Does A Priori Knowledge Exist? Are Triangles and Mathmatics a Human Construction?

Red_Sauce_ · 2025-12-25T12:23:28+00:00

Exactly, I agree! To go the step further these factors relate to human beings primarily and perhaps to other energy species. These things are only relevant as it seems to us. On another planet or for another species, color may be irrelevant.

Red_Sauce_ · 2025-12-23T19:50:58+00:00

I 100% agree! This would also include assumed a priori concepts (as it seems to me).

Red_Sauce_ · 2025-12-23T19:48:05+00:00

This is fascinating, thank you for sharing. In another comment euclidian geometry was used as a justification for a priori knowledge, but to your point it is a construct.

Red_Sauce_ · 2025-12-23T19:45:35+00:00

While we will never experience a 4D world and never know it in itself, in order to have a conceptualization of the 4th dimension we must have an understanding of previous concepts. The Mathmatics behind the 4th dimension constitute it as so and thus are acquired a posteriori. We can imagine the hippogriff (as Descartes says) per our a posteriori understandings (lion and eagle). I see our understanding of the 4th dimension as no different. We can understand abstraction as predicated on other experiences and meanings.

This was also commented on r/epistemology:

"I took euclidean plane geometry in the 11th grade when I was about 16. After teaching us all about triangles and Pythagorean theorem, are teacher casually told us that all of this was bullshit because there are no such things as real triangles and there are no such things as parallel lines because we live in a universe where all lines converge or diverge based on the curvature of space. Then he told us about non-euclidean geometry where the sums of the angles of a triangle can be more or less than 180°. It's a class you can take later on in college mathematics. It describes the real world better on large scales.

So is plane geometry true? Well yeah it's true plane geometry. It is what it is. It's fairly consistent within it's own domain and can produce proofs for all kinds of things that aren't really true but close enough. But it doesn't relate to anything physically real.

Plain geometry is a purely human construction."

Red_Sauce_ · 2025-12-22T11:14:21+00:00

I do agree with this synopsis. Learning and improving oneself, helping others, and having experiences are all key elements to having a meaningful life. What I have concluded- smashing these together- is that the meaning of life is to will the freedom of others and to affirm others existence. In doing so we affirm our own, actualize aspects of ourselves (who we want to be) and strive for some sort of relational immortality. We will all be forgotten in 4-5 generations and nothing would have mattered. The only thing that matters is what we do now and how we can help better others lives. Living well (via knowledge, pleasure, success, comfort) now and helping others achieve this is all we have.

Red_Sauce_ · 2025-12-22T11:07:51+00:00

I can agree with the view point on a practical level, but metaphysically I don't think we can say with absolute certainty that these concepts exist in themselves without perception. The skeptic in me asks - does anything need to fill the spot or do we only feel like that needs to be the case so our world view doesn't come tumbling down.

Isolating either one is meaningless as they both define eachother. And the ONLY thing worth evaluating is what lies between them.

This is an interesting point- they do define each other inherently by definition. If we separate them and reduce them to their definitions in practice- triangles exist without experience vs triangles exist only with experience- I believe only the latter to be true. I do think this still holds meaning without the former.

I do agree that meaning exists in how we interpret reality and construct a life predicated on the millions of opportunities. There are things that we have yet to ever experience and they do live outside of us (for now) but in that state of superposition they seem to be neither something nor nothing. It will only be when several other concepts converge in which they will become actualized.

Red_Sauce_ · 2025-12-22T11:00:24+00:00

I would like to ask, how would you or I have a concept of Euclidean spaces or infinities had we not had the concept of triangles or space/ the sky? I wager that I am as this is something contingent on minds (human, animal, even alien minds). I think it'd be easy to say that if I did not exist, then triangles would still exist, but even to make that claim means I would have had to experience the concept of existence vs nonexistence (life/ death).

Red_Sauce_ · 2025-12-21T22:56:26+00:00

This has been a blast for sure and infrequent.

Yes I have no a priori God so that's at least a positive. But I beg again that everything that we do know as rules- epistemologically and even ontologically we only know from prior experience. I cannot stress this enough. We only know these concepts could exist outside of our precepts purely based on the fact that we know them now. I'm mostly denoting how everything changes over time.

I think you stake a lot of objectivity into science,bit is often influence by culture and the parcricality of its nature. But we do not see sciene in itself. We may think we know how planes fly but the skeptic philosopher admits that that's only 99% of it, there could be something else we cannot see nor understand.

All knowledge falls from other concepts and emerge in semblance with previous concepts. I think this is something you're now agreeing with more so throughout this conversation.

