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[William Flynn Wallace]

He wanted to know the meaning of this statement:

Mathematics is true, but it doesn't exist."

bill w

[Lawrence Crowell]

This depends upon what you mean by exist.

LC

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[John Clark]

On Wed, Mar 24, 2021 at 3:33 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> He wanted to know the meaning of this statement: "Mathematics is true, but it doesn't exist."

> This depends upon what you mean by exist.

Yeah, if mathematics doesn't exist then I'd like to know how things would be different if it did exist. My own view is mathematics is the language of physics so everything in the physical world has a counterpart in mathematics, but the reverse may not be true. Parts of modern mathematics have so many layers of abstraction and generalization and byzantine convolutions that it might have nothing to do with the physical world, and that development is not really surprising for a language, after all English is a language and it can be used to write a scientific paper but it can also be used to write a Harry Potter novel. And even if a fantasy novel is smart and entertaining and has no logical plot holes it's still fiction, it doesn't correlate with reality.

John K Clark

[Lawrence Crowell]

Well that is a very physical idea of the status of mathematics. My sense is that I don't really know, I am not sure what in general it means for a mathematical object to exist. Also if you think about it, you can run from Brouwer intuitionism to Dedekind constructionism to more objective ideas similar to Platonism, and no matter what you are never completely happy with it. It is a bit strange.

LC

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[Dan TheBookMan]

On Mar 24, 2021, at 1:37 PM, Lawrence Crowell <goldenfield...@gmail.com> wrote:



Well that is a very physical idea of the status of mathematics. My sense is that I don't really know, I am not sure what in general it means for a mathematical object to exist. Also if you think about it, you can run from Brouwer intuitionism to Dedekind constructionism to more objective ideas similar to Platonism, and no matter what you are never completely happy with it. It is a bit strange.

LC

 

A view that has some popularity in philosophy of mathematics circles is mathematical naturalism. This is the notion that mathematics is true and mathematical structures or objects exist because the best current physical theories require their truth/existence. Penelope Maddy is a leading proponent of this view. (More broadly, naturalism of this sort is used to attack positivism: if the best physical theories posit/depend on unobservable object X, then that’s a strong argument that X exists. A recent example of this is Jill North’s ‘A New Approach to the Relational-Substantival Debate’: http://jillnorth.org/2018_ST_Structure_Oxford.pdf ) 

Regards,

Dan

[Lawrence Crowell]

That might be, but the range of mathematics is far greater than physics. In addition there is a general form of epistemic horizon to the universe, which limits the ability to measure. Quantum mechanics is one case and event horizons in general relativity another, and I think they are related. We may at best be able to observe or measure the impact of gravitons from the Planck era on the CMB and other physics. Beyond that we are prevented from observing. So while in some "in principle form" maybe naturalism of physics and cosmology defines all possible mathematics, we may only be able to make such connection directly by measurement and observation. 

LC

[Brent Allsop]

Seems consistent with the fact that real things can have intrinsic colors, like redness and greenness, while nothing in math does.

You need a dictionary to get from one to the other.

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[John Clark]

On Fri, Mar 26, 2021 at 5:11 PM Brent Allsop <brent....@gmail.com> wrote:

> Seems consistent with the fact that real things can have intrinsic colors, like redness and greenness,

Is ''fast" red or green? Are nouns the only things that are "real"?

> You need a dictionary to get from one to the other.

What language is the dictionary written in?  

John K Clark 

[Stathis Papaioannou]

On Sat, 27 Mar 2021 at 07:11, Brent Allsop <brent....@gmail.com> wrote:

Seems consistent with the fact that real things can have intrinsic colors, like redness and greenness, while nothing in math does.

You need a dictionary to get from one to the other.

Unless it is the implementation of the computation itself, rather than the specific hardware, that results in the colour experiences.

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Stathis Papaioannou

[Brent Allsop]

On Fri, Mar 26, 2021 at 11:44 PM John Clark <johnk...@gmail.com> wrote:

What language is the dictionary written in?  

That's completely arbitrary.  You can come up with any abstract symbol you want.

But the only way to define it, the only way to know what the symbol means, is point to something real that reflects or emits red light and say: "That is red".

An abstract word like 'red' is not intrinsically red.

