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Humanities Section => Philosophy & Rhetoric General Discussion => Topic started by: Baruch on August 30, 2018, 07:19:07 AM

Title: Did you know that mathematics is just a useful fiction?
Post by: Baruch on August 30, 2018, 07:19:07 AM
https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalism

There are objections.  But this gets back to Pythagoras' cult, Plato's Academy and other crap.  If arithmetic is a useful fiction (it exists because humans and other sentients invented it and found it useful) ... what of other cultural constructs, such as religion ;-)
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Mousetrap on August 30, 2018, 08:48:12 AM
 Create your own Universe (https://www.newscientist.com/article/mg19125591-500-create-your-own-universe/)

If you read the above publication from Zeeya Merali, which I read in 2006 in Popular Mechanics, you will actually be a witness to how creative theoretical scientists are.

One will think that they started off with almost nothing, got a space vacuum in a space vacuum, bubbles of nothing popped out, a cosmic string was caught, is was placed in this space bubble, and a whole new universe came into existance by scientists waiting and watching the bubble grow infinitely large from the inside, but from the outside it remained infinitely minute.

One eventually then realize that it was never done in any lab, but it was mathematical equations manipulated by theoretical physicists all over the globe, to speculate on how it should be done, but these scientists need billions of dollars to build larger accelerators.

then again on the other-hand, if it was not for mathematical calculations, we would not have had Transistors.
Or is that also a concoction in the story of science.

Well, at least Newton used maths and it proved to be correct.
Oh, wait.
He used maths to calculate the observation, not create maths to postulate on theories.



Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Mousetrap on August 30, 2018, 09:01:03 AM
 Popular mechanics edition (http://www.popularmechanics.co.za/science/create-your-own-universe/)
Oh, I found it here.
It is a pity that not the whole article is available, but just read this nail biting scientific devour done by Sakai, Linde, Eduardo Guendelman, Alan Guth, Ed Farhi, Willy Fischler, and Jacov Portnoy.

Now, they might be great mathe-maticians, but they are even greater Mathe-magicians.

Then people say I feed everyone BS!
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on August 30, 2018, 12:45:24 PM
Sorry, only one unconfirmed magnetic monopole observation in history.  So building your own universe will have to wait.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 12, 2018, 01:16:07 AM
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Create your own Universe (https://www.newscientist.com/article/mg19125591-500-create-your-own-universe/)

If you read the above publication from Zeeya Merali, which I read in 2006 in Popular Mechanics, you will actually be a witness to how creative theoretical scientists are.

One will think that they started off with almost nothing, got a space vacuum in a space vacuum, bubbles of nothing popped out, a cosmic string was caught, is was placed in this space bubble, and a whole new universe came into existance by scientists waiting and watching the bubble grow infinitely large from the inside, but from the outside it remained infinitely minute.

One eventually then realize that it was never done in any lab, but it was mathematical equations manipulated by theoretical physicists all over the globe, to speculate on how it should be done, but these scientists need billions of dollars to build larger accelerators.

then again on the other-hand, if it was not for mathematical calculations, we would not have had Transistors.
Or is that also a concoction in the story of science.

Well, at least Newton used maths and it proved to be correct.
Oh, wait.
He used maths to calculate the observation, not create maths to postulate on theories.

Observations (to the limits of available equipment, as an extension of our senses) are true in themselves.  Theories based on observations fall like leaves from trees in Autumn. 

And, forgive me if I misunderstand this, but didn't Newton use maths to explain the observations rather than the reverse?  I think you have it backwards.   
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Shiranu on September 12, 2018, 01:26:00 AM
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https://en.wikipedia.org/wiki/Philosophy_of_mathematics#Fictionalism

There are objections.  But this gets back to Pythagoras' cult, Plato's Academy and other crap.  If arithmetic is a useful fiction (it exists because humans and other sentients invented it and found it useful) ... what of other cultural constructs, such as religion ;-)

The concept of mathematics varies between cultures, which to me shows that there is at the very least no inherently "true, one way to do" math. It is simply a language... one that is extremely versatile and useful, but a language non-the-less and thus one that is influenced by the culture practicing it. There are concepts that stand true amongst essentially all cultures, but the same can be said of language... nouns, verbs, adjectives exist in essentially all modern languages but that doesn't make these concepts "true" any more than 1+1 = 2 "true".

Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 12, 2018, 01:30:26 AM
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The concept of mathematics varies between cultures, which to me shows that there is at the very least no inherently "true, one way to do" math. It is simply a language... one that is extremely versatile and useful, but a language non-the-less and thus one that is influenced by the culture practicing it. There are concepts that stand true amongst essentially all cultures, but the same can be said of language... nouns, verbs, adjectives exist in essentially all modern languages but that doesn't make these concepts "true" any more than 1+1 = 2 "true".

In what way is 1+1=2 not logically true? 
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Shiranu on September 12, 2018, 01:50:41 AM
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In what way is 1+1=2 not logically true? 

It is logically true in our system, but that is not a statement of "realness". In mathematical systems that allow for the division of zero, you can have equations such as 1+1=1 and it makes logical sense as well.

Again, mathematics is just a form of language... there is no entity in the universe that is "1", only abstract conceptualization of "1".

A good example is "zero"... was "zero" a true number before the Mesoamericans or Indians invented it? We would say yes, but to anyone who existed before the concept of zero was conceived... they would say no. Is either side right or wrong? It all is subjective to what culture you were born into, what "language" you speak, so I would argue no.

Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 12, 2018, 03:23:55 AM
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It is logically true in our system, but that is not a statement of "realness". In mathematical systems that allow for the division of zero, you can have equations such as 1+1=1 and it makes logical sense as well.

Again, mathematics is just a form of language... there is no entity in the universe that is "1", only abstract conceptualization of "1".

A good example is "zero"... was "zero" a true number before the Mesoamericans or Indians invented it? We would say yes, but to anyone who existed before the concept of zero was conceived... they would say no. Is either side right or wrong? It all is subjective to what culture you were born into, what "language" you speak, so I would argue no.

I have come across this argument before.  There is a reason why, in practical terms, there is "1" (a singular quantity).  And another "1" makes "2".  I actually doubt that this would be untrue in any universe or rational system of counting.

In theoretical maths, I suppose there are ways for this not to be true, because you can set up any axioms you choose.  5 +7 = 10 in base 12.  Does that make 1+1=20 in base 1? 

I live in base 10.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 12, 2018, 07:07:41 AM
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I have come across this argument before.  There is a reason why, in practical terms, there is "1" (a singular quantity).  And another "1" makes "2".  I actually doubt that this would be untrue in any universe or rational system of counting.

