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I've always had difficulty accepting the proposition that "1 + 1 = 2" is truly a universal. The reason is that it's not really a verifiable proposition -- it's an equation whose constituents are already defined relative to each other. The information content in '1 + 1' is absolutely identical in '2', just as they are absolutely identical to the cubic root of 8. So to call '1 + 1 = 2' a proposition or even a relationship is a redundancy. To say 2 always implies 1 + 1. The distinction in terminology is useful only because '1' constitutes something different independently.
By extension this is true of the pythagorean theorem, because in an equation you can always break down the constituents to expressions of equivalency. The terms define themselves, so any equation is ultimately a circular statment.
I think Russell, Frege, and others tried to demonstrate that all of mathematics were reducible to pure logic. But this was rebuffed by Godel's incompleteness theorem, which shows that not all of mathematics is logically demonstrable.
Aedes, don't you think that there must be something within space and time or within the nature of things that we must intuit a priori in order for it to be possible for us to construct positive propositions which would yield new knowledge? Something that our propositions conform to besides other propositions?
So, I disagree with what you seem to imply because it seems obvious to me that constructive positive knowledge is possible and such knowledge cannot be through and through a tautology. Constructive knowledge is a result of man's ability to 'put two and two together', a capacity which the brutes do not have and I see no other source for this capacity but that it exists a priori.
Yes, but intuiting something a priori does not prove or depend on its universality -- it only presupposes it.
But insofar as 2 is synonymous with 1+1, 1.9+0.1, 1.99+0.01, 1.999+0.0001, etc, all numbers and their relationships are a tautology. The reason that there cannot be another realm in which 1+1=5 is simply that that would contradict the way we define those terms. The universality germinates from our conventions, and it's our collective agreement on the meaning of concepts and words that allows us to assume their universality. But short of pure objectivity and true omniscience, it's not logically necessary for us to conclude or even presume that something known a priori contains universal truth.
What I would propose is that the entirety of nature, whatever it is, is intertwined and therefore universals cannot be said to enjoy an independent status but must be unified, interconnected and somehow available to us through reason or as the reasoning process in action.
I propose such a scheme because I think that if nature is said to be infinitely open regarding the production of natural 'classes' or types, then reason cannot, will not be grounded, cannot be said to posess real 'traction' at all and the ultimate justification for our knowing capacity is therefore illusory. Therefore, intelligibility or knowability must be limited not at the level of empirical nature (which is infinite and I believe merely probabalistic) but at the level of which our reason operates.
I would ask you, without a universal implication within the process of human knowledge, how then do you say we get things done? How is it possible to classify anything at all if what knowledge rests upon is a constantly moving picture without any real penetration by reason? Are you saying that knowledge itself is illusory? It seems incumbent upon you to pose some kind of answer to the question as to how knowledge can be possible, since you have merely negated thus far. But what you negate is a foundation for what we do take to be existence i.e. the advent of practically useful sciences.
The foundations of all knowledge, or the supposition of universals, are interesting food for speculation. I'm not sure, however, that they're all that important in any practical sense. Science does what it does -- it hopes that its discoveries and inferences approach truth, but absolute foundational truth is not built into science.
Ever Since Plato Philosophers Have been impressed by the fact that there are universal propositions which we can apparently know to be true with absolute certainty...
It is important to understand in exactly what sense a priori knowledge is "independent of experience." No philosopher has ever denied that a child has to learn that two and two make four by learning to count, and that the latter process involves contact with concrete objects. But this only means that without sense-experience one cannot acquire the concepts of number, in this case the concepts "two" and "four," that is, a child who has never learned to count, to associate different numerals with distinguishable objects, will not even understand what "two and two make four" means. What the philosophers who believe in a priori knowledge assert is only that once the concepts have been acquired, the proposition can be "seen" to be true by just thinking about it (by "the mere operation of thought," in Hume's phrase).
If the rest of your post is built on this sort of nonsense... It is an untrue statement from whatever angle viewed.
When you say that "philosophers have been impressed.." are you saying 'all'? Many? Some? Two? Sounds like a failed attempt at an 'appeal to popularity'; if everyone thinks or believes something, that don't make it so.
Science knows nothing to be true with absolute certainty. Nothing! That is the realm of fundamnentalist religion and zealotry, the 'delusions' of 'belief'.
Any science study will show you this, and show you why.
Also, calling something a 'fact' (which it is FAR from), again, don't necessarily make it so (another fallacy).
Nameless, I appreciate your strong feelings here.
But as far as the text that you have excerpted it was meant to eludicate the general problems related to a priori reasoning in philosophical propositions and arguments. They were meant to be purely pedogogical in nature. And by posting it I was just trying to stir constructive discussion.
As regards to whether or not human knowledge can be grounded in a form or forms of certainty I believe we should leave this question to philosophical type debates and not a priori preclude affirmative or negative proposals on the matter.
Furthermore if science cannot prove anything to be absolutely certain then how can it state with absolute certainty that nothing can be proved? It seems to me a kind of paradox is at work here.
Be well, Nameless
if everyone thinks or believes something, that don't make it so.
Science knows nothing to be true with absolute certainty. Nothing! That is the realm of fundamnentalist religion and zealotry, the 'delusions' of 'belief'.
Any science study will show you this, and show you why.
Also, calling something a 'fact' (which it is FAR from), again, don't necessarily make it so (another fallacy).
Quote:Originally Posted by nameless
if everyone thinks or believes something, that don't make it so.
Science knows nothing to be true with absolute certainty. Nothing! That is the realm of fundamnentalist religion and zealotry, the 'delusions' of 'belief'.
Any science study will show you this, and show you why.
Also, calling something a 'fact' (which it is FAR from), again, don't necessarily make it so (another fallacy).