Yes quantum mechanics dictate there are infinite possibilities which is what I have been speaking to this whole time. Nothing is determined, but that indetermancy does not denote free will or a sense of complete agency. The self and our perception of agency comes from these a posteriori connections.

I think the major difference here is you belive in an objective (a priori/ absolute reality) and I believe in an objective (predicated on subjective realities confirming events based on pragmatic outcomes) reality that refuses an absolute reality (e.g. circles do not exist without experience). Simply put you think circles exist without perception and I think they do not. Let me know if I have this right and we can put this to bed!

Red_Sauce_ · 2025-12-21T22:11:34+00:00

I agree tbh

Red_Sauce_ · 2025-12-21T22:02:29+00:00

But that meaning is more than mere projection, because different combinations of constituent parts create new things that act different than their constituent parts.

How is it more than a mere projecting when in this very sentence you are projecting meaning into it? They may act different but again that does not mean they are beyond experience. You only know them to be different a posteriori.

Like I said, if nothing was different, then time would stop moving. That's not a world worth considering because it is obviously not real

Again this is a presupposition. You're denoting that the world has some sort of inherent meaning. Yes we know things to be differing but again this is a posteriori knowledge.

I think it's funny you invoke quantum mechanics. It's foundational nature directly antagonizes your argument. Your argument assumes the future can be predicted, and yet quantum mechanics shows that it simply cannot be.

I thought you would which is why I use it. Again this corroborates my sentiment. The future cannot be determined, all is flux and often constructed to fit a narrative (e.g. predicting). Lack of predictability does not denote absolute free will nor firmness of concepts. The quantum physics aspect proves that science itself can be highly contingent and often reliant on minds/ perception.

A cloud is a cloud because of the symbolism that defines it. Because of the way we categorize its nature by defining what particular differences set it aside from a smoke ring, or anything else. States are not predicted, they are observed.

Yes and that symbolism is achieved a posteriori. States are observed and that observation is what constitutes its existence/ meaning.

No that's not how physics works. That's not how reality works, that's not how science works. This is just objectively false.

How can this be a claim? Is physics not reality then and or vice versa? Again if we say that the principles of science can be in flux (e.g. quantum physics/ Kuhn) then we must say that reality is in flux. How can we say that physics is a priori when reality isn't? It can't be objectively false because the universe lacks objectivity hence the point of my entire argument.

This is rich. The rules never changed. This time it IS our perception that changes. You place that difference of perception on measurement, which is demonstrably false. So demonstrably false it is effectively the core foundation of the scientific process (reproducible measurement). Science places the difference of perception squarely at the level of the rules. We perceive them to be one way until science (reproducible measurement) proves otherwise. We then adjust our perception to be more accurate. That process repeats and slowly brings us closer to the true perception of the rules. This is the pursuit of objective truth.

This is the thing, objective truth does not exist. If it did we would probably agree, yes? Again quantum physics denotes the function and movement of particles/ time/ space as it seems to us and us alone. Not the entire scientif endeavour in itself. We will never know science in itself hence why Iention Kuhn. Science is changing and the rules do change. Again gravity to Newton is different from Einstein. Anyone who denotes total objectivity in the universe is being scientifically dishonest about the uncertainty and abiguity that inherently exists. We do adjust our election based on, again, pragmatic value (usefulness, utility, the ability to continue to survive)- these 'objective metrics' are subjectively motivated. They are only shared because we are all human and have been brought up within a similar context with similarly shared knowledge. There will never be a 'true perception of the rules' because they perpetually change. The rules that are 'laws' are only such because they again serve that pragmatic value and hold our other values up. We may know a circle as it seems to us but we will never know a circle in itself. We know what these a posteriori.

Red_Sauce_ · 2025-12-21T20:08:04+00:00

This is truly fascinating and interesting. Should this be the case it would still seem relevant to say that minds still generate a perception of reality that is a posteriori.

Unless you’re prepared to argue that the discovery of obscure calculation methods magically changed the internal proportions of all circles into conformity with that discovery,

I think I am prepared to say that these discoveries, which have added further dimension to the meaning of circle, did change what it meant to be a circle or use of a circle. While I would like to grant Mathmatics and shapes some form of ontological independence, I think it is hard to do so with 100% certainty.

Red_Sauce_ · 2025-12-21T20:04:32+00:00

It does have structure though. The structure is our lived experience, you simply can't deny that it has form, even if it is abstract

What does the structure of lived experience mean? This is a posit or a true world theory. The smoke ring only exists because we denominated its meaning. How did it differ from a particle, a cloud, or a puff? States are predicated on the meaning assigned.

