendency to crash computers. But fearless Philosophers boldly go where scientists fear to tread : into Metaphysical Infinity, the realm of Possibility. :nerd:


Plato on the infinite :
The world of Forms: is a world in which everything “always is,” it “has no becoming,” and “does not change” (Timeaus, 28a). We know this world of Being by reason (i.e. through the rational part of our souls).
https://infinityonline.valzorex.com/plato.html

Actual infinity :
Aristotle postulated that an actual infinity was impossible, because if it were possible, then something would have attained infinite magnitude, and would be "bigger than the heavens." However, he said, mathematics relating to infinity was not deprived of its applicability by this impossibility, because mathematicians did not need the infinite for their theorems, just a finite, arbitrarily large magnitude.
https://en.wikipedia.org/wiki/Actual_infinity


Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical.
https://www.britannica.com/science/infinity-mathematics

So is a real particle... :wink: — EugeneW

Ah yes. As cognitive scientist Donald Hoffman postulated in his book : The Case Against Reality, all human mental models of Reality are essentially "illusions". By that, he simply means that our ideas are Ideal, not Real. Unfortunately, some people can't accept that their personal Reality is artificial and man-made. So, we should not take them as literally true, but as pointers to true reality. That's because each mental model of Reality is abstract & fragmentary, derived from a limited perspective and shaped by personal biases. Even the composite models of Science are incomplete. Presumably, only God, looking down on the world from outside, would have the True, Comprehensive, Objective perspective of Reality. Consequently, our abstract mental & mathematical models of Physical & Virtual particles are both "imaginary simulations" of Absolute True Reality. :joke:

The Case Against Reality :
https://www.theatlantic.com/science/archive/2016/04/the-illusion-of-reality/479559/

Mental models are personal, internal representations of external reality that people use to interact with the world around them. They are constructed by individuals based on their unique life experiences, perceptions, and understandings of the world.
https://www.ecologyandsociety.org/vol16/iss1/art46/

"False" models as an integral part of science :
The models that scientists use are no different from the models you use in everyday life. They are simultaneously false and useful. Learning even a small amount about scientific models can be quite useful in detecting major limitations of scientific approaches. This knowledge enables one to pose relevant questions to those who developed the model.
https://utw10426.utweb.utexas.edu/Topics/False.models/Text.html

Absolute True Reality — Gnomon

Assuming there is such a thing.

Absolute True Reality — Gnomon
Assuming there is such a thing. — jgill

In Reality, there is no such thing as "true reality". But absolute true Ideality, is another question. That's what Plato called the realm of "Forms". Ideality is a standard of perfection against which we compare & evaluate our imperfect world. Like "Infinity" we can conceive of such a perfect state, but we know better than to begin the journey to that destination. :joke:


What is reality? Why we still don't understand the world's true nature :
It’s the ultimate scientific quest – to understand everything that there is. But the closer we get, the further away it seems. Can we ever get to grips with the true nature of reality?
https://www.newscientist.com/article/mg24532670-700-what-is-reality-why-we-still-dont-understand-the-worlds-true-nature/

Ideality :
In Plato’s theory of "Forms", he argues that non-physical forms (or ideas) represent the most accurate or perfect reality. Those Forms are not physical things, but merely definitions or recipes of possible things. What we call "Reality" consists of a few actualized potentials drawn from a realm of infinite possibilities.
BothAnd Blog Glossary

Note __ A perfect circle is ideally defined by Pi D or PiR^2. But, in reality there are only polygons with a series of points & sides that approximate infinity.

Thanks a ton.

There's a lot to take in in your post.

The problem with paradoxes, basically contradictions, is that it makes any logical system in which they appear trivial (every proposition, including any and its negation, is true per ex falso quodlibet).

Does this mean that, despite denying it, vehemently, we're actually using some version of paraconsistent logic?

That's because each mental model of Reality is abstract & fragmentary, derived from a limited perspective and shaped by personal biases. — Gnomon

True. But that doesn't mean you can't consider them objective reality. You gotta think something is real. Other people see something different as real. There as many objective realities as there are people and animals.

So VP are as real as real particles which are as real as my fingers tapping. :wink:

The problem with paradoxes, basically contradictions — Agent Smith

Paradoxes seem to contradict expectation. On solving them, they're not paradoxal anymore.