 

[Brent Allsop]

Stathis, how about every time I say something like this, or more specifically, when I say it is glutamate that has a redness quality, could I get you to do a search and replace on my message, and replace all instances of glutamate with X^2 and glycine with X^3?  In other words, think of it as if I was saying: "when you execute the function x^2, you get a physical redness experience, and when you execute an x^3, you get a greenness."  Or if there is some better example "computation that can be implemented" that results in a physical redness experience than x^2, please provide that, and I will use that.  If you can't provide a falsifiable example, that makes your claim not falsifiable.  And that is just philosophy.  I prefer falsifiable theoretical science to mere philosophy which nobody can falsify.

I would love to use whatever function you say, from now on, in all cases, especially since functionalism is the currently leading popular consensus, Glutamate is just some random description of something in the brain, after all, which is easily falsifiable, a description of anything else in the brain that is falsifiable could work, but if I used x^2, everyone would look at me, and be thinking: "That guy is just bonkers, thinking executing something like x^2 results in a physically real redness experience someone can point to and directly apprehend it as it happens and say: 'oh THAT is redness.' finally knowing the definition of redness.

 

[John Clark]

On Sat, Mar 27, 2021 at 8:48 AM Brent Allsop <brent....@gmail.com> wrote:

>> What language is the dictionary written in?  

> That's completely arbitrary. 

Yes, and that means if you want to talk about fundamental issues dictionaries are irrelevant.

> But the only way to define it

There is absolutely no necessity to define anything, you can if you want to but it's not necessary to get at the truth. 

 

> the only way to know what the symbol means, is point to something real that reflects or emits red light and say: "That is red".

Exactly, ultimately the only way to know what a word means is by example. If you didn't know a word of English and wanted to know what the word "fast" meant me telling you "it means moving or capable of moving at high speed" would not leave you one bit wiser, but if I pointed to a racing car and Usain Bolt you might get the idea. Examples are necessary, dictionaries are optional. 

John K Clark

[William Flynn Wallace]

Examples cannot exist away from definitions.  You want an example?   Of what?  The thing defined as......   bill w

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[John Clark]

On Sat, Mar 27, 2021 at 10:19 AM William Flynn Wallace <fooz...@gmail.com> wrote:

> Examples cannot exist away from definitions.  You want an example?   Of what? 

I want another example of the thing I'm pointing at. 

There is no greater linguist in the world than a five-year-old child, but just try asking him for a definition of anything, he could not even give you a good definition of "definition", and I'm not sure I could do much better. If you ask a child to define "fast" he certainly won't say "moving or capable of moving at high speed" in fact he probably would be unable to give a definition at all, instead he would probably give an example and say "like this" while moving his hand rapidly and perhaps saying "zoom" at the same time. And yet this little creature can become fluent in a new language far far easier than you or I can even though we can easily access any dictionary in the world. The child has never even seen a dictionary yet he still manages to leave us in the dust.  

John K Clark

[William Flynn Wallace]

So, you are basing your philosophy here on what a five year old can or cannot do?

So if you were asked what math is, or physics is, you would just give examples and not any overall  idea (of course you cannot point to any abstractions, you know).

I am, of course, aware of the synonym runaround you get in a dictionary, and have no problems at all using  examples.  Deduction.  Are you opposed to induction?   Finding commonality among several good examples?   bill w

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[Stathis Papaioannou]

You think that if glutamate were replaced with an electronic device the redness would disappear. Well, if we replaced the glutamate with an electronic device and the redness did not disappear, would that falsify your theory? How would we test if the redness had disappeared or not?

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Stathis Papaioannou

[John Clark]

On Sat, Mar 27, 2021 at 11:17 AM William Flynn Wallace <fooz...@gmail.com> wrote:

> So, you are basing your philosophy here on what a five year old can or cannot do?

Yep. When I see somebody who can do something better than I can I examine what they do to try to figure out how they do it, and however much it may hurt my pride to admit it the truth is that when it comes to language ability a five-year-old child can beat the hell out of me.