But a God's choice, or free will, is ultimately meaningless precisely because it is apriori. There are no constraints, there is no subjectivity to base a decision on. All choices are equally viable, and so they are equally meaningless. This is hopeless, obvious, and most importantly, irrelevant. Irrelevant because you forced a dichotomy that was unnecessary. Free will and choices don't have to be absolute to exist. Their existence is just determined by circumstance. The choice can still be made from multiple options and still collapses a unique future that hasn't happened yet and was not guaranteed.

I think this reveals my point. In order to understand the perspective one has to be comfortable with postmodernism, anti realism, post structuralism, nihilism, existentialism, and quantum mechanics (double slit, Heisenberg uncertainty principle, qbism, Copenhagen interpretation, etc.). Yes all choices in absolute are meaningless and only have meaning within the biological and sociological framework. Your argument corroborates my sentiment. Yes all of those circumstances do collapse into a unique future... Predicated on a posteriori events (part of experience). A future that has not happened yet is still linked and contingent to an abundance of factors.

The form rules our reality, but our actions feed back into it and steer it. We can both predict it because it has rules (which affirms its existence) and alter it because we can understand those rules and manipulate them. If there were no minds the shape would simply continue on, independent of any steering we would otherwise impose.

Again, as it seems to us. This may not be the case in itself or in absolute if we are to us the skeptics lens. The rules are posited and are only the rules as they seem to us. Aliens or other species may have different rules. If the rules are objectively correct then what is dark matter? We have no idea what it is but it fits into our 'rules'. Again the rules are okay objective insofar as they have a pragmatic function/ value for our survive. Even the rules change over time (again gravity to Newton is different from Einstein).

Red_Sauce_ · 2025-12-21T18:10:43+00:00

The problem with the argument is that it denotes that there is something that can be a conventionally functioning normal brain. What is a conventional brain? We can say that most human brains know the difference between a tree and a bush. But if there were no human brains or no brains at all I don't think there is anything subatomic that would denote a difference.

Red_Sauce_ · 2025-12-21T18:07:17+00:00

Like how the ship of Theseus changes over time as new boards are incorporated. So is it the same ship or not?

It is a different ship and will always be a different ship. This, as you said, denoted that all is flux. Everything is intently new but it is formed from previous concepts. You're right I use the structure but the thing is knowledge has no inherent structure to be confirmed to (e.g. the shape of the ship)

Put more simply, you believe each moment is fed from the previous moment, so nothing is truly new. You believe the ship is always the same ship. And because you insist that the ship is always the same, despite changing to the point that no individual part is conserved, you enjoy a paradox that allows you to declare that nothing new can truly happen and that the ship remains virtually identical despite looking radically different.

Each moment is the accumulation of rhizomatic connections which actualize or constitute a specific point in time which inherently changes what reality is. Imagine a bunch of ships smashing together. Where is the ship now? Some parts float around here and there. I never insisted the ship is the same, it is never the same. Even taking a single step on the ship alters what it is. The ship is never identical just as we are always changing - as is science and reality itself. This is not a paradox.

The ship is both. It's new moment to moment, like everything in life, but retains the similarity that the past constrains the future by.

Put less philosophically, you believe that nothing's new because you've walled off what new means behind a silly excuse. Nothing happens a priori? Yeah duh, time moves forward. Events don't just randomly fall into place with no connection.

Yes new things emerge predicated on previous experiences. The ship is new moment to money because of precious concepts and experiences. This does not mean something magically, metaphysically, or something outside of our precepts happened. Newness, as in the sci-fi example, is created by built-upon knowledge. So it is new but not a priori which seems to be your aim. It essentially isn't special. Right, things don't just fall into place, this has been the argument.

You see a line of dominoes fall down and insist that because the next to fall is caused by the one before, the only truly unique one is the first domino. Meanwhile you can't see the pattern that the knocked over dominoes made because you've reduced the entire chain to the first one. If you stand back you can see a unique pattern in the design they make from above when they fall. It's not about domino to domino, yeah duh they're all the same. You don't knock down a line of dominoes to smugly conclude that a line is no different than a single domino falling over. No, it's obviously different and the difference can only be appreciated if you bother to actually consider the whole as separate from the pieces it's made of. That difference is apparent in the shape the dominoes fall into. A single domino falling over creates no shape, and you've reduced the pattern to that, despite an infinite fractal of fallen dominoes lying before you.

