On proof of existence.

@nameless,

Fido wrote:

I would suggest that 'knowledge' is the content of 'memory' as perceived through the ego. The more 'sure' of one's 'knowledge' one is, the more 'pride' is attached, the more 'identity', and the more to 'defend'!

[CENTER]TRUTH

[CENTER]KNOWLEDGE IS THOUGHT[/CENTER]

[CENTER]EDUCATION INCREASES THOUGHT[/CENTER]

[CENTER]WISDOM IS TRUTH[/CENTER]

[CENTER]ENLIGHTENMENT REDUCES THOUGHT[/CENTER]

[CENTER]TO A SINGLE SIMPLE TRUTH[/CENTER]

[CENTER]ONENESS OR EQUALITY[/CENTER]

[CENTER]THE SINGLE SIMPLE[/CENTER]

[CENTER]WISDOM OR[/CENTER]

[CENTER]TRUTH[/CENTER]

[CENTER]MJA[/CENTER]
[/CENTER]

@MJA,

MJA wrote:

[CENTER]TRUTH[/CENTER]

[CENTER]KNOWLEDGE IS THOUGHT

[CENTER]EDUCATION INCREASES THOUGHT[/CENTER]

[CENTER]WISDOM IS TRUTH[/CENTER]

[CENTER]ENLIGHTENMENT REDUCES THOUGHT[/CENTER]

[CENTER]TO A SINGLE SIMPLE TRUTH[/CENTER]

[CENTER]ONENESS OR EQUALITY[/CENTER]

[CENTER]THE SINGLE SIMPLE[/CENTER]

[CENTER]WISDOM OR[/CENTER]

[CENTER]TRUTH[/CENTER]

[CENTER]MJA[/CENTER]

[/CENTER]

(Do you think that if I centered my post, and used caps, it would seem more 'important and true'?)
I think that you are way off the mark equating 'knowledge' with 'thought'. Knowledge still exists in a thoughtless (meditational) state.
And your definition of 'truth' might be good for you, but does nothing for me.
Enlightenment reduces nothing (except ignorance), much less 'thought'. And there is no 'Truth' in thought. I guess that it all depends on your memory, the definition of the words that you use, and personal experience. I cannot support 'truth' in any manner in which you use it.
"The truth that can be (blythely) spoken is not the 'Truth'."
I guess that even caps and centering cannot make something more 'meaningful'.
I think, ultimately, the only supportable definition of 'knowledge' can be 'memory'.

@Didymos Thomas,

Didymos Thomas wrote:

Okay, so you are claiming there is no empirical evidence of infinity; however, in mathematics there is a clear need for infinity.

Fantasy games and nothing more. Like a board game with made-up rules. One of the 'made-up rules', unsupportable with any real evidence at all, is the fantasy of 'infinite'. They have a Zeus in books and superstition and stories, does that make Zeus a 'real' thing thereby?

Quote:

I think this was asked earlier 'Can you name the last integer?' If not, then you must admit that no such thing exists, thus there are at least an inifinite number thereof.

Nonsense! If you cannot name something, cannot see something, that is evidence of nothing other than your personal limitations.
Did the atmosphere exist before people could name it? Your logic is faulty. It is a non-sequitor.

Quote:

Why must there be something infinite within space time in order for infinity to exist?

Existence requires time/space, which is 'duality/context', to 'exist'.

Quote:

Infinity exists as an a priori expression, as far as I can tell.

There are no ultimate a priori truths. It is all pragmatic concensus and nothing more.
Believe as you must.
Positing an 'infinite' can certainly enrich and add depth to one's thoughts and problematic concepts, but it is an illusion nontheless.
Actually, mathematically, the notion of the infinite is being rejected more and more.
When I get back on my computer, I can give you some links for thinks.

@Didymos Thomas,

Didymos Thomas wrote:

Infinity is not a need, it's a logical conclusion.

It is hardly logical. Logics follow nature. Objects fall logically as well in reality because of gravity in reality. Gravity without reality makes as little sense as reality without gravity. Time changes everything. Time is change, and time even short of infinity proves all logic wrong and proves that logic wrong first which most depends upon a great stretch of time changing nothing.

