Recovery Board
: RfM
Recovery from Mormonism (RfM) discussion forum.
The following is a continuation of:
http://exmormon.org/phorum/read.php?2,821693,821693#msg-821693
which began here:
http://exmormon.org/phorum/read.php?2,819754,819754#msg-819754
Henry, please forgive me for the format of the following. I restate your words not because you have been unclear but because my abilities for comprehension are wanting. If you (or anyone) see that I have restated you unfairly, kindly point it out to me. Thank you. Also, I hope you don't mind my more or less ignoring the questions you pose to aid my thinking. You seem to wish for me to defend my belief in Universals but I already stated that I would be loath to argue for it.
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Here are some responses to comments by Human in “The Nature of Mathematics” thread.
[HUMAN] “2+2=4 is true, whether it is described in a Hindu-Arabic script or a Roman script (ii+ii=iv) or something else. Language is a vehicle that carries something, a vessel for "content". Erase the language (vehicle) from mankind and I think we would be hard-pressed to claim that suddenly 2+2 didn't still = 4: specifically, what "2" stands for, what "+" stands for, what "=" stands for, and what "4" stands for. If this is true, then where exactly does this truth exist?”
“archytas's example above to MJ is exactly right. Pi is not arbitrary, it exists apart from the numerals that "carry" it. Math is a series of discoveries, not inventions.”
[RESPONSE] What is being confused here is the distinction between mathematics as a language and mathematics as a description of the world. And, with “language” we include the mental states that they are associated with. With some universals, like “love,” language as the spoken written word must be separated from its accompanying denoted mental state. Let’s discuss this.
Of course, the language of mathematics was invented by humans. However, the fact that the physical world is “mathematical,” i.e. that it can be described by complex mathematical relationships is, of course, a feature of the world (universe) that is independent of language. Thus, the underlying mathematical structure of reality remains to be explained, even if we can explain “mathematics” proper as a human language game.
____________________________________________________________________________________
1. Math is a man-made language game used to describe the world.
2. That which Math describes in the physical world is "a feature of the world (universe) that is independent of language."
3. Language, whether spoken or written, must be separated from the mental state which accompanies it. You use the word "love" as an example. So the word "love" and the "mental state" which this word stands for must be separated.
4. Although "mathematics" is a language game, the "underlying structure of reality" matches it. This needs to be explained.
My response:
On points 1 and 2 I agree and is exactly what I said. On your 3rd point I'm not following you. By talking about "love" as a signifier for a "mental state" you are obviously talking about a particular instance of "love" and not Love as a Universal. On your last point, there isn't anything to wonder at. Language is *supposed* to match the reality it was invented to describe. Just as pi seems to match the "underlying structure of reality," the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?
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[HUMAN] “But I have to ask . . . if we are willing to give ontological status to mathematical objects why not also to other conceptual objects? If our minds *discovered* Pi rather than invented it, why cannot we also say that our hearts *discovered* Love rather than invented it? Same with Justice, same with Mercy same with etc.............(the implication for recovery from Mormonism is clear here, this leads to, yes, God.)”
[RESPONSE] Universals are not all created equal with respect to their relationship to the external world, as determined by “evidence.” With each one it must be asked what does the term in the language denote? Clearly some such terms, e.g. “game” are nothing more that human constructs invented for convenience of discourse. There is no ideal, Platonic “game” existing somewhere that our human term relates to in some way. But what about “mathematics,” and “love.” What do they denote?
Now, if we take the term “mathematics,” we are in a bit of a dilemma. Although this term certainly carries with it a purely human language aspect, including human derived axioms, rules, theorems, etc., we also find that the world behaves in accordance with those very mathematical principles that we have described in our language. Moreover, sometimes we discover the “rules” by studying the structure of the physical world. Moreover, geometrical figures, like the circle, can be mathematically idealized through concepts like “pi,” the properties of which seem to transcend simple human construct. After all, human beings did not invent the truth that the circumference of a circle is related to the number pi and its radius; they discovered this.
Does this mean we have not invented mathematics after all? It certainly means that there is something special about the structure and order of reality that we did not invent. As such, the temptation, right or wrong, is great to conclude that “mathematics” denotes something over and above our language conventions. Again, the mathematical structure of the world does not disappear with the disappearance of human language or the human mind, even though our mathematical terms do. On the other hand, a proposed Platonic universal “games” does seem to disappear.
Considering “love,” it too is, of course, is a word of convenience in human language invented to denote a certain emotion; a mental state. (not a brain state!) If there were no humans (or more broadly minds) the notion of “love” would seem to disappear. So, if we want to claim that “love” carries ontological status, there are two options: First, we might claim that love carries its ontological status as a mental “entity,” that arises from brain states. Or, second, we might make the more radical claim that love is something ontologically separate from mind; i.e. that the mind taps into. But, if that is the claim, what could it possibly be? Here we seem to have crossed over into pure mysticism. We know that consciousness exists. We know that mental states exist. And we know that love exists as a mental state. But that does not justify a view that “love” is a Platonic universal.
As a dualist, who believes that consciousness is ontologically separate from the brain that instantiates it, I am sympathetic to the first suggestion. Perhaps love is an aspect or property of mind that somehow has ontological status separate from both brains and consciousness. But here again, when we try to unpack this notion we get into immediate trouble. We have enough difficulty with consciousness itself, do we want to add love and the other emotions as well. Why can’t the ontological status of love simply be as aspect or property of mind?
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1. Evidence suggests (later amended with "reason") that not all Universals match up equally with the external world.
2. We must weigh and consider that which is denoted by the term we have invented for each Universal.
3. The term "mathematics" causes a dilemma: it is on the one hand "a purely human language aspect," and on the other it is evident that, "the world behaves in accordance" with it.
4. The circumference of a circle is related to the number pi and its radius. This is not an invented fact, it was discovered. "pi" is concept which "seems to transcend simple human construct."
5. Reality is not invented by humans. That "pi" is a concept *and* seems to fit the uninvented reality that pi=C/d means there is "something special about the structure and order of reality." Therefore, we are tempted to conclude that "mathematics" denotes something beyond language.
6. Sans human language and the human mind, the mathematical structure of the world still exists.
7. Sans human language and the human mind, the Universal "games" does not exist.
My response:
You begin by asserting that reason entails us to conclude that not all Universals match up equally with the external world. You then restate where I began, that mathematical objects exist apart from minds to apprehend them. Pi is the concept/reality archytas introduced and I affirmed. Then you conclude by saying that "games" as a universal fails to exist sans humans. What's missing in all of this of course is the reason!
*Why* does "games" fail and "maths" succeed? You don't say why. Just like pi, the concept "games" on the face of it matches very well to that which it denotes in the real world. That is what language is supposed to do.
(Of course, there is no Universal "games", or "mathematics" for that matter. Game plural denotes a set of particulars. The Universal Game would be that which all instances of games share. Like Socrates interrogating his interlocutor about the difference between a list of virtues and Virtue --that which all virtues share in, which makes them a particular instance of Virtue-- we may wonder about the difference between a list of games and Game --that which all games share in, which makes them a particular instance of Game.)
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[HUMAN “I acknowledge that I am placing something into that "gaping hole in our understanding of reality" that is "a metaphysical conclusion unsupported by any evidence." But as you've said many times before, a materialist assumption which precludes the possibility of a metaphysical reality is no less an assumption.”