In theoretical maths, I suppose there are ways for this not to be true, because you can set up any axioms you choose.  5 +7 = 10 in base 12.  Does that make 1+1=20 in base 1? 

I live in base 10.

Yes, in more abstract math, you can pretty much do anything you want, provided you are self-consistent.  Pythagoras was a demi-god, but he didn't know zero etc.  Euclid isn't a description of real space, for example, but it was thought to be so for 2000+ years.  This is why math isn't equivalent to reality.  It is the most abstract of languages, and is very useful as such, particularly in science and technology.  Interpolation is fairly reliable, but extrapolation less so.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on September 12, 2018, 01:50:28 PM
Why is there no 2 in base 2, no 3 in base 3, etc.?

;-P
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Hydra009 on September 12, 2018, 02:10:12 PM
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It is logically true in our system, but that is not a statement of "realness". In mathematical systems that allow for the division of zero, you can have equations such as 1+1=1 and it makes logical sense as well.
I suppose, but imho mathematics is a language meant to describe real-world interactions.  1 + 1 describes a set of one combining with another set of one to create a set of two, like a person with one cake acquiring another cake.  Mathematics is just the abstraction of that real-world scenario. 

Of course, not all math maps to reality - imaginary numbers and so forth exist because the logic that math operates on allows for i^2=-1 as well as 1+1=2.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 12, 2018, 02:21:56 PM
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Why is there no 2 in base 2, no 3 in base 3, etc.?

;-P

Because "3" in base 3 is "10".  Counting numbers in base 3 are 0, 1, 2, 10.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: pr126 on September 12, 2018, 02:23:00 PM
Study Claims Gifted Math Classes Promote 'Academic Apartheid' (https://pjmedia.com/trending/study-claims-gifted-math-classes-promote-academic-apartheid/)
Quote
A math education professor is arguing that gifted math classes cause “academic apartheid” among students, claiming that the practice is rooted in “capitalist exploitations and settler colonialism.”
LOL
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Draconic Aiur on September 12, 2018, 02:23:34 PM
Wikipedia? Really?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 12, 2018, 02:25:02 PM
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Study Claims Gifted Math Classes Promote 'Academic Apartheid' (https://pjmedia.com/trending/study-claims-gifted-math-classes-promote-academic-apartheid/)LOL

Even college professors can be idiots...
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 12, 2018, 08:58:04 PM
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Even college professors can be idiots...

Started with Plato, and his edible children's modeling clay ;-)
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 12, 2018, 09:01:31 PM
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Wikipedia? Really?

No, Beavis & Butthead.  But I liked Funk & Wagnalls better.

Encyclopedia Britannica is a British colonial plot!
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on September 13, 2018, 01:58:17 PM
I'm of the opinion that the universe is nothing but mathematics, at the most fundamental level.


Is the Universe Made of Math? (https://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/)

Mathematical universe hypothesis (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

Quote
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 13, 2018, 06:55:59 PM
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I'm of the opinion that the universe is nothing but mathematics, at the most fundamental level.


Is the Universe Made of Math? (https://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/)

Mathematical universe hypothesis (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

For a nihilist, it is base 0, all the way down ;-)

Pythagoras was a nut case.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: trdsf on September 14, 2018, 01:22:42 AM
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I'm of the opinion that the universe is nothing but mathematics, at the most fundamental level.


Is the Universe Made of Math? (https://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/)

Mathematical universe hypothesis (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)
It's an interesting idea, and I actually wouldn't be surprised if it points toward some interesting physics along the way, but I simply do not see how you get from a mathematical construct, even one describing a physical entity, to the actual physical entity.  The General Relativity field equation describes gravitation, it's not gravitation itself.

I will agree, of course, that the universe can be described mathematically, probably all the way down, and to high precision.  But I'll need to see a lot more before I'll seriously consider the possibility of reality being made of math.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: SGOS on September 14, 2018, 05:51:16 AM
Mathematics as fiction sounds like loose use to me.  As a philosophical topic where axioms are invented, and sematic creativity abounds maybe, but the math that describes reality falls apart in the unreal world.  For those who can't stand authority, reality is the ultimate authority and greatest challenge.  It cannot be defeated by what is not real.  It can be defied with words, but after all the wishful speculation, it will still be there.  And it applies to mathematicians as well as philosophers.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Sal1981 on September 14, 2018, 06:42:26 AM
Reality is what's left after you've stopped believing. I would think this is the same deal with mathematics and language.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 14, 2018, 07:18:40 AM
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Mathematics as fiction sounds like loose use to me.  As a philosophical topic where axioms are invented, and sematic creativity abounds maybe, but the math that describes reality falls apart in the unreal world.  For those who can't stand authority, reality is the ultimate authority and greatest challenge.  It cannot be defeated by what is not real.  It can be defied with words, but after all the wishful speculation, it will still be there.  And it applies to mathematicians as well as philosophers.

Ayn Rand would agree with you.  Ironic isn't it?

You can ignore reality, but not the effects of ignoring reality.  Please tell Maduro.  In reality, almost all humans are innumerate, so no wonder economics is a scary ride.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 15, 2018, 12:36:37 AM
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I'm of the opinion that the universe is nothing but mathematics, at the most fundamental level.


Is the Universe Made of Math? (https://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/)

Mathematical universe hypothesis (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

Maths are no more than our best guesses at interpretations of reality.  And I do think there IS reality.  In the future, maths will change to better reflect what we know about reality.  I don't have the slightest idea if we will EVER find maths (or other ways) to finally reflect reality, but I'm sure that our current maths are wrong. 

Here's a thought.  What is the speed of light ISN'T the best constant.  What if the universal inflation via dark energy is really "IT".  That would change everything, wouldn't it?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Draconic Aiur on September 15, 2018, 01:50:19 AM
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No, Beavis & Butthead.  But I liked Funk & Wagnalls better.

Encyclopedia Britannica is a British colonial plot!

As always the douche clown are we?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 15, 2018, 02:07:04 AM
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As always the douche clown are we?

There is just really no accounting for Baruch.  As best I can understand him, he has 3 goals;  Jokes, post count, and sarcasm without meaning.  There is always Some Person on every site like that.

They are unstoppable when there are weak admins and they annoy most of the serious posters.  I personally have to work around most of his posts to find legitimate ones to reply to from the serious posters.  Sometimes, there is nothing more frustrating than coming online and finding the last few dozen utterly meaningless posts all from Baruch.  I have to check each one to see if there was a previous poster with a sensible post.  Those, I respond to.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 15, 2018, 06:17:42 AM
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There is just really no accounting for Baruch.  As best I can understand him, he has 3 goals;  Jokes, post count, and sarcasm without meaning.  There is always Some Person on every site like that.