Quote:

It doesn't have to "fit in", that's not the point. You are denying infinity because nothing physical can be infinite. So what? As I've said, infinity is true purely a priori, there does not exist empirical evidence of it. If you reject a priori altogether, that's fine - if you do that might clear things up a bit. But otherwise you will need to explain why you demand empirical evidence of infinity - I certainly do not understand why you would.

If it is not about things, and is not about reality it is not about philosophy. Religion considers the infinite. Where is God not first eternal and only secondarily good? Nothing times time equals nothing squared. When you find something finite and you would like to examine then it is time for philosophy. I would not reject the a priori without rejecting insight and imagination, but not everything we imagine is real.

@Fido,

Fido wrote:

It is hardly logical. Logics follow nature. Objects fall logically as well in reality because of gravity in reality. Gravity without reality makes as little sense as reality without gravity. Time changes everything. Time is change, and time even short of infinity proves all logic wrong and proves that logic wrong first which most depends upon a great stretch of time changing nothing.

If it is not about things, and is not about reality it is not about philosophy. Religion considers the infinite. Where is God not first eternal and only secondarily good? Nothing times time equals nothing squared. When you find something finite and you would like to examine then it is time for philosophy. I would not reject the a priori without rejecting insight and imagination, but not everything we imagine is real.

I ask again. Is there a last integer in the series of integers? If so, please provide it. Is there a last number in the decimal expansion of pi? If so, please provide it. If in both cases, there is not last number, then the seriies are infinite.

@kennethamy,

"It is hardly logical. Logics follow nature."

As kennethamy has pointed out, twice, infinity is a logical conclusion. Either there is a greatest integer, or the number of integers is infinite.

"If it is not about things, and is not about reality it is not about philosophy."

How is infinity not about things? We call things beautiful, and say that being beautiful is something a thing can be, yet no think possesses some physical property beauty.

@kennethamy,

kennethamy wrote:

I ask again. Is there a last integer in the series of integers? If so, please provide it. Is there a last number in the decimal expansion of pi? If so, please provide it. If in both cases, there is not last number, then the seriies are infinite.

There is a last integer when man quits counting. Math lives so long as man lives, and no longer. If we are not infinite then it is not infinite. We do not give all that has being meaning. We give many things without being our meaning. Math is just one of those things. A number which does not represent a reality has no meaning. It is a sign without significance. If a sign points to nothing then nothing is its value, and math without context has no value. It then becomes a toy that in the hands of a man is a waste of time, and life.

@Didymos Thomas,

Didymos Thomas wrote:

"It is hardly logical. Logics follow nature."

As kennethamy has pointed out, twice, infinity is a logical conclusion. Either there is a greatest integer, or the number of integers is infinite.

"If it is not about things, and is not about reality it is not about philosophy."

How is infinity not about things? We call things beautiful, and say that being beautiful is something a thing can be, yet no think possesses some physical property beauty.

Math is logical. How can I argue with that. I don't. I point out that math or logic that is beyond proof has no use. It is a play thing. Logic and math without context do not exist without our donation of meaning. Meaning has never been measured. There is no national bank of meaning. But I trust that meaning is the measure of a man, that meaning is what keeps him alive, and that he suffers from a limited supply. I think I can give things like God, and math without context -meaning only by stealing it from something with being, from something which has a natural meaning, and from something more essential to my life.

How is infinity not about things? As I said: If space and time are not infinite there is not space or time enough for the infinite of any size. Do you believe beauty is physical property? I think it is a moral property. I don't think beauty can be quantified. I don't think beautiful is a thing a person can be. Beauty is a meaning we give to things, or find in things. It is a quality we think one has, but say one is. A feast to a starving man is beauty. A feast to a full man is torture. A feast is not beauty or torture, but has the meaning we feel its has according to its being and our condition. One thing we cannot do, and often try to do is to give meaning to reality beyond our existence. I trust this is an attempt to grasp the eternal because we are terminal.

@Fido,

I think infinity is everything beyond our minute and finite grasp of the universe. What do we truly know?
Perhaps if we try to define our finite knowledge, it would help us understand infinity.
Just an idea!