[RESPONSE] Well, you need to be careful here. Possibility is one thing; evidence is another. There is abundant evidence, in my view, that materialism, as a scientific worldview, is false. That I have said many times. But that does not leave us free to invent all sorts of metaphysical objects, or deem conventions of language as denoting the reality of our pet universals. Where to draw the line is, of course, difficult. But mathematics is on the credible side of this ledger, whereas love is on the more speculative, mystical side, in my view, simply because, as stated, mathematics is closely tied to the physical world, whereas love (the emotion) is dependent upon mind, which is itself ontologically elusive. This, of course, does not mean that love does not exist as a human emotion. It simply means that it probably does not exist outside of, and independent of, such emotions, and the minds that experience them.
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1. Materialism as a scientific worldview is false.
2. This, however, is not an invitation to invent metaphysical objects and declare them as existing.
3. Math highly correlates with the real world and thus credibly exists apart from the minds that conceive it.
4. Love is an emotion and is thus dependent upon mind, and so does not credibly exist apart from the mind that conceives it.
My response:
Somehow I sense that you dodge the question.
We already began with the proposition that mathematical objects like pi exist, are abstract and are not material and therefore are not sensible. As others said, in the real world there are no perfect circles to be sensed just as there is no one thing to be counted. Pi and "one" are abstract. Surely they exist. But *where* do they exist? is the question! You seem to be saying that pi exists in the "real world". But surely this is not the case, and if it was then it would by definition not be a Universal.
The question really isn't about the "real world." The question is purely philosophical.
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[HUMAN] “But I still can't help *feeling* that poetry is a vehicle which carries a content that exists apart from the words that convey it. *Convey* here is an interesting, pregnant word.”
[COMMENT] Yes, but what is this “content” that is being carried or conveyed? I would say that whatever it is, it resides in consciousness, and “the self” of those who experience it, whatever that turns out to be. Call it the soul, if you will. It is, for me, an experience that strikes to the heart of who we are as conscious beings. But we do not have to insist that this content is part of the world separate from the human beings who experience it. Surely, consciousness, love, the self, etc. are not just words; they denote “something.” But the ontological status of what they denote is tied, it seems to me, to our own ontological status as mental (an autonomous) beings, of which we do have abundant evidence.
Finally, based upon some of the responses to the original post, some simplistically ignore the fact that the universe is remarkably ordered in accordance with mathematical principles. True, humans may have invented mathematics proper even if the world was not so ordered; and the world would be so ordered even if there were no humans to invent mathematics proper. But it is a huge error to conclude that there is nothing metaphysically significant by the fact that the world is fantastically ordered in mathematical ways, notwithstanding human beings. And the question remains; Why? This question relates to the cosmological anthropic principle; i.e. why does the universe appear to be fine-tuned for life. The even more fundamental question here is, Why is the universe in fact ordered in conformance with mathematical laws.
______________________________________________________________________________
1. The "content" of poetical language resides in the mind, but does not exist apart from the minds who experience it.
2. Words denote "something", but the being of that "something" exists only as a mental state in those who use them.
3. We exist. But words exist only as far as we exist.
4. Mathematical principles correlate fantastically highly with the world. Mathematics is an invented language. Sans humans mathematical principles would still correlate fantastically highly with the world. There is something metaphysical about the world because of this.
5. We must ask, *why* do mathematical laws seem to conform so highly with the universe?
My response:
I simply am not following you, Henry. Surely "meadow" "grove" and "stream" denote "something" that exists as something more than mere mental states, right? What else could your mathematical principles correspond to other than real streams, groves and meadows?
But if you are willing to say (since you affirm the abstract existence of pi) that all circles partake in a common nature (universal) we call Circle, why are you not also willing to say that all meadows partake in a common nature we can call Meadow? That is my question.
Conclusion:
Henry, please correct me if I simplify you unfairly. Everything you wrote seems to boil down to this: the perfect circle and pi have a metaphysical existence because we can observe imperfect circles in the real world that highly correlate with pi. Love, on the other hand, does not have a metaphysical existence….because… it only exists in the minds of those who feel it. The materialist of course would ask how pi does not also only exist in the minds who perceive it?
You plead a special case for the language of mathematics but deny the same for the language of words. Why? That is my question. You answer that the made-up language of math correlates very highly with the observable world. But does not the made-up language of words also highly correlate to the observable world? After all, it wouldn't be of much use if it didn't. You say pi and I say Shakespeare. You agree that a list of particular circles share in a Universal called Circle but deny that a list of virtues can also share in a Universal called Virtue. Why? I didn't see an argument.
The board's materialists respond consistently: no metaphysical realms, period. They (I suppose) think that the idea of 2 the idea of + the idea of 2 the idea of = the idea of 4 does not exist anywhere outside human consciousness. You say that it does, presumably because we can take two sticks and place them beside to other sticks and count them and it will always count to 4. The materialist simply says this is imposing our language on an arbitrary observance, for there are not real 2 sticks and 2 sticks. There are only many particular instances of sticks. Nothing more.
I say 2+2=4 exists, is abstract and is true independent of minds to think it. I ask *where* this abstract exists since it does so not in space and time. I speculate that its existence is related somehow to the world of Universals.
Universals exist (if they do) independent of mind, space, time and material. Universals exist 'someplace' different from thoughts and feelings and physical objects. In fact "exist" is the wrong word. Universals have their *being* elsewhere and by definition cannot exist in the world of sense. The world of Universals is a world of being sans change, whereas everything else exists in a fleeting, ever changing world.
An aside:
This whole discussion began with Uncle Dale wondering if Plato led us astray. Whether Socrates is asking about not a list of courages but Courage itself (Laches), not a list of pieties but Piety itself (Euthyphro), not a list of beautiful things but Beauty itself (Cratylus), not a list of virtues but Virtue itself (Meno), not a list of true, good and beautiful things but Truth, Beauty and Goodness itself (Republic), whatever Socrates is asking about, he always goes first, he's the one asking! He's not playing chess, he's playing Tic Tac Toe! If he goes first he will always win or at the very least pull a draw. Clever.
Last night I looked again into Plato's Parmenides for an example of when Socrates pulls a draw instead of a win. Most interestingly, Plato in this Dialogue is representing a much younger Socrates at the beginning of his formulation of his theory of forms, of which he asks Parmenides and Zeno (Parmenides's student and master of paradox) to test. They test it. They seem to reduce his theory of Forms to an absurdity. Socrates admits to not having an adequate answer, and then for the rest of the Dialogue he demonstrates that their philosophy can be reduced to an even worse absurdity. The Dialogue just kind of hangs suspended on this point at the end.
Plato's Parmenides aside, the idea of Forms continued through Hellenistic neoplatonism of which early Christian thinkers found congenial. After being eclipsed somewhat in the High Middle Ages with the influx of Aristotle it found vigorous support in the Italian Renaissance with wondrously abundant results. Last night I searched frantically for my little beat-up volume of Bertrand Russell's Problems. I'm almost certain I have sketched on the inside of both the front and back covers my reasons for believing in Universals. Alas, I could not find it! (Half my library is boxed as we prepare to move in May or June.) But you said I should refrain from getting bogged down in philosophy so perhaps that was for the best.