Whether the point is true or not, your statement in regard to truth is not exactly true. Since people build a lot of their actual reality out of their vision of ultimate truth it is difficult to disregard both the truth as concieved and the reality built around it.
If I were to look at a historical figure like Sacrates or Jesus
, and say there is so much myth and little substance than I disregard the systems of thought or action built upon the mythic ideas of each.
Look at the moral world, the world beyond sensation, measure, or being- where we all reside
, and there truth is elusive and unverifiable; and there, clearly what is believed true and is false often holds more weight than what is true and cannot be proved.
And, it is this moral world where people live and invest their emotions.
If people wrap their lives around an error it does not mean they do not exist, and do not lend some of their truth to the error.
Truth is not just what is believed, or known, but what people do on the basis of what they believe and know.
Woah, dog, I don't see it like that at all. Most folks couldn't care less about "ultimate truth" (if there is such a thing); they accept their concepts from their perceptions, their sensory 'evidence', and accept concensus as long as it doesnt threaten the 'truth' of their perceptions, as their "actual reality"! What they see is all they get; what they 'get' is what they 'see'...
Bad try. There is evidence for Socrates being an actual historic figure, but there is no independent eyewitness evidence at all to support the theory of Jesus' actuality. Sorry, don't mean to 'niggle'.
One can learn from fables and mythology. The speaker is irrelevent (thus 'nameless'), it is the words that either have meaning or not. Personality has naught to do with it.
Again, woah!! WTF is a "moral world"? All morality is, is the judging of things/people as 'good' or 'bad/evil'. According to Xtianity, morality is the very first (and worst) sin!
Thats all it is, I know nothing of a 'moral world'... And I certainly do not 'reside' there: I am completely a-moral (not immoral). No 'morality' at all, so "we all" nothing!
What people accept as 'true' for themselves, is all that can be known of 'truth'. It is completely subjectively known.. small 't' 'truth' anyway, and constantly changes, anyway, within a 'living mind'.. Speaking as if there aught to be, or can be, any consensus of 'truth' is ridiculous. Thinking that 'your' (in general) truth aught to be everyone's (if they differ..) is ignorant vanity.
Again, this is meaningless to me.
Everything 'exists', everyone exists.
Error = '0'.
Multiply it by whatever you like, you still end up with 'bupkiss'! *__-
Actually, people's lives are 'believed/accepted' illusion that is accepted to be 'reality/truth'. That is fine also. Whatever works. It isn't like we have any choice in what to think, what to accept or believe. Most lives are spent asleep as the great dream/illusion/delusion. It is still a wild ride. We are all unique perspectives, all equally 'valid'. Enlightenment is illusion/dream, so is nonlucid day to day sleepwalking dreaming. Everyone has their part in the great Tapestry of existence.
Your definitions of 'truth' seem to be rather 'personal', and somewhat unique (of course), but slowly unfolding to my understanding of your intended meaning of 'truth'.
I rather avoid the word 'truth', like 'love' or 'god' as everyone has their own personal concepts and baggage involved, and there is no evidence that those 'concepts' have any 'value' beyond the mind of the conceiver.
Just occurred to me, how about a definition of 'truth' as being everyone's memory. If it is in your memory, it is your 'truth' (as most people feel that way anyway). Your 'truth', his 'truth', all different, all unique, all equally 'true'.
(It does seem to render the term meaningless, though.)
I'll agree that most people do not care about truth. To be more exact, truth is not something they think, but feel. No one feels themselves false, and all have an emotional attachment to their view of truth, and this is why a challenge to their view of truth brings anger.
If you are talking to someone who does not know, and knows he does not know, and only the educated have the illusion of knowledge, then truth can never be certain, and should never be certain. For believing people the truth of their beliefs transend all of reality, and it is not in what is real that they believe.
Bad try on your part. Even the Jews recognize Jesus, and He is followed on the testimony of followers. But, you malign philosophy here as much as religion, for Jesus was a philosopher king has much as a God.
Actually myths, magic, and religion tells us a great deal of history and society that we could only guess at without them. And we still have to presume a lot.
Don't get me wrong, ...the world we actually live in for the most part is moral.
It is filled out by ideas like virtue, honor, liberty, morality, social equality, love, and all manor of concepts which point to meanings without being. We can measure the weight of an atom better than any quantity of justice for example. We must determine that there is such a thing as justice with moral considerations, effects, needs, consequences, and etc.
Truth in every respect, like every other concept is not only a form,
but a form of relationship. People recognize others and realize each other through forms like shared and commonly accepted truth.
I define truth as a reproduction of reality.
Just because a person's concepts are not true to the reality they represent
The more true our truth is to reality the more useful and dangerous it becomes.
nameless - Science knows nothing to be true with absolute certainty
Isn't this statment self defeating? Or is it not a form of science that this statement is derived from?
Sorry to be off topic, I just enjoy statements like: 'Everything is relative'.
I will try to post on this topic when I catch up with what is going on. (which seems hard since it has taken many directions.)
Isn't this statment;
Quote:Quote:nameless - Science knows nothing to be true with absolute certainty
self defeating? Or is it not a form of science that this statement is derived from?
Sorry to be off topic, I just enjoy statements like: 'Everything is relative'.
...the true strength of science isn't in what it can prove; the strength lies in its honesty, especially in this sense, where it continuously states that nothing it finds or invents is absolute.
So, science at least is honest. Scientists on the other hand may "overstate the significance of their results" for various reasons.
Isn't this statment self defeating? Or is it not a form of science that this statement is derived from?
Sorry to be off topic, I just enjoy statements like: 'Everything is relative'.
I will try to post on this topic when I catch up with what is going on. (which seems hard since it has taken many directions.)