=
MJA

@Fido,

Fido wrote:

There is a last integer when man quits counting. Math lives so long as man lives, and no longer. If we are not infinite then it is not infinite. We do not give all that has being meaning. We give many things without being our meaning. Math is just one of those things. A number which does not represent a reality has no meaning. It is a sign without significance. If a sign points to nothing then nothing is its value, and math without context has no value. It then becomes a toy that in the hands of a man is a waste of time, and life.

We don't know there is no greatest integer because someone is still counting and not getting to the end. We know it because we know that no matter how long we count we can never get to the end. So being able to count has nothing whatever to do with our knowledge that there is no greatest integer. But I thinks you are talking about numerals, not numbers. The numeral "three" ("3", "iii", 'drei", "trois", "tres", etc.) points to the numbers of which the numerals are the names. The numeral, "three" is the name of the number, three. And, if there are three cows in the pasture, then the number of cows in the pasture is, three. And that is the reality that the numeral, three, points to. Namely, the successor to two; the predecessor of two; the first prime after two, and that square root of nine; among other of the properties of the number, three. And, if something has properties, then it must exist. As Descartes wrote, "nothing has no properties".

@MJA,

MJA wrote:

I think infinity is everything beyond our minute and finite grasp of the universe. What do we truly know?
Perhaps if we try to define our finite knowledge, it would help us understand infinity.
Just an idea!

=
MJA

If you were to read, One, Two, Three, Infinity by George Gamow, you would learn a good deal about infinity. There is a field of mathematics of working mathematicians who are learning and teaching about infinity. All it takes is to find out about what you think we do not know.

@MJA,

MJA wrote:

I think infinity is everything beyond our minute and finite grasp of the universe. What do we truly know?
Perhaps if we try to define our finite knowledge, it would help us understand infinity.
Just an idea!

=
MJA

If you hear a sound it is just me pulling my size eleven redwing out of my mouth.. Okay. That is what I say: concentrate on the finite because that is what we can know. Now, here is the problem. Every day people push back the infinite by defining more of the finite. But even with finite reality the possibility of finding more of it, and more about it is there for the price of looking. So knowledge will never be so complete that we can judge finally even the finite around us with certainty.

So this question of knowledge dissolves into a moral question: do we know enough to recognize good, and to do good? Existence as we know it is life, and life we generally recognize as good, and so much so that we will do harm to others and to the environment to maintain it. Do we know enough to support this good we call life without causing harm? I trust that this is as close to an ultimate test of knowledge as we have, which is, what do we do with it? Knowledge is as knowledge does, and as Socrates said: Knowledge is virtue. I trust if we cannot do good with what we know, we in fact, know nothing.

kennethamy wrote:

We don't know there is no greatest integer because someone is still counting and not getting to the end. We know it because we know that no matter how long we count we can never get to the end. So being able to count has nothing whatever to do with our knowledge that there is no greatest integer. But I thinks you are talking about numerals, not numbers. The numeral "three" ("3", "iii", 'drei", "trois", "tres", etc.) points to the numbers of which the numerals are the names. The numeral, "three" is the name of the number, three. And, if there are three cows in the pasture, then the number of cows in the pasture is, three. And that is the reality that the numeral, three, points to. Namely, the successor to two; the predecessor of two; the first prime after two, and that square root of nine; among other of the properties of the number, three. And, if something has properties, then it must exist. As Descartes wrote, "nothing has no properties".

Nothing of a mental nature divorced from reality has properties. Numbers have meaning because as signs they point to a reality. Remove the reality and you have a sign without significance. It is a dream of a ghost with a key that fits no door that leads to no where. Logic has no purpose without reality, and no thought police to enforce its laws. Give it up.

kennethamy wrote:

If you were to read, One, Two, Three, Infinity by George Gamow, you would learn a good deal about infinity. There is a field of mathematics of working mathematicians who are learning and teaching about infinity. All it takes is to find out about what you think we do not know.

What do you know about infinity? What does george know about infinity? You don't know tomorrow. You don't know the day after. We have only one way of proving yesturday and it is only our testimony today. It is garbage philosophy to suggest any knowledge beyond the finite. Go git to church. Theology knows all there is to know about infinity, and take George with you.

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