Okay….that's a long enough lunch. Cheers.
Human
http://exmormon.org/phorum/read.php?2,821693,821693#msg-821693
which began here:
http://exmormon.org/phorum/read.php?2,819754,819754#msg-819754
Henry, please forgive me for the format of the following. I restate your words not because you have been unclear but because my abilities for comprehension are wanting. If you (or anyone) see that I have restated you unfairly, kindly point it out to me. Thank you. Also, I hope you don't mind my more or less ignoring the questions you pose to aid my thinking. You seem to wish for me to defend my belief in Universals but I already stated that I would be loath to argue for it.
_____________________________________________________________________________________
Here are some responses to comments by Human in “The Nature of Mathematics” thread.
[HUMAN] “2+2=4 is true, whether it is described in a Hindu-Arabic script or a Roman script (ii+ii=iv) or something else. Language is a vehicle that carries something, a vessel for "content". Erase the language (vehicle) from mankind and I think we would be hard-pressed to claim that suddenly 2+2 didn't still = 4: specifically, what "2" stands for, what "+" stands for, what "=" stands for, and what "4" stands for. If this is true, then where exactly does this truth exist?”
“archytas's example above to MJ is exactly right. Pi is not arbitrary, it exists apart from the numerals that "carry" it. Math is a series of discoveries, not inventions.”
[RESPONSE] What is being confused here is the distinction between mathematics as a language and mathematics as a description of the world. And, with “language” we include the mental states that they are associated with. With some universals, like “love,” language as the spoken written word must be separated from its accompanying denoted mental state. Let’s discuss this.
Of course, the language of mathematics was invented by humans. However, the fact that the physical world is “mathematical,” i.e. that it can be described by complex mathematical relationships is, of course, a feature of the world (universe) that is independent of language. Thus, the underlying mathematical structure of reality remains to be explained, even if we can explain “mathematics” proper as a human language game.
____________________________________________________________________________________
1. Math is a man-made language game used to describe the world.
2. That which Math describes in the physical world is "a feature of the world (universe) that is independent of language."
3. Language, whether spoken or written, must be separated from the mental state which accompanies it. You use the word "love" as an example. So the word "love" and the "mental state" which this word stands for must be separated.
4. Although "mathematics" is a language game, the "underlying structure of reality" matches it. This needs to be explained.
My response:
On points 1 and 2 I agree and is exactly what I said. On your 3rd point I'm not following you. By talking about "love" as a signifier for a "mental state" you are obviously talking about a particular instance of "love" and not Love as a Universal. On your last point, there isn't anything to wonder at. Language is *supposed* to match the reality it was invented to describe. Just as pi seems to match the "underlying structure of reality," the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?
_____________________________________________________________________________________
[HUMAN] “But I have to ask . . . if we are willing to give ontological status to mathematical objects why not also to other conceptual objects? If our minds *discovered* Pi rather than invented it, why cannot we also say that our hearts *discovered* Love rather than invented it? Same with Justice, same with Mercy same with etc.............(the implication for recovery from Mormonism is clear here, this leads to, yes, God.)”
[RESPONSE] Universals are not all created equal with respect to their relationship to the external world, as determined by “evidence.” With each one it must be asked what does the term in the language denote? Clearly some such terms, e.g. “game” are nothing more that human constructs invented for convenience of discourse. There is no ideal, Platonic “game” existing somewhere that our human term relates to in some way. But what about “mathematics,” and “love.” What do they denote?
Now, if we take the term “mathematics,” we are in a bit of a dilemma. Although this term certainly carries with it a purely human language aspect, including human derived axioms, rules, theorems, etc., we also find that the world behaves in accordance with those very mathematical principles that we have described in our language. Moreover, sometimes we discover the “rules” by studying the structure of the physical world. Moreover, geometrical figures, like the circle, can be mathematically idealized through concepts like “pi,” the properties of which seem to transcend simple human construct. After all, human beings did not invent the truth that the circumference of a circle is related to the number pi and its radius; they discovered this.
Does this mean we have not invented mathematics after all? It certainly means that there is something special about the structure and order of reality that we did not invent. As such, the temptation, right or wrong, is great to conclude that “mathematics” denotes something over and above our language conventions. Again, the mathematical structure of the world does not disappear with the disappearance of human language or the human mind, even though our mathematical terms do. On the other hand, a proposed Platonic universal “games” does seem to disappear.
Considering “love,” it too is, of course, is a word of convenience in human language invented to denote a certain emotion; a mental state. (not a brain state!) If there were no humans (or more broadly minds) the notion of “love” would seem to disappear. So, if we want to claim that “love” carries ontological status, there are two options: First, we might claim that love carries its ontological status as a mental “entity,” that arises from brain states. Or, second, we might make the more radical claim that love is something ontologically separate from mind; i.e. that the mind taps into. But, if that is the claim, what could it possibly be? Here we seem to have crossed over into pure mysticism. We know that consciousness exists. We know that mental states exist. And we know that love exists as a mental state. But that does not justify a view that “love” is a Platonic universal.
As a dualist, who believes that consciousness is ontologically separate from the brain that instantiates it, I am sympathetic to the first suggestion. Perhaps love is an aspect or property of mind that somehow has ontological status separate from both brains and consciousness. But here again, when we try to unpack this notion we get into immediate trouble. We have enough difficulty with consciousness itself, do we want to add love and the other emotions as well. Why can’t the ontological status of love simply be as aspect or property of mind?
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1. Evidence suggests (later amended with "reason") that not all Universals match up equally with the external world.
2. We must weigh and consider that which is denoted by the term we have invented for each Universal.
3. The term "mathematics" causes a dilemma: it is on the one hand "a purely human language aspect," and on the other it is evident that, "the world behaves in accordance" with it.
4. The circumference of a circle is related to the number pi and its radius. This is not an invented fact, it was discovered. "pi" is concept which "seems to transcend simple human construct."
5. Reality is not invented by humans. That "pi" is a concept *and* seems to fit the uninvented reality that pi=C/d means there is "something special about the structure and order of reality." Therefore, we are tempted to conclude that "mathematics" denotes something beyond language.
6. Sans human language and the human mind, the mathematical structure of the world still exists.
7. Sans human language and the human mind, the Universal "games" does not exist.
My response:
You begin by asserting that reason entails us to conclude that not all Universals match up equally with the external world. You then restate where I began, that mathematical objects exist apart from minds to apprehend them. Pi is the concept/reality archytas introduced and I affirmed. Then you conclude by saying that "games" as a universal fails to exist sans humans. What's missing in all of this of course is the reason!
*Why* does "games" fail and "maths" succeed? You don't say why. Just like pi, the concept "games" on the face of it matches very well to that which it denotes in the real world. That is what language is supposed to do.
(Of course, there is no Universal "games", or "mathematics" for that matter. Game plural denotes a set of particulars. The Universal Game would be that which all instances of games share. Like Socrates interrogating his interlocutor about the difference between a list of virtues and Virtue --that which all virtues share in, which makes them a particular instance of Virtue-- we may wonder about the difference between a list of games and Game --that which all games share in, which makes them a particular instance of Game.)
