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Author | Topic: Time and Beginning to Exist | |||||||||||||||||||||||
Straggler Member Posts: 10333 From: London England Joined: |
NN writes: Actually you said that ideas don't exist outside of the brain. Then you misunderstood. I have never stipulated that human brains are the only possible material basis. However you have asserted that ideas exist in the absence of any physical medium at all.
NN Previously writes: What I believe ideas to be are abstract concepts that are separate from the thoughts, writings, and objects that express them. For example, the story of Goldilocks and the three bears is independent from any medium or thought that contains that story. Does the above remain your position?
NN writes: To respond to that assertion, I don't need to address the more difficult task of showing that ideas can be immaterial. Given that I never made the assertion that you are attributing to me maybe a focus on your own assertions would be of more merit. Why won't you answer direct questions about your own example?
NN writes: I don't believe the concept four is tied to a human mind. I'm not sure I do either. I think it can be argued that the concept four is an aspect of logic and thus objective realiy. But I don't think the same can be said of Goldilocks and the three bears. Or my idea for a novel. Or indeed the vast majority of ideas which are subjective rather than objective. Objective mathematical concepts and stories like Goldilocks are inherently different in this respect. No?
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Straggler Member Posts: 10333 From: London England Joined: |
Rahvin writes: "Four" is still a subjective concept, it only exists in your head, it's a symbol that represents something in reality. OK. Can you give an example of a concept that is objective rather than subjective? And explain in what sense it is objective in a way that "four" is not?
Rahvin writes: Objective reality is that which exists regardless of whether anyone, human or alien, believes it does. I would suggest that mathematical concepts such as 4 and Pi arguably meet that criteria at least as well as any other concepts you can name.
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Straggler Member Posts: 10333 From: London England Joined: |
Well I don't really disagree with any of that. But to nitpick.
Rahvin writes: I don't think there's any such thing as an "objective concept." A "concept" by definition can exist only within the confines of an intelligent mind. It's an abstract representation of something else, which may or may not actually exist in objective reality. OK. But that doesn't mean that all concepts are equally subjective does it? You can see what is meant when I describe the concept of 4 as having objective existence in a way that my as yet unwritten or unstated idea for a novel does not - Right? The concept of an apple has an objective basis in a way that the concept of the Easter Bunny or Goldilocks doesn't.
Rahvin writes: I would argue that the parts of reality represented by "4" and "Pi" are objective, but that the words and concepts themselves are our own invention. Well obviously the words, symbols and exact conception are human inventions. But let me ask you this: Do you think that reality is innately logical? Do you think that a concept like pi is arguably an aspect of objective reality and thus can meaningfully be said to have been discovered rather than invented? We would presumably agree that any suitably advanced civilisation would be aware of this relationship
The symbols used are indisputably just human conventions. But the relationship being expressed is arguably a property of objective reality. No?
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Straggler Member Posts: 10333 From: London England Joined: |
Last questions:
Do apples objectively exist? Does pi objectively exist? Does the Easter Bunny objectively exist? Are mathematical concepts like pi closer in nature to empirical things like apples than they are to wholly subjective notions such as the Easter Bunny?
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Straggler Member Posts: 10333 From: London England Joined: |
Whatever objectively exists can only ever be experienced and conceived of subjectively. This seems to be your main point. And I couldn’t agree with it more. This much is essentially inarguable. But I still take issue with one key thing that you have said.
Rahvin writes: "Four" is still a subjective concept, it only exists in your head, it's a symbol that represents something in reality. I would suggest that mathematical entities such as 4 and Pi can be said to exist objectively. In fact I would suggest that they arguably have a greater claim to objective existence than things like apples. Now of course there are all sorts of provisos to this. Of course we take linguistic shortcuts regarding the necessarily subjective nature of ALL experience and ALL concepts. But it would be taking things to the absurd to conclude that apples don’t objectively exist because of these limitations wouldn’t it? We can hopefully both agree that apples do indeed exist (aforementioned provisos implicit). So the question is — Does Pi exist? It obviously doesn’t exist in the same physical sense that apples do. But I think you can very meaningfully say it exists as a property of reality. I think to say that 4 or Pi only exist subjectively is no more sensible than saying that my conviction in the existence of apples is a subjective belief.
Straggler writes: We would presumably agree that any suitably advanced civilisation would be aware of this relationship
Rahvin writes: Agreed I put it to you that this relationship is therefore not something that we (or any other suitably advanced alien civilisation that may be out there) have invented. I put it to you that this relationship is instead an aspect of objective reality that we have discovered.In short I put it to you that this relationship objectively exists in some sense that is independent of the minds conceiving it. What do you think? Rahvin writes: You're taking this as part of the never-ending idiocy of "subjectivity vs. objectivity." But I'm not RAZD. I think the sort of subjective-objective shenanigans we have both engaged in with RAZD elsewhere are different and not overly relevant to anything being discussed here. I think the link between reality and maths as the language of logic is fascinating and very possibly tells us something rather deep about the nature of reality itself.
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Straggler Member Posts: 10333 From: London England Joined: |
Good post. The disagreement is getting smaller. But it hasn’t vanished yet
Straggler writes: I put it to you that this relationship is therefore not something that we (or any other suitably advanced alien civilisation that may be out there) have invented. I put it to you that this relationship is instead an aspect of objective reality that we have discovered. In short I put it to you that this relationship objectively exists in some sense that is independent of the minds conceiving it. What do you think? Rahvin writes: We invented the mathematical symbols and even the relationship to represent something we observe that we did not invent. The reason I chose that relationship is that I don’t see how it can possibly be derived from empirical observation. It is a mathematical relationship. So what observations are you suggesting it is based on?