They are unstoppable when there are weak admins and they annoy most of the serious posters.  I personally have to work around most of his posts to find legitimate ones to reply to from the serious posters.  Sometimes, there is nothing more frustrating than coming online and finding the last few dozen utterly meaningless posts all from Baruch.  I have to check each one to see if there was a previous poster with a sensible post.  Those, I respond to.

As an Uber-Admin ... as you frequently desire .. you would make all posters do 100 push ups or else.  Rather Germanic that.

See, the admins do allow moderate ad hominem ... thought I am not fond of getting personal myself.  Your contribution is ...

Curmugeon
Geriatricism
Fur Ball

Not that there is anything wrong with being even older than I am.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 07:13:21 AM
Mathematics and logic both start with axioms. If that's what you mean by "useful fiction" then they're a useful fiction.

But the problem is... you can't even make a distinction between fictional and non-fictional without first accepting the fundamental axioms of logic. And we only need the fundamental axioms of logic to get at least basic numeracy going. As mathematics is basically logic with numbers.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 07:25:57 AM
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Mathematics and logic both start with axioms. If that's what you mean by "useful fiction" then they're a useful fiction.

But the problem is... you can't even make a distinction between fictional and non-fictional without first accepting the fundamental axioms of logic. And we only need the fundamental axioms of logic to get at least basic numeracy going. As mathematics is basically logic with numbers.

I accept basic axioms.  1+1=2, plane triangles are 180 degrees, etc. 
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 07:41:52 AM
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I accept basic axioms.  1+1=2, plane triangles are 180 degrees, etc.

I think we have to, at the very least, accept the law of identity... otherwise we can't even accept the fact that we exist, let alone objective reality.

Even "I think therefore I am" replies upon "I think=I think", "therefore=therefore" and "I am=I am"... "Cogito, ergo sum." relies on the law of identity.

But of course, this is when we're talking about logical and rational knowledge. In the sense of conscious awareness.... we all know our consciousness exists simply by being aware of it... whether we accept that consciousness=consciousness and awareness=awareness or not. We need the law of identity to prove to another person that they are conscious, but if they are conscious they still know it, in the sense that they are aware of it, whether we can convince them or not.

Hell, if reptiles are semi-conscious then they are at least semi-conscious of their own semi-consciousness. And in that sense they 'know' that they are aware... whether they can articulate it rationally or not.

So... consciousness is the most fundamental starting point of knowledge if by knowledge we are referring to empiricism.... but the law of identity is the most fundamental starting point of knowledge if we're talking of rationalism.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 07:44:54 AM
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I think we have to, at the very least, accept the law of identity... otherwise we can't even accept the fact that we exist, let alone objective reality.

Even "I think therefore I am" replies upon "I think=I think", "therefore=therefore" and "I am=I am"... "Cogito, ergo sum." relies on the law of identity.

But of course, this is when we're talking about logical and rational knowledge. In the sense of conscious awareness.... we all know our consciousness exists simply by being aware of it... whether we accept that consciousness=consciousness and awareness=awareness or not. We need the law of identity to prove to another person that they are conscious, but if they are conscious they still know it, in the sense that they are aware of it, whether we can convince them or not.

Hell, if reptiles are semi-conscious then they are at least semi-conscious of their own semi-consciousness. And in that sense they 'know' that they are aware... whether they can articulate it rationally or not.

So... consciousness is the most fundamental starting point of knowledge if by knowledge we are referring to empiricism.... but the law of identity is the most fundamental starting point of knowledge if we're talking of rationalism.

Oh crap, you are a philosopher! 

Sorry, I'm real.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: SGOS on September 27, 2018, 08:18:56 AM
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Oh crap, you are a philosopher! 

Sorry, I'm real.
I'm tracking with him pretty well.  I think he's actually saying what you are saying, but explaining with some logical examples.  I would paraphrase his intent by saying 1 + 1 = 2 can be considered philosophy but differs in that it is logical, and not the equivalent of what drunk college students do in their dorm rooms at 2:00 AM while proposing that they have come up with some important philosophical achievement.  You know like, "atoms resemble our solar system with particles swirling about a heavy center.  Therefore, maybe we are just part of some giant frying pan." 

So far, I think he has his feet on the ground, maybe making it more complicated than necessary, which creates kind of an impression that he might suddenly lapse into some esoteric and useless philosophy.  But I think what he says is pretty basic.  I don't think he is questioning identity.  Some people may, but don't assume he is trying to lead you off into a world of absurd confusion.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 10:01:00 AM
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I'm tracking with him pretty well.  I think he's actually saying what you are saying, but explaining with some logical examples.  I would paraphrase his intent by saying 1 + 1 = 2 can be considered philosophy but differs in that it is logical, and not the equivalent of what drunk college students do in their dorm rooms at 2:00 AM while proposing that they have come up with some important philosophical achievement.  You know like, "atoms resemble our solar system with particles swirling about a heavy center.  Therefore, maybe we are just part of some giant frying pan." 

So far, I think he has his feet on the ground, maybe making it more complicated than necessary, which creates kind of an impression that he might suddenly lapse into some esoteric and useless philosophy.  But I think what he says is pretty basic.  I don't think he is questioning identity.  Some people may, but don't assume he is trying to lead you off into a world of absurd confusion.

I respect your opinion,  but philosophy just leaves me laughing.  Beyond "I think, therefore I am.", the rest is pretty much either obvious or silly.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: trdsf on September 27, 2018, 01:30:23 PM
My favorite definition of philosophy is the one offered by comedian Alexei Sayle: 'picking fights with dead people'.

I generally lose interest when it becomes wooly and waffly.  I like things that can be measured and quantified.  Light with a wavelength of 700nm is measurably that, without any regard as to whether we experience that shade of red the same way.  I call something 'red' and you call it 'orange' and the spectrometer says "It's got a wavelength of 622nm and your names for that aren't relevant."
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:33:20 PM
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Oh crap, you are a philosopher! 

Sorry, I'm real.

I'm a philosophizer. I don't have a job as a philosopher. I'm a philosopher if all you mean is that I'm a philosophizer.

Yes, you are real. No need to apologize.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 01:37:17 PM
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I'm a philosophizer. I don't have a job as a philosopher. I'm a philosopher if all you mean is that I'm a philosophizer.

Yes, you are real. No need to apologize.