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[HUMAN “I acknowledge that I am placing something into that "gaping hole in our understanding of reality" that is "a metaphysical conclusion unsupported by any evidence." But as you've said many times before, a materialist assumption which precludes the possibility of a metaphysical reality is no less an assumption.”
[RESPONSE] Well, you need to be careful here. Possibility is one thing; evidence is another. There is abundant evidence, in my view, that materialism, as a scientific worldview, is false. That I have said many times. But that does not leave us free to invent all sorts of metaphysical objects, or deem conventions of language as denoting the reality of our pet universals. Where to draw the line is, of course, difficult. But mathematics is on the credible side of this ledger, whereas love is on the more speculative, mystical side, in my view, simply because, as stated, mathematics is closely tied to the physical world, whereas love (the emotion) is dependent upon mind, which is itself ontologically elusive. This, of course, does not mean that love does not exist as a human emotion. It simply means that it probably does not exist outside of, and independent of, such emotions, and the minds that experience them.
______________________________________________________________________________
1. Materialism as a scientific worldview is false.
2. This, however, is not an invitation to invent metaphysical objects and declare them as existing.
3. Math highly correlates with the real world and thus credibly exists apart from the minds that conceive it.
4. Love is an emotion and is thus dependent upon mind, and so does not credibly exist apart from the mind that conceives it.
My response:
Somehow I sense that you dodge the question.
We already began with the proposition that mathematical objects like pi exist, are abstract and are not material and therefore are not sensible. As others said, in the real world there are no perfect circles to be sensed just as there is no one thing to be counted. Pi and "one" are abstract. Surely they exist. But *where* do they exist? is the question! You seem to be saying that pi exists in the "real world". But surely this is not the case, and if it was then it would by definition not be a Universal.
The question really isn't about the "real world." The question is purely philosophical.
_____________________________________________________________________________
[HUMAN] “But I still can't help *feeling* that poetry is a vehicle which carries a content that exists apart from the words that convey it. *Convey* here is an interesting, pregnant word.”
[COMMENT] Yes, but what is this “content” that is being carried or conveyed? I would say that whatever it is, it resides in consciousness, and “the self” of those who experience it, whatever that turns out to be. Call it the soul, if you will. It is, for me, an experience that strikes to the heart of who we are as conscious beings. But we do not have to insist that this content is part of the world separate from the human beings who experience it. Surely, consciousness, love, the self, etc. are not just words; they denote “something.” But the ontological status of what they denote is tied, it seems to me, to our own ontological status as mental (an autonomous) beings, of which we do have abundant evidence.
Finally, based upon some of the responses to the original post, some simplistically ignore the fact that the universe is remarkably ordered in accordance with mathematical principles. True, humans may have invented mathematics proper even if the world was not so ordered; and the world would be so ordered even if there were no humans to invent mathematics proper. But it is a huge error to conclude that there is nothing metaphysically significant by the fact that the world is fantastically ordered in mathematical ways, notwithstanding human beings. And the question remains; Why? This question relates to the cosmological anthropic principle; i.e. why does the universe appear to be fine-tuned for life. The even more fundamental question here is, Why is the universe in fact ordered in conformance with mathematical laws.
______________________________________________________________________________
1. The "content" of poetical language resides in the mind, but does not exist apart from the minds who experience it.
2. Words denote "something", but the being of that "something" exists only as a mental state in those who use them.
3. We exist. But words exist only as far as we exist.
4. Mathematical principles correlate fantastically highly with the world. Mathematics is an invented language. Sans humans mathematical principles would still correlate fantastically highly with the world. There is something metaphysical about the world because of this.
5. We must ask, *why* do mathematical laws seem to conform so highly with the universe?
My response:
I simply am not following you, Henry. Surely "meadow" "grove" and "stream" denote "something" that exists as something more than mere mental states, right? What else could your mathematical principles correspond to other than real streams, groves and meadows?
But if you are willing to say (since you affirm the abstract existence of pi) that all circles partake in a common nature (universal) we call Circle, why are you not also willing to say that all meadows partake in a common nature we can call Meadow? That is my question.
Conclusion:
Henry, please correct me if I simplify you unfairly. Everything you wrote seems to boil down to this: the perfect circle and pi have a metaphysical existence because we can observe imperfect circles in the real world that highly correlate with pi. Love, on the other hand, does not have a metaphysical existence….because… it only exists in the minds of those who feel it. The materialist of course would ask how pi does not also only exist in the minds who perceive it?
You plead a special case for the language of mathematics but deny the same for the language of words. Why? That is my question. You answer that the made-up language of math correlates very highly with the observable world. But does not the made-up language of words also highly correlate to the observable world? After all, it wouldn't be of much use if it didn't. You say pi and I say Shakespeare. You agree that a list of particular circles share in a Universal called Circle but deny that a list of virtues can also share in a Universal called Virtue. Why? I didn't see an argument.
The board's materialists respond consistently: no metaphysical realms, period. They (I suppose) think that the idea of 2 the idea of + the idea of 2 the idea of = the idea of 4 does not exist anywhere outside human consciousness. You say that it does, presumably because we can take two sticks and place them beside to other sticks and count them and it will always count to 4. The materialist simply says this is imposing our language on an arbitrary observance, for there are not real 2 sticks and 2 sticks. There are only many particular instances of sticks. Nothing more.
I say 2+2=4 exists, is abstract and is true independent of minds to think it. I ask *where* this abstract exists since it does so not in space and time. I speculate that its existence is related somehow to the world of Universals.
Universals exist (if they do) independent of mind, space, time and material. Universals exist 'someplace' different from thoughts and feelings and physical objects. In fact "exist" is the wrong word. Universals have their *being* elsewhere and by definition cannot exist in the world of sense. The world of Universals is a world of being sans change, whereas everything else exists in a fleeting, ever changing world.
An aside:
This whole discussion began with Uncle Dale wondering if Plato led us astray. Whether Socrates is asking about not a list of courages but Courage itself (Laches), not a list of pieties but Piety itself (Euthyphro), not a list of beautiful things but Beauty itself (Cratylus), not a list of virtues but Virtue itself (Meno), not a list of true, good and beautiful things but Truth, Beauty and Goodness itself (Republic), whatever Socrates is asking about, he always goes first, he's the one asking! He's not playing chess, he's playing Tic Tac Toe! If he goes first he will always win or at the very least pull a draw. Clever.
Last night I looked again into Plato's Parmenides for an example of when Socrates pulls a draw instead of a win. Most interestingly, Plato in this Dialogue is representing a much younger Socrates at the beginning of his formulation of his theory of forms, of which he asks Parmenides and Zeno (Parmenides's student and master of paradox) to test. They test it. They seem to reduce his theory of Forms to an absurdity. Socrates admits to not having an adequate answer, and then for the rest of the Dialogue he demonstrates that their philosophy can be reduced to an even worse absurdity. The Dialogue just kind of hangs suspended on this point at the end.
Plato's Parmenides aside, the idea of Forms continued through Hellenistic neoplatonism of which early Christian thinkers found congenial. After being eclipsed somewhat in the High Middle Ages with the influx of Aristotle it found vigorous support in the Italian Renaissance with wondrously abundant results. Last night I searched frantically for my little beat-up volume of Bertrand Russell's Problems. I'm almost certain I have sketched on the inside of both the front and back covers my reasons for believing in Universals. Alas, I could not find it! (Half my library is boxed as we prepare to move in May or June.) But you said I should refrain from getting bogged down in philosophy so perhaps that was for the best.