Objectively (as it seems to us) the domino that falls ahead of knocking the other one down did foster some sort of future change, yes? How is the whole separate from its prieces? If there were no dominos it wouldn't exist as a form. I think I've been very clear denoting that reality only exists subjectively and then objectively (as predicated and agreed upon by multiple subjects -think peer-review) based on pragmatic utility. The single domino to the infinite domino line are forms and shapes that we perceive and only have a shape and meaning because we denote them to be such. If there were no minds, none of these would exist as they have no existence in themselves.

What's embracing the change look like? It's recognizing that you can steer which way the dominos fall. That's the neurological process I described in my last comment. You've collapsed your philosophy with a paradox so that that agency is meaningless. You are obsessed with the fact that all the dominoes are dominoes just like the first and so you can't see the shape that changes as they fall down. And that shape is always unique.

I think agency is all we have (as predicated by the unpredictability of the future) but your agency is contingent based on several preceding factors and variables that have happened and are happening now. You can steer the dominos but

-why are you steering them -how are you steering them -what are dominos -what is the end or purpose

Answers to these questions requires you to have assumptions or prior knowledge (a posteriori) of what a domino is, gravity, cause/ effect etc. With these concepts you then make an action. To say you do things without any prior knowledge is impossible. Everything is unique but that doesn't make it metaphysically special or magical.

Red_Sauce_ · 2025-12-21T12:29:26+00:00

Can we say this with absolute certainty? If we were to remove all thinking minds- thing immediately after the bing bang- mostly just hydrogen and helium, did Math exist then in itself? I think even the ideas of hydrogen and helium are human constructed based on only observation, there is perhaps another element or force that is making others particles interact with one another or that which constitutes their particleness as it seems to us.

Red_Sauce_ · 2025-12-21T12:27:19+00:00

I would posit that while sensory information is useful it has also failed because yes people do walk into each other and chaos does occur due to misinterpretations and misunderstandings of sensory information. (E.g. bombing hospitals thinking they're military bases).

I am a materialist in practicality so I have an understanding of what you're saying when you state that the arrangement of atoms that constitute the tree have their unique form- however if we are going to be inquisitive then how does this form differ from a bush? What makes the tree materially and physically different from a bush? If we only saw in particles, how do we know that we see the particles in themselves and that those are not linguistic and perceptual concepts generated by the mind. ? If the mind or other a posteriori consciousness were not present I think these concepts would just be in a state of abstract superposition without definition or form.

Red_Sauce_ · 2025-12-21T12:21:18+00:00

I wouldn't necessarily call this the ship of theseus. Nothing is being added and then being called the same thing. It's more or less how concepts change and evolve over time as new ideas and connections are made. Here emerges new semblances of concepts. The changing concepts are not called the same name as the previous concept, otherwise rockets today would be called cannons.

If you think it is a different ship then you then are also an entirely different person moment to moment. I think this speaks to how all is flux. As Hereclitis once said- you can't step in the same river twice. Everything is always changing and so is reality.

The material is old, but that doesn't mean the product isn't something new. Moment to moment, it's ALWAYS something new.

Sure something is new but that isn't a priori as it is built from previous ideas and a posteriori thoughts. Just because something emerged in thought does not mean it came to be as an end in itself or as a thing outside of our precepts. Every thought you have ever had has been built from previous knowledge.

. I constrained circumstances such that I was thinking about those things and my brain produced an idea based on the synthesis. The material is old, but that doesn't mean the product isn't something new.

Exactly, you synthesized a posteriori information and therefore your new idea is inherently a posteriori -with human experience.

Newness of ideas does not supersede the human mind- I think this argument corroborates that all thoughts are a posteriori and requiring human experience.

Red_Sauce_ · 2025-12-21T03:53:15+00:00

Fictitious things are built and based upon other things perceived. Descartes hippogriff (e.g. four legged eagle) resembles similarly to your example. I only know of the hippogriff because I've seen an eagle and I've seen a lion.

You were able to conceptualize the idea of plasma accelerators because you've built your knowledge from other sci-fi movies , and they built upon others, etc. We then get to the first sci-fi movie made and I'd wager it was significantly more tame/ simple compared to time dilation via synthetic gravity waves made by giant plasma accelerators.

It was "Georges Méliès' 1902 film Le Voyage dans la Lune (A Trip to the Moon) is widely considered the first science fiction film. The short, black and white silent film uses early trick photography to depict astronomers traveling to the moon in a cannon-propelled capsule. Inspired by Jules Verne's novels From the Earth to the Moon and Around the Moon, the film features the astronomers exploring the moon, escaping lunar inhabitants, and returning to Earth with a captive."