I should be kinder...  Have you ever been on a discussion board before?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Hydra009 on September 27, 2018, 01:39:36 PM
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I respect your opinion,  but philosophy just leaves me laughing.  Beyond "I think, therefore I am.", the rest is pretty much either obvious or silly.
Obvious now.  Not obvious then.  Or at least not formalized.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: SGOS on September 27, 2018, 01:46:56 PM
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I'm a philosophizer. I don't have a job as a philosopher. I'm a philosopher if all you mean is that I'm a philosophizer.
Some people philosophize.  Other's don't.  Fortunately, you can ignore either group.  Unless, everything is predetermined, and then you're screwed.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:50:50 PM
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I don't think he is questioning identity.  Some people may, but don't assume he is trying to lead you off into a world of absurd confusion.

Indeed. I was doing the opposite of questioning identity. I was saying that identity is the most important logical axiom of all, because without it, nothing else makes sense logically. And you can't even make a distinction between true and false, or logical and illogical, without first accepting it.

I then went on to say that the only thing that is known even deeper than that is the fact that our own consciousness exists. "I think therefore I am".... but even that requires the law of identity if we are to know it in terms of logic, because we have to assume that I=I and thinking=thinking.

But I also said that to know it empirically, to be aware of our awareness, we don't have to know or accept logic at all. And even animals can do that. So in that sense the ultimate and deepest truth of all is our own consciousness and that can be known even without the law of identity... it just can't be known in terms of logic without the law of identity, because the law of identity is the beginning of logic.

Far from being someone who doesn't even accept objective truth... I believe all truth is objective... and the very meaning of truth already presupposes the law of identity and logic.... so I believe that the logical absolutes are indeed absolute and 100% true and couldn't not be and they'd be true whether I existed or not. And yes, that is because truth presupposes the law of identity, but that doesn't stop it being the most logical axiom to accept. there is no sense in which the logical absolutes can't be true... the only way they can't be true is if nothing is true... which doesn't even make any sense to say. Making sense of anything in logical terms requires the logical absolutes.

I don't know how better to explain it really. Basically, just because we have to use certain definitions before we can make sense of even the law of identity, doesn't mean that we don't even know that the law of identity is true. As, to know anything at all logically, we already have to assume it. So, if we're talking about knowledge, we're already talking about the law of identity, if we're talking about logical knowledge.

Hmm. Let me see if I can try and simplify it even further as that's still probably too convoluted to a lot of people.

Okay how about this: If I say that we have to presuppose the law of identity to even know that we ourselves exist in logical terms and the response we get is "You're saying that you don't know you exist!"... the response to that is for us to say "To even talk of knowledge at all is already to presuppose it. So how can I be saying I don't know something if the whole concept of knowledge only makes sense once I already accept that I know it?". Also, it's important to note that I'm saying that we need to accept the law of identity before we can know that we exist in logical terms. As I already pointed out, even without logic, and without the law of identity, we know that we exist in empirical terms simply by having experiences.... whether we accept that having an experience is having an experience and we are ourselves or not. The law of identity doesn't even need to be accepted in order to know that we exist simply by our being aware of it. We can know that we exist in the empirical sense without any logic at all.

But, in a way, consciousness itself is the beginning of the law of identity. Because the one thing that we intrinsically know exists, is our own existence. Basically, we know our experience simply by having it. That is self referential... and perhaps the law of identity developed out of that.

"Even if the whole of reality exists... my subjective experience exists. The experience I am having is whatever it is. If I call my experience E then E=E."

In order to make sense of our experience in logical terms we have to develop the law of identity, perhaps, rather than presuppose it. Maybe the very reason we develop the law of identity in the first place, then, is the fact that we know that we are having an experience. But again, this would be knowledge in the empirical sense. So logical knowledge may presuppose logical knowledge. But, indeed, to have any logical knowledge at all that at least first presupposes the law of identity.

Hopefully my repetitiousness has made things more clear because if explaining X didn't make say by explaining it one way, perhaps it made sense in a second, third, fourth or fifth way. If none of my explanations make sense to anyone but myself then I don't really know what more I can do really. I'm trying.

But if my views differ from anybody else's, I offer this quotation:

"My aim is not to try to convince anyone of anything, but to record the truth of the matter as far as I can. " - Galen Strawson
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:52:14 PM
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I respect your opinion,  but philosophy just leaves me laughing.  Beyond "I think, therefore I am.", the rest is pretty much either obvious or silly.

I'm not at all surprised that you have this view of philosophy. I've already made an assessment on the logicality (or lack thereof) of your responses to me thus far on this forum, and perhaps a little analytic philosophy (at least) would do you some good.

Fair enough if you're not interested and if it leaves you laughing though. Each to their own.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 01:53:14 PM
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Some people philosophize.  Other's don't.  Fortunately, you can ignore either group.  Unless, everything is predetermined, and then you're screwed.

You don't have to be a philosopher to understand reality.  Oh wait, that IS what they argue about.  Cogito ergo sum, and don't kill your neighbor works pretty well.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:53:38 PM
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I should be kinder...  Have you ever been on a discussion board before?

Yes, I have been on at least one discussion board before.

I haven't seen any unkindness coming from your direction.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:56:49 PM
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Some people philosophize.  Other's don't.  Fortunately, you can ignore either group.  Unless, everything is predetermined, and then you're screwed.

I don't think everything is predetermined by some kind of God. It depends what you mean by "predetermined". I don't think that the future is already "out there", and I don't think that it has already happened... as, as far as I am concerned, the future is what will happen but hasn't happened yet. The future is unavoidable and inevitable, but that's true regardless of whether the future is determined or undetermined.

I think that there is exactly one possible future... but that's simply because I think that believing that is more parsimonious than believing that there's more than one possible future. There could easily be more than one possible future . . . but in either case, the future is unavoidable and inevitable, whether it's determined or not. We can't change what will happen into what won't happen any more than we can change what was into what wasn't.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 01:59:37 PM
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You don't have to be a philosopher to understand reality.  Oh wait, that IS what they argue about.  Cogito ergo sum, and don't kill your neighbor works pretty well.

I'm far more interested in what's correct than what works.

But, as it happens, sometimes the most useful approach in the long run is to not directly seek what's useful, and to instead start with what's true and factual, regardless of utility.

I see that as what I call "the paradox of pragmatism"... where directly trying to be pragmatic ends up being less pragmatic in the long run....

I came up with the name for "the paradox of pragmatism" after seeing it to be analogous with "the paradox of hedonism".... the idea that sometimes the best way to be happy is to not directly aim for happiness.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 02:02:34 PM
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I'm not at all surprised that you have this view of philosophy. I've already made an assessment on the logicality (or lack thereof) of your responses to me thus far on this forum, and perhaps a little analytic philosophy (at least) would do you some good.

Fair enough if you're not interested and if it leaves you laughing though. Each to their own.