Okay….that's a long enough lunch. Cheers.
Human
I am going to have to respond to each set of points separately, and hope time permits completion.
[HUMAN]
On points 1 and 2 I agree and is exactly what I said. On your 3rd point I'm not following you. By talking about "love" as a signifier for a "mental state" you are obviously talking about a particular instance of "love" and not Love as a Universal. On your last point, there isn't anything to wonder at. Language is *supposed* to match the reality it was invented to describe. Just as pi seems to match the "underlying structure of reality," the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?
[RESPONSE]
Regarding point 3, the intent was to point out that language is one thing, but mind is another. “Love” (in quotes) is a concept in a language that denotes an emotional experience of a particular sort, which is a mental state. The fact that human beings invent words to denote their mental states is not as interesting as the mental state itself. A universal is a general term, i.e. a word in a language. The question in this post is whether love as a universal term (the emotion, or whatever else it might be) can be identified as a Platonic idealized “entity” having independent existence of some sort, or is only associated with, and generalized from, individual instances of love. However, in neither case are we talking about the word “love,” but rather the emotion, or whatever metaphysical “entity” idealizes it. Similarly, when considering "redness" we are not talking about the word, but whatever entity "redness" denotes in the Platonic realm. In this case, because love (the emotional experience) is entirely subjective, and only loosely connected to physical reality, it seems to me that unlike “mathematics,” which on some level appears to be a core essence of physical reality, it is more difficult to posit a metaphysical idealization.
I do not think there is any question that language is a practical invention, and a general term in a language is invented to denote particulars, not a Platonic universal. Plato, and realism generally posits the metaphysical existence of the universal in an attempt to explain what the essence is that allows individuals to have certain properties in common. Plato’s metaphysics are very archaic in this regard, and most universals are not considered to be anything but language devices. Mathematics is an exception.
Your comment: “Just as pi seems to match the ‘underlying structure of reality,’ the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?” seems off base to me. The physical relationships denoted by Pi are encompassed by the structure of the natural world. As such, Pi does not merely match reality, what it denotes is imbedded in reality. Can you say the same about the Complete Shakespeare? Or love? The fact that Shakespeare was a human being, and as such just as much part of reality as anything else, misses the point. We are not talking about Shakespeare as an entity, we are taking about the works of Shakespeare, i.e. language only. Now maybe there is something transcendent about such works; something to idealize. But what ontological form would that take? It just seems too forced. A response to Shakespeare, or poetry, just seems to be only an individual emotional response, and nothing more.
[HUMAN]
On points 1 and 2 I agree and is exactly what I said. On your 3rd point I'm not following you. By talking about "love" as a signifier for a "mental state" you are obviously talking about a particular instance of "love" and not Love as a Universal. On your last point, there isn't anything to wonder at. Language is *supposed* to match the reality it was invented to describe. Just as pi seems to match the "underlying structure of reality," the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?
[RESPONSE]
Regarding point 3, the intent was to point out that language is one thing, but mind is another. “Love” (in quotes) is a concept in a language that denotes an emotional experience of a particular sort, which is a mental state. The fact that human beings invent words to denote their mental states is not as interesting as the mental state itself. A universal is a general term, i.e. a word in a language. The question in this post is whether love as a universal term (the emotion, or whatever else it might be) can be identified as a Platonic idealized “entity” having independent existence of some sort, or is only associated with, and generalized from, individual instances of love. However, in neither case are we talking about the word “love,” but rather the emotion, or whatever metaphysical “entity” idealizes it. Similarly, when considering "redness" we are not talking about the word, but whatever entity "redness" denotes in the Platonic realm. In this case, because love (the emotional experience) is entirely subjective, and only loosely connected to physical reality, it seems to me that unlike “mathematics,” which on some level appears to be a core essence of physical reality, it is more difficult to posit a metaphysical idealization.
I do not think there is any question that language is a practical invention, and a general term in a language is invented to denote particulars, not a Platonic universal. Plato, and realism generally posits the metaphysical existence of the universal in an attempt to explain what the essence is that allows individuals to have certain properties in common. Plato’s metaphysics are very archaic in this regard, and most universals are not considered to be anything but language devices. Mathematics is an exception.
Your comment: “Just as pi seems to match the ‘underlying structure of reality,’ the Complete Shakespeare seems to match "the underlying structure of reality" as well. For Humans are just as much a part of reality as anything else, aren't we?” seems off base to me. The physical relationships denoted by Pi are encompassed by the structure of the natural world. As such, Pi does not merely match reality, what it denotes is imbedded in reality. Can you say the same about the Complete Shakespeare? Or love? The fact that Shakespeare was a human being, and as such just as much part of reality as anything else, misses the point. We are not talking about Shakespeare as an entity, we are taking about the works of Shakespeare, i.e. language only. Now maybe there is something transcendent about such works; something to idealize. But what ontological form would that take? It just seems too forced. A response to Shakespeare, or poetry, just seems to be only an individual emotional response, and nothing more.
Human Wrote:
-------------------------------------------------------
>
> 1. Math is a man-made language game used to
> describe the world.
>
> 2. That which Math describes in the physical world
> is "a feature of the world (universe) that is
> independent of language."
>
> 3. Language, whether spoken or written, must be
> separated from the mental state which accompanies
> it. You use the word "love" as an example. So
> the word "love" and the "mental state" which this
> word stands for must be separated.
>
> 4. Although "mathematics" is a language game, the
> "underlying structure of reality" matches it.
> This needs to be explained.
As someone with a background in math and physics I would have
to elucidate here.
1. SOME math is used to describe SOME aspects of the world.
There are still many areas of mathematics which are waiting for
and application. There are still many aspects of the world
which have resisted mathematical description.
2. That which math describes in the world is more than just
described by the math. Mathematical theories of physical
phenomena can also use the mathematics to reason (i.e. derive)
further aspects of the world that would be true if the
correspondence to the mathematics was perfect. Such further
aspects present us with ways to test the strength of the
original mathematical description--they present us with
concepts for experiments to test the theory. The "theory" in
this case would be the claim of correspondence between physical
phenomena and their mathematical description that has been
given.
4. The thing that needs to be explained is the fact that
mathematical theories correspond so closely to natural
phenomena at all. For example Maxwell's electromagnetic theory
("Maxwell's Equations") has been shown to be accurate to one
part in a trillion. There is no known phenomena which
contradict it. On the other hand I know of no mathematical
theories in psychology that have claim to any such accuracy and
universality.
-------------------------------------------------------
>
> 1. Math is a man-made language game used to
> describe the world.
>
> 2. That which Math describes in the physical world
> is "a feature of the world (universe) that is
> independent of language."
>
> 3. Language, whether spoken or written, must be
> separated from the mental state which accompanies
> it. You use the word "love" as an example. So
> the word "love" and the "mental state" which this
> word stands for must be separated.
>
> 4. Although "mathematics" is a language game, the
> "underlying structure of reality" matches it.
> This needs to be explained.
As someone with a background in math and physics I would have
to elucidate here.