Does this mean that, despite denying it, vehemently, we're actually using some version of paraconsistent logic? — Agent Smith

Oh yes. Inconsistency in logic is a common glitch in human reasoning. That's why the first rule of philosophy is "don't fool yourself". One way to check your own assumptions & arguments is to be aware of common fallacies. They may masquerade as commonsense, but often others will see through your facade before you do. So exchanging views on a forum like this will expose your personal "paraconsistencies" to the skeptical eye of other truth-seekers. In most cases, they will be gentle with you, because they are aware of their own shortcomings. But those who hold their own beliefs with unconditional faith, may pounce on your apparent or real errors with pitiless fervor. So, you'll need to develop a thick skin. :smile:

True. But that doesn't mean you can't consider them objective reality. You gotta think something is real. — EugeneW

True! That's what Hoffman is talking about in his book, The Case Against Reality. He labels "what you think is real" as a mental model of reality, not reality as such (ding an sich). Those models are maps or guidebooks to Objective Reality, not the terrain itself. However, our maps are useful abstractions of the real world. If our models were not good approximations of the terrain though, we would soon get lost. Of course, you could "consider" your model to be "objective reality", but that would be self-deceptive. :smile:

Hoffman himself argues for Model Dependent Realism (MDR),concluding that “it is pointless to ask whether a model is real, only whether it agrees with observation.” . . .
However, he explains, “there is an objective reality. But that reality is utterly unlike our perceptions of objects in space and time.”
BothAnd Blog, post 105

We humans are permanently in subjective reality, as are all conscious life forms. Objection — Objective reality must exist independent of subjective reality. Just because we do not or cannot perceive it, does not mean it does not exist.
https://en.wikiversity.org/wiki/Does_objective_reality_exist%3F

“Let us remember that our knowledge of the world begins not with matter but with perceptions. I know that my pain exists, my “green” exists, and my “sweet” exists. I do not need any proof of their existence, because these events are a part of me; everything else is a theory.” [ My bold ]
___ Andrei Linde, theoretical physicist (cosmological inflation)

Objective reality must exist independent of subjective reality. Just because we do not or cannot perceive it, does not mean it does not exist. — Gnomon

I think it's incorrect to say here "just because we do not or cannot perceive it". We do perceive objective reality, but it's only a perception. So, we really do not know objective reality. What we do know is our perception of it.

Now some would try to be sleazy about this by saying, then how do you know what you're perceiving is the objective reality and not something else? Good point! So what is that "something else"? Don't answer this directly.

Instead, ask back "Then why posit perception at all if we're not gonna settle on something being perceived?". So, now we are forced, and rightly so, to take the path of least resistance -- CAUSAL THEORY OF PERCEPTION.

There is no perception without the perceiver who is in fact part of objective reality, and there is no perceiver without a cause to it being a perceiver. You know, instead of a perceiver, maybe a vegetable like turnips or eggplant?

Oh yes. Inconsistency in logic is a common glitch in human reasoning. That's why the first rule of philosophy is "don't fool yourself". One way to check you own assumptions & arguments is to be aware of common fallacies. They may masquerade as commonsense, but often others will see through your facade before you do. So exchanging views on a forum like this will expose your personal "paraconsistencies" to the skeptical eye of other truth-seekers. In most cases, they will be gentle with you, because they are aware of their own shortcomings. But those who hold their own beliefs with unconditional faith, may pounce on your apparent or real errors with pitiless fervor. So, you'll need to develop a thick skin. :smile: — Gnomon

Good advice. If I were to add anything then either develop a thick skin, like you said AND/OR improve your logic. No solace there for most of us I fear, both are hard! :smile:

Paradoxes seem to contradict expectation. On solving them, they're not paradoxal anymore. — EugeneW

Yes, that's the received wisdom on paradoxes.

Apart from knowing the outside we can understand the inside of things. Which means we can understand what we know. Knowledge is about perception (the chart), understanding about the the object an Sich (terrain). The terrain is still there when I don't look. The perception is gone. What is perceived and understood depends on the observer.

The terrain is still there when I don't look. — EugeneW

This is the falsity which Kant taught us about. What the map maps, i.e. "the terrain", is phenomena, which is a product of sensation. Therefore the terrain really is not there when you don't look. That there is some sort of correlation between "the terrain", as a product of your sensations, and the thing itself, is just an assumption people make.

That there is some sort of correlation between "the terrain", as a product of your sensations, and the thing itself, is just an assumption people make. — Metaphysician Undercover

But there is a difference between a dreamt storm and a storm in the world we see when we're awake. The noumenon and the phenomenon are equally real. If nobody perceives the sound as a sound, the sound waves are still there but the conscious experience of them is not. An assumption which we can never proof, as we're not there in that scenario. But a reasonable one, seems to me.

The noumenon and the phenomenon are equally real. — EugeneW

I agree they are equally real, but they are not the same, and are therefore "real" in completely different ways. That the noumenon is real, requires an assumption, the one dealt with by Descartes in the brain in a vat scenario. So I agree that the noumenon is real, but I do so only by rejecting scenarios like the brain in the vat, by saying that there must still be some sort of externally sourced stimulation to the brain to create the appearance of the phenomenon, even if it was just a brain in a vat.