OMNEG, yer killing me here!  Look "philosophy" is for young or confused people who are troubled by reality.  I had my time of that in college.  But then I grew up.

If you want to argue ethics and such, I'll by glad to engage.  But please don't bother me with "what is reality".  Been there, done that,  look around, and use your senses...
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 02:15:30 PM
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OMNEG, yer killing me here!  Look "philosophy" is for young or confused people who are troubled by reality.  I had my time of that in college.  But then I grew up.

If you want to argue ethics and such, I'll by glad to engage.  But please don't bother me with "what is reality".  Been there, done that,  look around, and use your senses...

It is clear that you already hold the philosophical view of empiricism then.

But you do make other logical mistakes that I've already pointed out elsewhere.

Sure, we can argue ethics, but metaphysics and epistemology are very relevant to ethics as is metaethics and normative ethics.

Let's not argue ethics on this thread though.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 02:24:52 PM
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It is clear that you already hold the philosophical view of empiricism then.

But you do make other logical mistakes that I've already pointed out elsewhere.

Sure, we can argue ethics, but metaphysics and epistemology are very relevant to ethics as is metaethics and normative ethics.

Let's not argue ethics on this thread though.

Well, why not?  We can all grouply hijack the thread.    Do you think people act on morals or do they act on ethics?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 02:28:50 PM
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Well, why not?  We can all grouply hijack the thread.    Do you think people act on morals or do they act on ethics?

Neither. I think people act on self-interest.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: SGOS on September 27, 2018, 02:30:23 PM
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I don't think everything is predetermined by some kind of God. It depends what you mean by "predetermined". I don't think that the future is already "out there", and I don't think that it has already happened... as, as far as I am concerned, the future is what will happen but hasn't happened yet. The future is unavoidable and inevitable, but that's true regardless of whether the future is determined or undetermined.

I think that there is exactly one possible future... but that's simply because I think that believing that is more parsimonious than believing that there's more than one possible future. There could easily be more than one possible future . . . but in either case, the future is unavoidable and inevitable, whether it's determined or not. We can't change what will happen into what won't happen any more than we can change what was into what wasn't.
Don't make too much of it.  I was just making a joke. 
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 02:33:29 PM
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Neither. I think people act on self-interest.

Is there no sense of altrusim in you philosophism?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 02:35:45 PM
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Don't make too much of it.  I was just making a joke.

Oh. I completely missed it.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 02:52:56 PM
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Is there no sense of altrusim in you philosophism?

It depends how altruism is defined.

People can and do indeed engage in acts of self-sacrifice... but I also think that they at least subconsciously believe that they have some benefit to engaging in such an act.

But, I mean, if someone saves the life of their child and ends up dying because they care for their child, could we really call such an act selfish simply because the reason that they care for their child may ultimately be because they care for their own values and they see their child as part of what is most valuable to them (even if on the surface it may seem that they selflessly care about their child)?

If even the most selfless acts can be called selfish... then that seems like an incredibly loose definition of selfish.

But this is why I said self-interest. I think people ultimately do what is in their self interest, whether they know it or not, and this includes even the most selfless and self-sacrificing acts. I wouldn't call such acts selfish because of the negative connotation that I think doesn't apply there. But I do think that everything we do is ultimately down to self-interest. I mean, all our motives come from our self, and our motives and interests are synonymous as far as I'm concerned. If we're motivated to care about others then we're interested in caring about others.

If we didn't get any sort of benefit at all from engaging in self-sacrificing acts I don't think we would do them.

I mean, for starters, if someone who deeply cared about their children didn't sacrifice themselves to save their child... they may spend the rest of their life suffering greatly due to their regret of not saving their child when they had the opportunity to. So on the one hand you may say they only have such regret because they're selfless enough to care about their child... but on the other hand you may also say that people who are motivated to care about their child may be driven to do so because they don't want to feel the pain of regret or remorse if they don't save their child. But, of course, the person will be convinced that they genuinely care about their child and it has nothing to do with the regret or remorse they will feel if they don't save their child. But people can easily be mistaken about how selfish or selfless they are which is kind of what I'm getting at.

So, I'm a psychological egoist: I think people do what is in their self interest. You could say that I'm also an ethical egoist because I obviously must think people should do what their only option is as it would make no sense for me to say that someone shouldn't do what they must do... but that would be misleading. I think that acts of self-sacrifice for others can be a very ethical thing to do. I just think that people can only do it when it is ultimately in their own interest to do so. And, if I think that ALL acts already are in one's own self interest... then it's kind of just as redundant for me to say that all acts should be in our self interest as it would be to say that no acts should be in our self interest. If our our only option is A then it seems silly to say that we should do A simply because it's our only option. If it's our only option then there isn't really an option. The whole should or shouldn't thing doesn't make sense without more than one option, in a way.

This would seem that I am a moral nihilist. I'm not though. I think there is objective right and wrong. I just don't think it makes sense to say that people are morally obligated if people don't have any moral options. When I say that morality is objective all I'm saying is that some results are better than others. Some things are worse for people than others, morally speaking, regardless of choice.

But some people would say that objective morality without moral obligation isn't really morality... as what people ought to or ought to not be obligated to do is required for morality... according to some. To some, it's not enough for me to say "X would be objectively the right action to take if one could take it" because some would say that ought implies can...

But, by denying obligations, I guess I am saying that there are right answers in theory but not in practice. I am saying that if one could do otherwise, if one could do Y instead of X, then Y would be the right action, for objective reasons.

Perhaps it would make more sense to say that I believe in objective moral values, even if I still deny objective moral obligations, but if the word "moral" is still problematic there (as some believe that morality implies obligation), then I think it's perhaps most correct to say that I believe in objective right and wrong behavior.

I don't know. Basically, take objective morality and then take the obligation part out of it... and that's my view. I think some actions really are wrong and others really are right... I just think it makes no sense for others to be obligated to do otherwise if all the can really do is what's in their own interest.

Now, I'm talking in logical terms. In practical terms, moral obligations obviously do make sense. It makes sense to hold people responsible in certain situations even if they aren't, if that is the best for society and that is the best for individuals. A kind of practical moral responsibility and obligation can make sense even if it isn't possible logically. The idea is that acting as if such things made sense, is better for everyone.

Then there's those who would say that the practical terms are just as important and just as real.... therefore it is real. And I would say, yes, of course, just not in the same sense.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on September 27, 2018, 03:12:59 PM
Well said.  I do think there is a difference between self-sacrifice and making decisions for "the greater good" in a general sense.

I don't vote for my specific benefit often, more for a generally functional nation, for example.