1. SOME math is used to describe SOME aspects of the world.
There are still many areas of mathematics which are waiting for
and application. There are still many aspects of the world
which have resisted mathematical description.
2. That which math describes in the world is more than just
described by the math. Mathematical theories of physical
phenomena can also use the mathematics to reason (i.e. derive)
further aspects of the world that would be true if the
correspondence to the mathematics was perfect. Such further
aspects present us with ways to test the strength of the
original mathematical description--they present us with
concepts for experiments to test the theory. The "theory" in
this case would be the claim of correspondence between physical
phenomena and their mathematical description that has been
given.
4. The thing that needs to be explained is the fact that
mathematical theories correspond so closely to natural
phenomena at all. For example Maxwell's electromagnetic theory
("Maxwell's Equations") has been shown to be accurate to one
part in a trillion. There is no known phenomena which
contradict it. On the other hand I know of no mathematical
theories in psychology that have claim to any such accuracy and
universality.
Thank you for this. Let me just push this a little.
We might ask, "What is the nature of the remarkable 'correspondence' between the physical world and mathematical principles? As you point out, to suggest that mathematics proper (the human construct) is merely descriptive does not do justice to the scope and intricate details of this correspondence. Mathematics appears to be more than just a human construct that is incidentially useful to practically assess the physcial world. The physical world itself encompasses complex mathematical relationships as intrinsic properites of independent natural law. As such, the question as to the ontological status of mathematics becomes important indeed, which is why some mathematicians give it the status of a Platonic universal; i.e. as a fundamental aspect of reality.
We might ask, "What is the nature of the remarkable 'correspondence' between the physical world and mathematical principles? As you point out, to suggest that mathematics proper (the human construct) is merely descriptive does not do justice to the scope and intricate details of this correspondence. Mathematics appears to be more than just a human construct that is incidentially useful to practically assess the physcial world. The physical world itself encompasses complex mathematical relationships as intrinsic properites of independent natural law. As such, the question as to the ontological status of mathematics becomes important indeed, which is why some mathematicians give it the status of a Platonic universal; i.e. as a fundamental aspect of reality.
If you want to claim that anything in nature arranges itself by mathematical anything, show the universe doing the mathematical calculations required to arrange anything by mathematical principals.
In other words, PI is a mathematical principle, show one place in the universe where PI is actually used to organize a circle.
I can certainly show where PI is used to describe a circle created in nature, but for the life of me, I can not see where nature ever uses or even "cares" about PI.
Sorry, the idea of "complexity" fails in proving a God and it fails in proving mathematics is anything other than a human construct.
No language that describes something is a universal no matter how well it describes the complexity.
Edited 1 time(s). Last edit at 03/13/2013 10:21AM by MJ.
In other words, PI is a mathematical principle, show one place in the universe where PI is actually used to organize a circle.
I can certainly show where PI is used to describe a circle created in nature, but for the life of me, I can not see where nature ever uses or even "cares" about PI.
Sorry, the idea of "complexity" fails in proving a God and it fails in proving mathematics is anything other than a human construct.
No language that describes something is a universal no matter how well it describes the complexity.
Edited 1 time(s). Last edit at 03/13/2013 10:21AM by MJ.
[Addressing your second point set]
[HUMAN]
"You begin by asserting that reason entails us to conclude that not all Universals match up equally with the external world. You then restate where I began, that mathematical objects exist apart from minds to apprehend them. Pi is the concept/reality archytas introduced and I affirmed. Then you conclude by saying that "games" as a universal fails to exist sans humans. What's missing in all of this of course is the reason!"
[RESPONSE]
O.K. Why is that "games" is less compelling as a Platonic universal than "mathematics?" Is it not reasonable to assess the distincitions between these terms? Since we are talking about ontology; i.e. their existence, or being, we should, I think, consider the relationship between the words and the physical world. Although there are individual things we call games, and individual things we call mathematics (equations on paper) can we identify what a identifying properties of all "games" there might be to instantiate an ontological universal? We cannot even do that intuitively. The line is fuzzy. Is language a game? How about dating? It is quite ellusive. On the other hand, mathematics is not only conceptually concrete, it is intricately tied to the physical world. This is way I said that not all general terms, or universals, are created equal when considering ontological questions.
[HUMAN]
*Why* does "games" fail and "maths" succeed? You don't say why. Just like pi, the concept "games" on the face of it matches very well to that which it denotes in the real world. That is what language is supposed to do.
[RESPONSE]
See above. "Games" does not match very well to particulars in the real world. We can define it, but when identifying particulars, we have trouble at the fringes.
[HUMAN]
(Of course, there is no Universal "games", or "mathematics" for that matter. Game plural denotes a set of particulars. The Universal Game would be that which all instances of games share. Like Socrates interrogating his interlocutor about the difference between a list of virtues and Virtue --that which all virtues share in, which makes them a particular instance of Virtue-- we may wonder about the difference between a list of games and Game --that which all games share in, which makes them a particular instance of Game.)
[RESPONSE] But the whole issue with universals, i.e. Platonic forms, is ontology. Platonic universals are "entities" of some sort that do exist independent of language. That is way Plato said that good things "participate" in the form of the good. The form of the good is not a reference to language, it is a reference to actual being, or existence. The question then is what general or universal terms might still, centuries later, be considered as having some sort of Platonic existence. Games, no; mathematics, maybe.
[HUMAN]
"You begin by asserting that reason entails us to conclude that not all Universals match up equally with the external world. You then restate where I began, that mathematical objects exist apart from minds to apprehend them. Pi is the concept/reality archytas introduced and I affirmed. Then you conclude by saying that "games" as a universal fails to exist sans humans. What's missing in all of this of course is the reason!"
[RESPONSE]
O.K. Why is that "games" is less compelling as a Platonic universal than "mathematics?" Is it not reasonable to assess the distincitions between these terms? Since we are talking about ontology; i.e. their existence, or being, we should, I think, consider the relationship between the words and the physical world. Although there are individual things we call games, and individual things we call mathematics (equations on paper) can we identify what a identifying properties of all "games" there might be to instantiate an ontological universal? We cannot even do that intuitively. The line is fuzzy. Is language a game? How about dating? It is quite ellusive. On the other hand, mathematics is not only conceptually concrete, it is intricately tied to the physical world. This is way I said that not all general terms, or universals, are created equal when considering ontological questions.
[HUMAN]
*Why* does "games" fail and "maths" succeed? You don't say why. Just like pi, the concept "games" on the face of it matches very well to that which it denotes in the real world. That is what language is supposed to do.
[RESPONSE]
See above. "Games" does not match very well to particulars in the real world. We can define it, but when identifying particulars, we have trouble at the fringes.
[HUMAN]
(Of course, there is no Universal "games", or "mathematics" for that matter. Game plural denotes a set of particulars. The Universal Game would be that which all instances of games share. Like Socrates interrogating his interlocutor about the difference between a list of virtues and Virtue --that which all virtues share in, which makes them a particular instance of Virtue-- we may wonder about the difference between a list of games and Game --that which all games share in, which makes them a particular instance of Game.)
[RESPONSE] But the whole issue with universals, i.e. Platonic forms, is ontology. Platonic universals are "entities" of some sort that do exist independent of language. That is way Plato said that good things "participate" in the form of the good. The form of the good is not a reference to language, it is a reference to actual being, or existence. The question then is what general or universal terms might still, centuries later, be considered as having some sort of Platonic existence. Games, no; mathematics, maybe.