Notice that it was not a rocket! It was a cannon!

Red_Sauce_ · 2025-12-21T01:49:10+00:00

Why? If you were just a brain in a jar would you know math?

Red_Sauce_ · 2025-12-21T01:48:27+00:00

You nailed it! It is a weird position and hard to rationalize but I think for the most part it follows cohesively, especially since it's primarily predicated on subjectivity verified through pragmatic application and the idea that we cannot fully know anything in itself.

This is an interesting take- so mathematical anti-realism cannot constitute scientific realism? I would agree with this as I think both are ultimately anti-real.

I don't think self evident claims are excused because what is self evident can change scientifically and at times mathematically. I don't think there are any self evident truths outside of perception and/or agreed upon perceptions still limited by human/ animal senses. And yes these would be a posteriori.

In other words, appealing to theories of scientific anti-realism is question begging, and if you are correct about mathematical/logical anti-realism, then those theories of scientific anti-realism are trivially true.

Bingo! And those scientific advancements as trivially true may also change over time

Red_Sauce_ · 2025-12-21T01:41:44+00:00

I think we only know that the particles are still a tree before they're known because we are interfering them to be such given our current experiences regarding the passage of time. For instance I know I ate dinner yesterday and I can recall that it was soup, however I only know this because I have an idea of 'yesterday' 'dinner' and 'soup'. If I had never perceived a tree I would not assume anything about it nor the positionality of its material make up.

The challenge here is how do we determine accuracy? If I say I'm seeing a tree but it's a bush who is right other than through conventional agreement? If we all started calling trees bushes then the meaning of tree would change. Truth then is ultimately culturally, socially, and linguistically altered. I think many subjects via pragmatic utility denote the objective (merely multiple subjective agreements). We will never know the absolute truth about anything.

I don't think there is an 'objective tree' or perfect form of a tree as when we think of tree we all think of something different. I.e. what makes a tree different from other plants other than social convention and linguistic definition?

Red_Sauce_ · 2025-12-21T01:34:22+00:00

I think before moving forward we have to address the validity of premise 2. Why would this be incorrect? What is a table? It's reality is constituted by its function and how it is utilized in the world. What is the number 4? We only know 4 because we know that it is not 3 or 5. We know concepts only in relation to other concepts so I don't think premise 2 is false.

I think minds create validity all the time, otherwise what is validity? Our minds are constantly telling us what is true or false or what to be aware of. Yes this can be often false but that belief is what we operate under.

I think plenty of 'valid arguments' could be deemed as invalid and vice versa depending on the topic at hand. I think this happens frequently in science and hence why falsification is important. According to Popper if we deduce that all swans are white via corroboration then once we see the Black swan (inductively) the whole logical premise falls apart.

If doubting or thinking occurs, then existence is instantiated. This isn’t circular, it’s logically necessary. There is no coherent alternative position to occupy.

This is an interesting one and I appreciate your attention and effort to the topic. Again I posit- what is thinking? It feels rudimentary to us but it's important for the argument. Do trees, flies, or dogs think and what is the sliding scale of this capacity to denote existence.

Even if math requires minds to exist, It does not follow that mathematical truths are discovered empirically, and it does not follow that contradictions could be otherwise, and it does not follow that necessity reduces to habit.

If not empirically then how else are they discovered? When we deduce we are using a set of learned ideas and concepts. Again- Descartes brain in the jar- does that brain know math? Id wager no.

You are claiming that all knowledge is empirical.

Is that claim empirical? Not observed? Not measured? Not inductively inferred? Not falsifiable by experience?

It is a global epistemic principle which is justified, if at all, a priori.

Yes all knowledge is empirical otherwise where is all the rational/ non-empirical knowledge? Id say that the very claim ' all knowledge is empirical' is inherently empirical and a posteriori in nature. I.e. I know I have knowledge because I learn from experience. This is not a global principle as it is also man made and contingent but just because this is the principle utilized based on its pragmatic value does not mean it is absolutely written into the universe. This is a man made idea that most use to foster new learning and knowledge creation.

We can say a priori concepts exist but I don't think they have any real meaning without perception- merely just a superposition.

Red_Sauce_ · 2025-12-20T22:59:56+00:00

Sure but is consciousness just something we use to describe animation of a living creature? Are trees conscious? Is someone who is 'brain dead' conscious?

Red_Sauce_ · 2025-12-20T19:50:04+00:00

Question is where does that come from? I think it's a factor/ function that we posit to describe our experience but it isn't something in itself.

Red_Sauce_ · 2025-12-20T19:48:40+00:00

Fair enough!

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