And I've heard your argument mostly from business majors and politicians, to be honest, which isn't the best ethical support.  Your opinion gets you into Hobbes and Locke and Son Of Nature, etc.

But I've been online since 8 pm EDT yesterday and haven't eaten AND I have a blog post to finish, so I need to make breakfast/lunch/dinner and feed the cats (again) etc. 

It will be interesting to see where this has gone in a few days when I return. 

EOL
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on September 27, 2018, 04:08:06 PM
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Well said.  I do think there is a difference between self-sacrifice and making decisions for "the greater good" in a general sense.

What do you think that difference is?

Quote
I don't vote for my specific benefit often, more for a generally functional nation, for example.

So my view is that the reason why you vote for the benefit of a generally functional nation rather than for your own benefit... is ultimately because it's in your own self-interest to do so. You obviously want to vote for a generally functional nation, and are interested in a generally functional nation, for whatever reasons.

So when I am talking about self-interest I mean it in the incredibly broad sense. I am certainly not saying that people directly always go for what's in their own self-interest... as if that were the case acts of self-sacrifice wouldn't even be possible.

Voting for your own benefit would be directly acting in your own self interest. You say that voting for the benefit of your nation is not an act of self-interest... whereas I say that the very reason why you vote for the benefit of your nation is because you want to, so it's ultimately an act of self-interest.

Quote
And I've heard your argument mostly from business majors and politicians, to be honest, which isn't the best ethical support.

I'm not making an argument for ethics right now though. At the moment I'm only being descriptive, not prescriptive. And, in fact, I said that I think that acts of self-sacrifice can be morally good. I don't see how that aligns with "business majors and politicians".

 
Quote
Your opinion gets you into Hobbes and Locke and Son Of Nature, etc.

I don't know how you draw that conclusion. And, if anything, when you said that you vote for the benefit of your nation, rather than yourself, I think that gets you closer to Hobbes than me. Hobbes had a very collectivist view, and spoke of the Leviathan, and formed a particular conceptualization of the social contract in order to get what's best for society. But I'm not interested in what's best for society. I'm interested in what's best for individuals. But not just me, other people too. I just think that the only reason I care about others, or others care about me, is because it's in my self interest to care about others and in the interest of others to care about me.

But If you suggest that caring about others can't be good if they ultimately come from selfish motives then you're committing the genetic fallacy. So it's not at all problematic for helping others to be motivated by self interest.

I'm not prescribing or obligating people to do what's best for society, others, or even themselves. I'm saying that I think acts of self-sacrifice can be objectively good... but even when people do those acts they do them because that's in their own self-interest. That was a descriptive claim, not a prescriptive one. If I made any prescriptive claims at all I claimed that helping others can be good. And absolutely nowhere did I say that being selfish at the expense of others can be good.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 28, 2018, 05:31:44 AM
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Mathematics and logic both start with axioms. If that's what you mean by "useful fiction" then they're a useful fiction.

But the problem is... you can't even make a distinction between fictional and non-fictional without first accepting the fundamental axioms of logic. And we only need the fundamental axioms of logic to get at least basic numeracy going. As mathematics is basically logic with numbers.

I know you are very bright.  That is evidence of a quality British education (what is that?  many here are Americans, stop using big words).

If you get deeper into higher level logic, into modal logic, into paraconsistent logic ... then no, the Law of Identity doesn't hold.  The question about axioms isn't absolute but relative.  Under which conditions does the axiom hold, and under what conditions does it not hold.  Unless of course you have fallen into the black hole of the Principia Mathematica ... and there is no hope for you ;-)

Cavebear is right in this way ... in Principia Mathematica, Russell and Whitehead took 350 pages of proof to show that 1 + 1 = 2.  I am not impressed.  It would seem they were pushing the rope, not yet aware (how could they) the relationship between logic an algebra.  Mathematics is more dialectical than deductive ... unless you are David Hilbert.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 28, 2018, 05:35:29 AM
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Some people philosophize.  Other's don't.  Fortunately, you can ignore either group.  Unless, everything is predetermined, and then you're screwed.

Another target rich environment.  Gotta reload my chain gun.

I agree with your.  But to opportunistically reply to the new poster ... the law of identity has been already disposed of by Heraclitus.  And a succeeding thinker, whose name escapes me ... says "you can't even step into the same river once".  That trickiness is why most here eschew philosophy, aside from a few pragmatic or artistic views.

The forum on Philosophy Today might be the best place for this kind of discussion.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: SGOS on September 28, 2018, 05:50:44 AM
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Another target rich environment.  Gotta reload my chain gun.

I agree with your.  But to opportunistically reply to the new poster ... the law of identity has been already disposed of by Heraclitus.  And a succeeding thinker, whose name escapes me ... says "you can't even step into the same river once".  That trickiness is why most here eschew philosophy, aside from a few pragmatic or artistic views.

The forum on Philosophy Today might be the best place for this kind of discussion.

And furthermore:

Paraconsistent logic (paraconsistent doesn't even make it past my spell checker) is not consistent.  Theists love this sort of shit. 

Quote
From Wiki:  Suppose we are faced with a contradictory set of premises Γ and wish to avoid being reduced to triviality. In classical logic, the only method one can use is to reject one or more of the premises in Γ. In paraconsistent logic, we may try to compartmentalize the contradiction. That is, weaken the logic so that Γ→X is no longer a tautology provided the propositional variable X does not appear in Γ. However, we do not want to weaken the logic any more than is necessary for that purpose. So we wish to retain modus ponens and the deduction theorem as well as the axioms which are the introduction and elimination rules for the logical connectives (where possible).

Yes, don't let the Bible thumpers get a hold of this one, or you'll never hear the end of it.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 28, 2018, 05:53:37 AM
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And furthermore:

Paraconsistent logic (paraconsistent doesn't even make it past my spell checker) is not consistent.  Theists love this sort of shit. 

Yes, don't let the Bible thumpers get a hold of this one, or you'll never hear the end of it.

We had an earlier string on this, so I won't repeat.  There is a difference between paraconsistent logic (as defined by professionals) and just pulling things out of your nether regions.  I deal with inconsistency in databases every day.  Maybe that problem doesn't exist in Plato's World Of Forms.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Hakurei Reimu on September 28, 2018, 06:09:41 PM
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I agree with your.  But to opportunistically reply to the new poster ... the law of identity has been already disposed of by Heraclitus.  And a succeeding thinker, whose name escapes me ... says "you can't even step into the same river once".  That trickiness is why most here eschew philosophy, aside from a few pragmatic or artistic views.
Yet you can't make sense of that statement (Heraclitus's original was "you cannot step twice into the same stream" — except it was in Greek) unless you have some notion of what "the same river/stream" means. Just because some things don't retain their physical identical-ness across time doesn't mean there's no such thing as identity, nor that the law of identity is invalid. Indeed, the statement loses its profundity if the law of identity is not a thing.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on September 28, 2018, 06:51:18 PM
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Yet you can't make sense of that statement (Heraclitus's original was "you cannot step twice into the same stream" — except it was in Greek) unless you have some notion of what "the same river/stream" means. Just because some things don't retain their physical identical-ness across time doesn't mean there's no such thing as identity, nor that the law of identity is invalid. Indeed, the statement loses its profundity if the law of identity is not a thing.