Here is a response to the rest of your post:
Response to third point set:
[HUMAN]
"Somehow I sense that you dodge the question.
"We already began with the proposition that mathematical objects like pi exist, are abstract and are not material and therefore are not sensible. As others said, in the real world there are no perfect circles to be sensed just as there is no one thing to be counted. Pi and "one" are abstract. Surely they exist. But *where* do they exist? is the question! You seem to be saying that pi exists in the "real world". But surely this is not the case, and if it was then it would by definition not be a Universal."
[RESPONSE] No, we begin with the question as to whether mathematical objects (language constructs), even if not material, carry ontological status through a Platonic universal. I have not committed myself either way on this. The fact that there are no perfect material circles is beside the point. Pi is part of an overall mathematical scheme that could conceivably be represented in a Platonic universal that is identified as mathematics. You need to differentiate between a universal as a general term in language, and a Platonic universal, which carries non-material ontological status in reality. It is possible that I have not always made a clear and definite distinction in my posts, thinking that the context made such clear.
[HUMAN]
"The question really isn't about the "real world." The question is purely philosophical."
[RESPONSE] No. The question, i.e. regarding Platonic universals, is about what really exists in the "real world" or the universe, as encompassing all of reality.
Response to the next point set: Here I have to address the points as well.
"1. The "content" of poetical language resides in the mind, but does not exist apart from the minds who experience it."
[RESPONSE] The content of language is the meaning that is applied to those words, which requires mind. Without mind there is no content.
"2. Words denote "something", but the being of that "something" exists only as a mental state in those who use them."
[RESPONSE] No. Words can and do often denote objects, or sets of objects in the real world, as experienced by the language user. Whether those denoted objects actually exist, and what the properties of such objects are is a philosophical question.
"3. We exist. But words exist only as far as we exist."
[RESPONSE] Yes, if you mean words in a language as invented by human beings.
"4. Mathematical principles correlate fantastically highly with the world. Mathematics is an invented language. Sans humans mathematical principles would still correlate fantastically highly with the world. There is something metaphysical about the world because of this."
[RESPONSE] Well, this isn't clear. First, you must recognize a distinction between "mathematics" the human language, and mathematics as certain logical relationships existing in nature. Surely, there is a relationship between the two. We know the source of the first, i.e. humans. As for the second, we do not know, and must conjecture whether the source, whatever it is, carries separate existence from the first; i.e. is like a Platonic universal; or is only a construct of human minds. That is the whole debate. If you are a strict materialist, you have a number of problems here. First, where do we find the logic of mathematics in the real world, except as a metaphysical aspect of the material world. Second, if you deny Platonic realism, then you are left to explain mind (the source of our mathematical logic). I think there are problems with both approaches, which is why I reject materialism as a scientific worldview.
5. We must ask, *why* do mathematical laws seem to conform so highly with the universe?
[HUMAN]
I simply am not following you, Henry. Surely "meadow" "grove" and "stream" denote "something" that exists as something more than mere mental states, right? What else could your mathematical principles correspond to other than real streams, groves and meadows?
[RESPONSE] Well, that is a good question. Hopefully, the above has clarified the issues. We do not know, or understand, what mathematics, as a Platonic universal, would be like; i.e. how its ontological status might be described. We are into metaphysics here, with all of its problems. But again, there is something extremely compelling about the correlation between mathematics and reality that suggests that there are tied together in ways that go beyond human language and human mind.
[HUMAN]
"But if you are willing to say (since you affirm the abstract existence of pi) that all circles partake in a common nature (universal) we call Circle, why are you not also willing to say that all meadows partake in a common nature we can call Meadow? That is my question."
[RESPONSE] See above. First, remember, I have not made a commitment one way or the other with respect to mathematics as a sort of Platonic universal. But I am willing to reject the idea that most other universals are noting more than constructs of language. (Note that consciousness is another problematic example. Is consciousness, or mind, as general terms, encompassed by Platonic universals which have ontological status over and above human language, or individual human minds?)
[HUMAN]
"Henry, please correct me if I simplify you unfairly. Everything you wrote seems to boil down to this: the perfect circle and pi have a metaphysical existence because we can observe imperfect circles in the real world that highly correlate with pi. Love, on the other hand, does not have a metaphysical existence….because… it only exists in the minds of those who feel it. The materialist of course would ask how pi does not also only exist in the minds who perceive it?"
[RESPONSE] Hopefully, I have clarified this above.
"You plead a special case for the language of mathematics but deny the same for the language of words. Why? That is my question. You answer that the made-up language of math correlates very highly with the observable world. But does not the made-up language of words also highly correlate to the observable world? After all, it wouldn't be of much use if it didn't. You say pi and I say Shakespeare. You agree that a list of particular circles share in a Universal called Circle but deny that a list of virtues can also share in a Universal called Virtue. Why? I didn't see an argument."
[RESPONSE] Well, I would not try to address whether a proposed Platonic universal of mathematics encompassed separate and distinct universals for each concept in mathematics, like Pi. But as part of an overall mathematical logical structure, I would say that Pi carries more ontological weight as a Platonic form than the works of Shakespeare. But, more to the point, you seem to think that I am somehow diminishing Shakespeare, or art. I do not think so at all. Human beings experience art on a personal level, that's all I am saying; as individual selves. Why do we need some overall unifying entity that unites the artistic experience?
[HUMAN]
"The board's materialists respond consistently: no metaphysical realms, period. They (I suppose) think that the idea of 2 the idea of + the idea of 2 the idea of = the idea of 4 does not exist anywhere outside human consciousness. You say that it does, presumably because we can take two sticks and place them beside to other sticks and count them and it will always count to 4. The materialist simply says this is imposing our language on an arbitrary observance, for there are not real 2 sticks and 2 sticks. There are only many particular instances of sticks. Nothing more."
[RESPONSE] Don't confuse Platonic forms and metaphysics. Platonic forms are, of course, metaphysical. But so is mind and consciousness; and for that matter, the nature of reality itself. Materialists are not wrong to question Platonic forms--even with respect to mathematics. But they are wrong to question whether consciousness and mind are separate and distinct from the physical world.
[HUMAN]
"I say 2+2=4 exists, is abstract and is true independent of minds to think it. I ask *where* this abstract exists since it does so not in space and time. I speculate that its existence is related somehow to the world of Universals."
[RESPONSE] Fine. I think this is a fair speculation, for reasons noted.
[HUMAN]
"Universals exist (if they do) independent of mind, space, time and material. Universals exist 'someplace' different from thoughts and feelings and physical objects. In fact "exist" is the wrong word. Universals have their *being* elsewhere and by definition cannot exist in the world of sense. The world of Universals is a world of being sans change, whereas everything else exists in a fleeting, ever changing world."
[RESPONSE] Yes. I think this is mostly correct as to Platonic universals. But I would caution against requiring too much here when the issue is removed from merely Plato's thought. All we should say, I think, is that such universals carry independent ontological status from their particulars.
Human: I hope the above was helpful both to you and others. I appreciate very much your willingness to present your thoughts, both here and on other posts. I value you perspective highly. I left my email address with Susan. If you care to discuss this, or anything else, privately, I invite you to contact me.