If nobody perceives the sound as a sound, the sound waves are still there but the conscious experience of them is not. — EugeneW

This requires the assumption that the description, of sound waves, is actually true. Your proposition "the sound waves are still there", is only true if the description of what causes the phenomenon of hearing something (i.e. sound waves), is a true description. If the brain in the vat is the truth, then the sound waves description is actually false, and only what we were led into believing through some sort of deception.

An assumption which we can never proof, as we're not there in that scenario. But a reasonable one, seems to me. — EugeneW

The assumption that we know how the phenomenon relates to the noumenon is not a reasonable one in my mind.

So I agree that the noumenon is real, but I do so only by rejecting scenarios like the brain in the vat — Metaphysician Undercover

The brain in vat is a persistent fantasy indeed. A brain needs us or animals to live in and can't be separated from it to live in an artificial vat, not even in fantasy. This assumes noumenon and phenomenon can be separated while in reality they are attached to each other.

The assumption that we know how the phenomenon relates to the noumenon is not a reasonable one in my mind. — Metaphysician Undercover

That's not the assumption. The assumption is that noumenon exists independently of us. When we appear, phenomenon appear and shape the noumenon.

So, now we are forced, and rightly so, to take the path of least resistance -- CAUSAL THEORY OF PERCEPTION. — L'éléphant

I wasn't familiar with the various theories of Perception, but the "Causal theory" seems intuitive to me. However, the "Emission Theory" seemed sensible to Plato. And Superman's X-ray Vision is a form of emission perception. So, I guess, what you Perceive is still somewhat dependent on what you Conceive. :cool:

The causal theory of perception consists roughly of the claim that necessarily, if a subject S sees an object O, then O causes S to have a visual experience. Some have held that this claim is a conceptual truth.
https://philpapers.org/browse/the-causal-theory-of-perception

Theories of Preception :
The four main bottom-up theories of form and pattern perception are direct perception, template theories, feature theories, and recognition-by-components theory. Bottom-up theories describe approaches where perception starts with the stimuli whose appearance you take in through your eye.
https://philpapers.org/browse/the-causal-theory-of-perception

Emission theory (vision) :
Emission theory or extramission theory (variants: extromission) or extromissionism is the proposal that visual perception is accomplished by eye beams ...
https://en.wikipedia.org › wiki › Emission_theory_(visi...

What is perceived and understood depends on the observer. — EugeneW

Yes. The eye is not the only component in vision. The brain interprets the visual stimuli in order to understand what is being seen. And even the brain has more than one way to Perceive, as exemplified in the "Blindsight" phenomenon. Moreover, the brain can Conceive of something that isn't there, as in illusions and mirages. So human perception is a combination of physical and non-physical functions. By "non-physical" I mean the interpretation of physical inputs into non-physical meaning in the Mind. Percepts are converted into Concepts. So, "what you see, ain't always what you got". :nerd:


Blindsight is the ability of people who are cortically blind due to lesions in their striate cortex, also known as the primary visual cortex or V1, to respond to visual stimuli that they do not consciously see.
___Wiki

is the ability of people who are cortically blind due to lesions in their striate cortex, also known as the primary visual cortex or V1, to respond to visual stimuli that they do not consciously see — Gnomon

Yes! There are people who reside in the dark but at the same time see motion.

Theories of Preception :
The four main bottom-up theories of form and pattern perception are direct perception, template theories, feature theories, and recognition-by-components theory. Bottom-up theories describe approaches where perception starts with the stimuli whose appearance you take in through your eye.
https://philpapers.org/browse/the-causal-theory-of-perception — Gnomon

Yup! Interesting. Thanks for the link.

Emission theory (vision) :
Emission theory or extramission theory (variants: extromission) or extromissionism is the proposal that visual perception is accomplished by eye beams ... — Gnomon

:grin:
Yeah, this is the superman theory of perception. Where we give off beams from our eyes and we see objects behind walls.

That there is some sort of correlation between "the terrain", as a product of your sensations, and the thing itself, is just an assumption people make. — Metaphysician Undercover

That may be true in an abstract cognitive sense. But, if we didn't make the "connection" or "assumption" that a cliff edge (absence of solid ground) is really there, we could take a fatal step into the abyss. Our eyes & brains interpret edges as a sign that a surface changes direction. That's a useful assumption to assure evolutionary survival. Even in a Virtual Reality goggle, you'd be wise to assume, without proof, that an edge means either a real obstacle or an absent precipice. :joke:

Assumption : 1. a thing that is accepted as true or as certain to happen, without proof.

‘Ancient Brain’ Helps Us Interpret Edges :
https://theserf.org/news/ancient-brain-helps-us-interpret-edges/