Oh know, should have quoted the original Greek, which had no punctuation ... the horror!

But you didn't even bother to help me with the naming they ancient guy who hyperbolicised Heraclitean flux.  And I know that what you know of logic is undergraduate level.  Not bad for the kinds of problems given to them.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 01, 2018, 08:10:40 AM
Both Baruch and Luckswallowsall engage in the same fallacy.  That unfactual philosophy (being mostly mid-experiments) has meaning in a rational world.  Their problem is that they can't use actual facts to support their arguments because their arguments are not fact based.  And any argument not fact-based isn't worth the paper it cannot be printed on in less than 5,000 pages.



Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 01, 2018, 12:41:00 PM
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Both Baruch and Luckswallowsall engage in the same fallacy.  That unfactual philosophy (being mostly mid-experiments) has meaning in a rational world.  Their problem is that they can't use actual facts to support their arguments because their arguments are not fact based.  And any argument not fact-based isn't worth the paper it cannot be printed on in less than 5,000 pages.

While I agree that philosophy can be mostly chasing your own tail ... not all of it is.  And yes, you need grounding in actual facts (from which deductions can then be made).
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 01, 2018, 12:58:11 PM
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While I agree that philosophy can be mostly chasing your own tail ... not all of it is.  And yes, you need grounding in actual facts (from which deductions can then be made).

Name a fact-based philosopher...  I say Kant comes closest, mostly because he rejects other philosophers and is mostly reality-based.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 01, 2018, 01:04:38 PM
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Name a fact-based philosopher...  I say Kant comes closest, mostly because he rejects other philosophers and is mostly reality-based.

Sorry, David Hume was anti-BS ... more than any other.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on October 01, 2018, 01:10:15 PM
I'd say Bertrand Russell comes pretty close to being the most fact-based philosopher.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 01, 2018, 01:12:57 PM
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I'd say Bertrand Russell comes pretty close to being the most fact-based philosopher.
  Well, I was thinking more classical philosophers, but OK.  Tell me what Russell thought.  I could look it up, but I value your interpretation.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 01, 2018, 07:28:22 PM
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I'd say Bertrand Russell comes pretty close to being the most fact-based philosopher.

Bertrand Arthur William Russell, 3rd Earl Russell, OM FRS was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

Very unaccomplished person.  An even changed his mind sometimes.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on October 01, 2018, 08:24:29 PM
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  Well, I was thinking more classical philosophers, but OK.  Tell me what Russell thought.  I could look it up, but I value your interpretation.

He also had a very progressive school for the time. I don't know that I can actually summarize his work, since there was quite a lot of it, and I haven't read it all. I have read, and treasure, Why I Am Not a Christian.

One of his gems is: “What really moves people to believe in God is not any intellectual argument at all. Most people believe in God because they have been taught from early infancy to do it, and that is the main reason.”
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 05:09:30 AM
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Bertrand Arthur William Russell, 3rd Earl Russell, OM FRS was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

Very unaccomplished person.  An even changed his mind sometimes.

And you told me absolutely nothing useful about him... 
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 05:12:19 AM
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He also had a very progressive school for the time. I don't know that I can actually summarize his work, since there was quite a lot of it, and I haven't read it all. I have read, and treasure, Why I Am Not a Christian.

One of his gems is: “What really moves people to believe in God is not any intellectual argument at all. Most people believe in God because they have been taught from early infancy to do it, and that is the main reason.”

THAT I can understand.  Most people remain just as they were raised to be.  Some start to think for themselves.  SOME few actually manage it.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:07:02 AM
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And you told me absolutely nothing useful about him...

Apparently none of those things ... philosophy, mathematics etc are useful to you.

And yes, you do find it useful to have echo-chamber confirmation of your own views.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 07:14:38 AM
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Apparently none of those things ... philosophy, mathematics etc are useful to you.

And yes, you do find it useful to have echo-chamber confirmation of your own views.

The last thing I want is an echo chamber.

The last thing I want is an echo chamber.

LOL!
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:19:35 AM
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The last thing I want is an echo chamber.

The last thing I want is an echo chamber.

LOL!

Echo (nymph) was in love with the boy Narcissus ... figures.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 07:21:52 AM
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Echo (nymph) was in love with the boy Narcissus ... figures.

Yes, I know the basic myths and some odd ones too.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: luckswallowsall on October 04, 2018, 10:40:54 AM
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I know you are very bright.  That is evidence of a quality British education (what is that?  many here are Americans, stop using big words).

None of this is relevant.

Quote
If you get deeper into higher level logic, into modal logic, into paraconsistent logic ... then no, the Law of Identity doesn't hold.

The opposite is the case. I mean, for starters, modal logic can't even make sense without the law of identity. Something is what it is. A=A. Modal logic talks of possible worlds and also of how some worlds are logically impossible... but logical possibility and logical impossibility can only hold as concepts if they can hold as concepts. if A=A.

Literally all of logic falls apart without the law of identity.

 The question about axioms isn't absolute but relative.  Under which conditions does the axiom hold, and under what conditions does it not hold.
[/quote]

For any axiom to exist at all an axiom has to be an axiom. No other laws can make any sense without the law of identity. Without the law of identity all there is is illogical equivocation and confusion. And even that would prove the law of identity because if it's true to say that there's illogicality then it's true to say that there's illogicality... literally even arguing against the law of identity confirms the law of identity. The law of identity is the starting axiom for the whole of logic.

Quote
Cavebear is right in this way ... in Principia Mathematica, Russell and Whitehead took 350 pages of proof to show that 1 + 1 = 2.  I am not impressed.

Whether you are impressed or not is irrelevant. And whether or not 1+1=2 can be proven or not is irrelevant to the fact that the law of identity is the foundation of logic. You can't deny it without denying it and if denying it is denying it then it is true and so your very own denying it is undeniably illogical. Any argument against the law of identity is self-defeating because to argue against it is to presuppose it.

Quote
It would seem they were pushing the rope, not yet aware (how could they) the relationship between logic an algebra.  Mathematics is more dialectical than deductive ... unless you are David Hilbert.