HB
Response to third point set:
[HUMAN]
"Somehow I sense that you dodge the question.
"We already began with the proposition that mathematical objects like pi exist, are abstract and are not material and therefore are not sensible. As others said, in the real world there are no perfect circles to be sensed just as there is no one thing to be counted. Pi and "one" are abstract. Surely they exist. But *where* do they exist? is the question! You seem to be saying that pi exists in the "real world". But surely this is not the case, and if it was then it would by definition not be a Universal."
[RESPONSE] No, we begin with the question as to whether mathematical objects (language constructs), even if not material, carry ontological status through a Platonic universal. I have not committed myself either way on this. The fact that there are no perfect material circles is beside the point. Pi is part of an overall mathematical scheme that could conceivably be represented in a Platonic universal that is identified as mathematics. You need to differentiate between a universal as a general term in language, and a Platonic universal, which carries non-material ontological status in reality. It is possible that I have not always made a clear and definite distinction in my posts, thinking that the context made such clear.
[HUMAN]
"The question really isn't about the "real world." The question is purely philosophical."
[RESPONSE] No. The question, i.e. regarding Platonic universals, is about what really exists in the "real world" or the universe, as encompassing all of reality.
Response to the next point set: Here I have to address the points as well.
"1. The "content" of poetical language resides in the mind, but does not exist apart from the minds who experience it."
[RESPONSE] The content of language is the meaning that is applied to those words, which requires mind. Without mind there is no content.
"2. Words denote "something", but the being of that "something" exists only as a mental state in those who use them."
[RESPONSE] No. Words can and do often denote objects, or sets of objects in the real world, as experienced by the language user. Whether those denoted objects actually exist, and what the properties of such objects are is a philosophical question.
"3. We exist. But words exist only as far as we exist."
[RESPONSE] Yes, if you mean words in a language as invented by human beings.
"4. Mathematical principles correlate fantastically highly with the world. Mathematics is an invented language. Sans humans mathematical principles would still correlate fantastically highly with the world. There is something metaphysical about the world because of this."
[RESPONSE] Well, this isn't clear. First, you must recognize a distinction between "mathematics" the human language, and mathematics as certain logical relationships existing in nature. Surely, there is a relationship between the two. We know the source of the first, i.e. humans. As for the second, we do not know, and must conjecture whether the source, whatever it is, carries separate existence from the first; i.e. is like a Platonic universal; or is only a construct of human minds. That is the whole debate. If you are a strict materialist, you have a number of problems here. First, where do we find the logic of mathematics in the real world, except as a metaphysical aspect of the material world. Second, if you deny Platonic realism, then you are left to explain mind (the source of our mathematical logic). I think there are problems with both approaches, which is why I reject materialism as a scientific worldview.
5. We must ask, *why* do mathematical laws seem to conform so highly with the universe?
[HUMAN]
I simply am not following you, Henry. Surely "meadow" "grove" and "stream" denote "something" that exists as something more than mere mental states, right? What else could your mathematical principles correspond to other than real streams, groves and meadows?
[RESPONSE] Well, that is a good question. Hopefully, the above has clarified the issues. We do not know, or understand, what mathematics, as a Platonic universal, would be like; i.e. how its ontological status might be described. We are into metaphysics here, with all of its problems. But again, there is something extremely compelling about the correlation between mathematics and reality that suggests that there are tied together in ways that go beyond human language and human mind.
[HUMAN]
"But if you are willing to say (since you affirm the abstract existence of pi) that all circles partake in a common nature (universal) we call Circle, why are you not also willing to say that all meadows partake in a common nature we can call Meadow? That is my question."
[RESPONSE] See above. First, remember, I have not made a commitment one way or the other with respect to mathematics as a sort of Platonic universal. But I am willing to reject the idea that most other universals are noting more than constructs of language. (Note that consciousness is another problematic example. Is consciousness, or mind, as general terms, encompassed by Platonic universals which have ontological status over and above human language, or individual human minds?)
[HUMAN]
"Henry, please correct me if I simplify you unfairly. Everything you wrote seems to boil down to this: the perfect circle and pi have a metaphysical existence because we can observe imperfect circles in the real world that highly correlate with pi. Love, on the other hand, does not have a metaphysical existence….because… it only exists in the minds of those who feel it. The materialist of course would ask how pi does not also only exist in the minds who perceive it?"
[RESPONSE] Hopefully, I have clarified this above.
"You plead a special case for the language of mathematics but deny the same for the language of words. Why? That is my question. You answer that the made-up language of math correlates very highly with the observable world. But does not the made-up language of words also highly correlate to the observable world? After all, it wouldn't be of much use if it didn't. You say pi and I say Shakespeare. You agree that a list of particular circles share in a Universal called Circle but deny that a list of virtues can also share in a Universal called Virtue. Why? I didn't see an argument."
[RESPONSE] Well, I would not try to address whether a proposed Platonic universal of mathematics encompassed separate and distinct universals for each concept in mathematics, like Pi. But as part of an overall mathematical logical structure, I would say that Pi carries more ontological weight as a Platonic form than the works of Shakespeare. But, more to the point, you seem to think that I am somehow diminishing Shakespeare, or art. I do not think so at all. Human beings experience art on a personal level, that's all I am saying; as individual selves. Why do we need some overall unifying entity that unites the artistic experience?
[HUMAN]
"The board's materialists respond consistently: no metaphysical realms, period. They (I suppose) think that the idea of 2 the idea of + the idea of 2 the idea of = the idea of 4 does not exist anywhere outside human consciousness. You say that it does, presumably because we can take two sticks and place them beside to other sticks and count them and it will always count to 4. The materialist simply says this is imposing our language on an arbitrary observance, for there are not real 2 sticks and 2 sticks. There are only many particular instances of sticks. Nothing more."
[RESPONSE] Don't confuse Platonic forms and metaphysics. Platonic forms are, of course, metaphysical. But so is mind and consciousness; and for that matter, the nature of reality itself. Materialists are not wrong to question Platonic forms--even with respect to mathematics. But they are wrong to question whether consciousness and mind are separate and distinct from the physical world.
[HUMAN]
"I say 2+2=4 exists, is abstract and is true independent of minds to think it. I ask *where* this abstract exists since it does so not in space and time. I speculate that its existence is related somehow to the world of Universals."
[RESPONSE] Fine. I think this is a fair speculation, for reasons noted.
[HUMAN]
"Universals exist (if they do) independent of mind, space, time and material. Universals exist 'someplace' different from thoughts and feelings and physical objects. In fact "exist" is the wrong word. Universals have their *being* elsewhere and by definition cannot exist in the world of sense. The world of Universals is a world of being sans change, whereas everything else exists in a fleeting, ever changing world."
[RESPONSE] Yes. I think this is mostly correct as to Platonic universals. But I would caution against requiring too much here when the issue is removed from merely Plato's thought. All we should say, I think, is that such universals carry independent ontological status from their particulars.
Human: I hope the above was helpful both to you and others. I appreciate very much your willingness to present your thoughts, both here and on other posts. I value you perspective highly. I left my email address with Susan. If you care to discuss this, or anything else, privately, I invite you to contact me.
HB