Rahvin writes: Assuming our measurement of that real relationship is accurate , any independent observer capable of taking similarly accurate measurements would arrive at the same representative relationship expressed in the equation, even if the symbols used were different. What accurate measurements are you suggesting are required in order to derive that particular relationship? Whether Pi has been calculated to 10 decimal places or 10 million decimal places doesn’t make any real difference to the truth of this relationship does it?
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Straggler Member Posts: 10333 From: London England Joined: |
Rahvin writes: That's basically my point. If we can only calculate pi to 10 decimals, we're less accurate than if we can calculate it to 100, or 1000. Pi is a geometric entity relating to perfect circles. Perfect circles don't physically exist. The value of pi to 39 decimal places will tell you the radius of the circumference of the known universe to an accuracy of the radius of a hydrogen atom. Try empirically measuring that. The last time I looked we had calculated pi to about 5 trillion decimal places. And yet any similarly advanced alien civilisation unencumbered by human cultural or psychological baggage but with comparable computational power at their disposal could agree this same entity to this same degree of astonishing accuracy (differences in nomenclature implicit) The idea that Pi objectively exists is not limited to what can be physically/empirically observed or measured. In fact it has little to do with physical measurements or observations at all.
Rahvin writes: Mathematics is essentially a language of symbols that represent observations in the "real" world. But that's the question here. Is that true? Both the value of Pi beyond measurable accuracy and the relationship are objectively true. Yet these things cannot be derived empirically from the physical world.
Wiki on philosophy of mathematics writes: Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. You seem to disagree. You seem to be taking a much more empirical approach. But are you simply assuming that anything which can be called "real" (i.e. actually exist) must be exist in some physical sense or is there some definite reason to take the empirical stance that you seem to be advocating?
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Straggler Member Posts: 10333 From: London England Joined: |
NN writes: As for the rest of your comment, I'm still on the fence about whether numbers exist outside of the mind, but I'm leaning towards believing that they do. I think a lot of people will intuitively go along with the idea that numbers objectively exist in some sense because numbers do relate so well to the physical world. But the notion that the objectivity of mathematical entities is necessarily dependent on aspects of physical reality is rather limiting and leads to some strange conclusions . For example we all seem to agree that 4 can be said to exist independently of conceiving minds. But what about infinity? Many would be less willing to conclude that infinity exists in the same sense that 4 does because it seems to lack any similar physical basis. But if 4 does objectively exist because it has a physical basis but infinity doesn’t then logically there must be some integer that is the largest number to have a physical basis (i.e. the total number of elementary particles in the universe or something like that). But It seems a bit absurd to suggest that some integers do objectively exist whilst others don’t.. Anyway - I am sort of arguing the mathematical realist case in this thread but in truth I don't know what I think either.
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Straggler Member Posts: 10333 From: London England Joined: |
Chuck writes: Are you guys trying to figure out if math is objective/subjective? Not really. I think the three of us agree that maths is objective. So then it becomes an exercise in philosophical navel gazing about the nature of existence and whether the objectivity of maths means that mathematical entities can be said to "exist" in some sense that is independent of minds. Are mathematical entities aspects of objective reality - That sort of thing. Or - To put it another way - Do we invent or discover maths?
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Straggler Member Posts: 10333 From: London England Joined: |
Dr A writes: Hmm ... I'd say that we discover math and that mathematical entities don't exist. We are not discovering things, which exist, but facts, which are true. If these facts are properties of reality then they are "things". Not physical "things". But "things" which can meaningfully be said to "exist" and thus be discovered. But the fact that I feel the need to splatter inverted commas all over the place when writing that should tell you that I am not entirely convinced of that myself.
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Straggler Member Posts: 10333 From: London England Joined: |
Chuck writes: If no one is around to observe it does math still exist? Or is it soley a human invention? Chuck writes: ....is math a product of our environment. Chuck writes: Am I anywhere in the ballpark of what you guys are talking about? Yeah - Sort of. Rahvin was making the case for maths having a purely empirical basis. I am sort of putting forward the case for mathematical realism.
Wiki on mathematical realism writes: Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. Dr A is making a distinction between facts that can be discovered and things which can be discovered. I suspect the difference between him and I is a semantic one based on whether or not facts are "things" that can be said to "exist". Unfortunately the philosophical area of ontology is fraught with such distinctions and as a result is mostly navel gazing nonsense. But it can still be "fun"......
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Straggler Member Posts: 10333 From: London England Joined: |
Dr A writes: This is a fact (which is true). Is there a thing (which exists) corresponding to the fact? Yes. Logic. Does logic exist? Is logic a property of reality?
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Straggler Member Posts: 10333 From: London England Joined: |
Dr A writes: Well, that's a bit broad. Maybe so. But that, I suspect, is what all this boils down to. If we discover rather than invent maths then it is because ultimately maths is our method of exploring the logic innate in reality. Or something like that.
Dr A writes: Would you say that the "thing" corresponding to Pythagoras' theorem was math? To Pythagoras theorem specifically I guess the "thing" we are specifically applying logic to is the geometric form known as a triangle. But in your Snufflepuff example there was nothing that makes it specific to Snufflepuffs. In fact you would be better off generalising your statement to something like: If ALL X are Y and ALL Y are Z Then ALL X are Z A simple and generic statement of pure logic that applies to the frungibleness of snufflepuffs or anything else which meets the same logical criteria.
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Straggler Member Posts: 10333 From: London England Joined: |
2 snufflepuffs + 2 snufflepuffs equals 4 snufflepuffs.
The truth of this isn't dependent on snufflepuffs existing in any sense whatsoever. Nor is the logic in your example dependent on the existence of snufflepuffs. So I think we can meaningfully say that these logical relationships (2+2=4 and "If ALL X are Y and ALL Y are Z Then ALL X are Z") exist without invoking any Platonic snufflepuffs.
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