Algebra is like symbolic logic with numbers. The fact that you are acknowledging the relationship between mathematics and logic, works in my favor, not yours. Truths don't help you to argue against my point when those truths are either irrelevant to my point or support my point rather than yours.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on October 04, 2018, 02:52:53 PM
A renowned mathematician, Sir Michael Atiyah (https://en.wikipedia.org/wiki/Michael_Atiyah),  has recently claimed to have proved the Riemann hypothesis, a long-standing problem in mathematics. He will likely try to claim the prize offered by the Clay institute for a solution. But it has yet to be seen whether his solution really does constitute a proof:

https://www.newscientist.com/article/2180504-riemann-hypothesis-likely-remains-unsolved-despite-claimed-proof/

It would be fantastic if Riemann were indeed proven, since much of modern mathematics hinges on the truth of it. There are many mathematical results which are known to be true if the Riemann Hypothesis is be proven to be true.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 03:05:31 PM
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A renowned mathematician, Sir Michael Atiyah (https://en.wikipedia.org/wiki/Michael_Atiyah),  has recently claimed to have proved the Riemann hypothesis, a long-standing problem in mathematics. He will likely try to claim the prize offered by the Clay institute for a solution. But it has yet to be seen whether his solution really does constitute a proof:

https://www.newscientist.com/article/2180504-riemann-hypothesis-likely-remains-unsolved-despite-claimed-proof/

It would be fantastic if Riemann were indeed proven, since much of modern mathematics hinges on the truth of it. There are many mathematical results which are known to be true if the Riemann Hypothesis is be proven to be true.

It just HAD to be about prime numbers, LOL!  That's OK, it will never make the slightest practical difference in my life. 
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on October 04, 2018, 03:13:41 PM
Well, actually, it could. I've heard that if Riemann is proven, the entire internet might become a vast wasteland, or something.

Maths holy grail could bring disaster for internet (https://www.theguardian.com/technology/2004/sep/07/highereducation.science)
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 03:19:14 PM
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Well, actually, it could. I've heard that if Riemann is proven, the entire internet might become a vast wasteland, or something.

Maths holy grail could bring disaster for internet (https://www.theguardian.com/technology/2004/sep/07/highereducation.science)

Like a trinary computer.  When I see it, I'll buy it.  But most obscure math solutions stay that way for old farts like me.  "Impractical in my lifetime".  I've been waiting for my flying car since 1968...
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Hydra009 on October 04, 2018, 03:35:19 PM
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Well, actually, it could. I've heard that if Riemann is proven, the entire internet might become a vast wasteland, or something.

Maths holy grail could bring disaster for internet (https://www.theguardian.com/technology/2004/sep/07/highereducation.science)
I feel like I don't know enough about math to read even an executive summary of Riemann hypothesis.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Unbeliever on October 04, 2018, 03:41:21 PM
Well, it's pretty simple, really: All of the non-trivial zeros of the zeta function lie on the line 1/2 in the complex plane

See, simple!
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 03:48:56 PM
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Well, it's pretty simple, really: All of the non-trivial zeros of the zeta function lie on the line 1/2 in the complex plane

See, simple!

Uh huh...  So a duck, a badger, and an ostrich go into a bar...  The rest will make if you check out the joke thread...
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Hydra009 on October 04, 2018, 03:56:50 PM
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Well, it's pretty simple, really: All of the non-trivial zeros of the zeta function lie on the line 1/2 in the complex plane

See, simple!
*brains leak out his ears*
*collapses out of his chair*
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 04, 2018, 03:59:32 PM
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*brains leak out his ears*
*collapses out of his chair*

Oh well the Zeta function, of course.

No, I haven't a clue either.  I lost math at "e".
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:28:49 PM
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Like a trinary computer.  When I see it, I'll buy it.  But most obscure math solutions stay that way for old farts like me.  "Impractical in my lifetime".  I've been waiting for my flying car since 1968...

Computer busses already use 3 level logic.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:30:11 PM
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A renowned mathematician, Sir Michael Atiyah (https://en.wikipedia.org/wiki/Michael_Atiyah),  has recently claimed to have proved the Riemann hypothesis, a long-standing problem in mathematics. He will likely try to claim the prize offered by the Clay institute for a solution. But it has yet to be seen whether his solution really does constitute a proof:

https://www.newscientist.com/article/2180504-riemann-hypothesis-likely-remains-unsolved-despite-claimed-proof/

It would be fantastic if Riemann were indeed proven, since much of modern mathematics hinges on the truth of it. There are many mathematical results which are known to be true if the Riemann Hypothesis is be proven to be true.

Not truth ... consistent relative to some set of axioms.  Euclidean geometry isn't true, but in its final Hilbert version it is both rigorous and consistent.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:31:36 PM
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Well, it's pretty simple, really: All of the non-trivial zeros of the zeta function lie on the line 1/2 in the complex plane

See, simple!

The function makes a recursive infinitely deep fractal.  Such things are hard to prove yeah or neah.  You can always zoom into more detail.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 04, 2018, 07:32:53 PM
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Well, actually, it could. I've heard that if Riemann is proven, the entire internet might become a vast wasteland, or something.

Maths holy grail could bring disaster for internet (https://www.theguardian.com/technology/2004/sep/07/highereducation.science)

I you can break two-key (public/private) encryption, the Internet is toast.  This is why quantum computers are being developed.  Intelligence agencies are hoping for a free lunch.  I think a longer key can compete with a long enough q-bit chain.  This is the spook equivalent of Santa Claus.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 07, 2018, 03:30:36 AM
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Computer busses already use 3 level logic.

3 level logic is not the same as trinary.   I know it sounds similar, though.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 07, 2018, 04:11:14 AM
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3 level logic is not the same as trinary.   I know it sounds similar, though.

You didn't bother to explain.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 07, 2018, 04:28:28 AM
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You didn't bother to explain.

I'm not the one who introduced 3 level logic to the discussion.  You mentioned it, you explain it.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 07, 2018, 08:43:28 AM
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I'm not the one who introduced 3 level logic to the discussion.  You mentioned it, you explain it.

There is more than one kind, you didn't clearly identify which you meant.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 07, 2018, 10:12:21 AM
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There is more than one kind, you didn't clearly identify which you meant.

What part of...

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Computer busses already use 3 level logic.

don't you recall?
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Baruch on October 07, 2018, 11:40:14 AM
I do ...

Quote
3 level logic is not the same as trinary.   I know it sounds similar, though.
Title: Re: Did you know that mathematics is just a useful fiction?
Post by: Cavebear on October 07, 2018, 12:24:39 PM
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I do ...

You are conveniently forgetting who said what first.