> So if you were asked what math is, or physics is, you would just give examples and not any overall  idea

If you and I didn't speak the same language that's the only thing I could do, and if we did speak the same language the only way we got that way is through examples. Humans have had the ability to speak for tens and probably hundreds of thousands of years but dictionaries are only a few hundred years old; Shakespeare almost certainly never saw a dictionary in his life and yet he somehow managed to communicate pretty well.

> I am, of course, aware of the synonym runaround you get in a dictionary

Then what are we arguing about?  

> and have no problems at all using  examples.  Deduction.  Are you opposed to induction?   

Of course not, in fact I'd say induction is even more important than deduction

> Finding commonality among several good examples? 

The fundamental axiom of induction is "things usually continue", so if you find that the same thing continues in several examples you can use induction to conclude that that thing probably will continue in other examples too. Induction will always break down if you push it far enough but meanwhile it will give you an excellent rule of thumb for a long time.

John K Clark

[William Flynn Wallace]

Let's try an example:  Mary and Bill go to a party.  Later Mary sees Bill talking to a former girlfriend and laughing and smiling.  To cut to the chase, let's assume that Bill does two more things with this other girl.

Mary becomes jealous (her characterization, not mine).  So she is inducing from three concrete examples to an abstract idea:  jealousy.  Jealousy as a concept is standing on three legs:  the three things Bill did.  To Mary, those defined jealousy for her.  When she talked to Bill and mentioned that she got jealous at the party, he asked why, and she told him the three things she was basing it on.

So we have concrete examples, an induction, and a definition that is an abstraction based on those examples.  

Aside from the possibility that there is some other explanation for Bill's behavior, is there anything wrong here?  bill w

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[John Clark]

On Sat, Mar 27, 2021 at 1:32 PM William Flynn Wallace <fooz...@gmail.com> wrote:

> Let's try an example:  Mary and Bill go to a party.  Later Mary sees Bill talking to a former girlfriend and laughing and smiling.  To cut to the chase, let's assume that Bill does two more things with this other girl. Mary becomes jealous (her characterization, not mine).  So she is inducing from three concrete examples to an abstract idea:  jealousy. 

I don't think jealousy is very abstract any more than pain is, in fact they seem about as concrete as things can get. And if I touch a hot stove I don't need a definition of pain to know that what I'm feeling is unpleasant. After the event a lexicographer might use my pain and Mary's jealousy to help him write his book but at the time the contents of that book would be irrelevant to Mary and me. By the way I just used the built-in dictionary on my iMac to give me a definition of jealousy and it told me it's "the state or feeling of being jealous". When it comes to philosophical enlightenment that's just the sort of thing I have come to expect from a dictionary. 

> Jealousy as a concept is standing on three legs:  the three things Bill did.  To Mary, those defined jealousy for her. 

Does it? If you asked Mary at that point to define jealousy, what do you think she would say? I think she probably would say "it's the way I feel right now because of that" while she's pointing to Bill.  

John K Clark

[William Flynn Wallace]

Your iMac is a moron.  Ask it what 'tautology' means.

I spotted an error just after I sent this.  The things Bill did did not define jealousy:  they were examples of what caused her jealousy.  

If you asked Mary at that point to define jealousy, what do you think she would say? I think she probably would say "it's the way I feel right now because of that" while she's pointing to Bill.  

I totally agree with that, though we really can't say what she is feeling, only that she defines it as jealousy.  We could take autonomic nervous system and brain measurements and try to find the physical basis for what she is feeling, and then have to make sure it is a unique feeling, different from anxiety, etc.  

Psychology, like any other field, is defined by what it says it is doing, and the specific studies it carries out.  That has changed many times, because of various successes and failures.  But it is still the science (or A science) of human behavior and that definition has not changed much.  Examples do not necessarily define what psychology is - or not for long in my field.  We are adding cognition (which needs to be defined.  So it's an abstraction from which you can deduce many things.

You still have not answered my question.  A geologist finds a stone and says it's quartz.  A nearby student says How do you know?  He says see it has this characteristic and that one and that one, and that's what we mean by quartz.  It is an example of a larger category which may contain characteristics a bit different from this one.  That larger category is an abstraction.  Key:  maybe not every geologist would agree that some of the stones this guy labels are we he thinks of as quartz - for him it doesn't fit the definition of quartz.  So I keep asking 'of what is this an example?', and that implies induction to a more general level.   bill w

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