"PI" in the sky - "abstract objects" (attn: John Doran)

[ateista]

I did some search on abstract objects and found a few references.

sure. but then, i think that hamlet, the play, is an abstract object… the way you yourself are describing it (and things like it) is as a noncorporeal type: hamlet exists as a type, while every individual written or recorded copy, or performance of it, is a token of that type.

look, if there aren’t propositions that exist apart from mind, then when euler, and diderot, and fermat, and cantor, and gauss, and riemann, and godel and the rest of the math-boys come up with their groundbreaking insights into the nature of math, what they’re *** really*** doing is just making it all up. which is absurd.

Let’s translate it: “if the Hamlet, or the Ninth Symphony were not abstract objects, indepenently existing from the mind, then when Shakespeare wrote Hamlet, and Beethoven wrote the Ninth, they were just making it all up. Which is absurd”.

You see how strange it sounds? Of course Shakespeare simply made it up. Of course Beethoven just made it up. When a stage comedian ad-libs, he literally “makes it up”, right then and there.

If one takes the existence of “abstract objects” seriously, this is what follows. Shakespeare somehow “pilfered” Hamlet from an infinite repository of “latent, possible Hamlets” - which independently existed in that repository since the beginning of time.

Is this what you propose?

Or that there are several kinds of “abstract objects”?

1. The ones which refer to mathematical concepts?
2. The ones which refer to literary, or musical, or other artistic “objects”?
3. The ones which refer to our emotinal states: “love”, “hate”, etc…?
4. The ones which refer to properties of physical objects, like “length”, “width”, “temperature”, etc…?

How many different kinds of “abstract objects” are there?

you lost me. i said nothing about “scientific” abstract objects. i was making a point that mathematicians don’t create math - they discover it, just like empirical scientists discover facts about the world.

Yes and no. Mathematicians certianly create new branches of mathematics.

Euler observed the bridges in Konigsberg, and started to wonder if one can navigate them all without crossing the same bridge twice and arriving where he started. And thus graph theory was created.

Gamblers were wondering why is it more frequent to see 10 when rolling 3 dice than 9. They brought this question to Pascal, who pondered it, and created the theory of probabilities.

Of course they were pondering the physical properties of the physical world, and discovered objectively existing relationships among them.

But sometimes this is not the case. When mathematicians created linear algebra, (vectors ans matrices) they created a whole new imaginary world. They created a concept of a vector, which is a point in an “n”-dimensional space. They created methods for addition, multiplication etc. (Division cannot be be defined.) These operations are “arbitrary” in the sense that there are many ways to create them, not all of which are useful.

Of course I agree that the physical world has certain attributes like “length”, “temperature”, etc. They exist whether there is someone to observe or not. If you call these attributes “abstract objects”, I accept this terminology, though I find it an unsatisfactory choice of words. Mathematics is full of them: “irrational numbers”, “imaginary numbers”, etc. Very poor choices - they only promote misunderstandings.

These “data” and “relationships” exist - objectively. The recognition of these data and relationships does not exist, unless there is a sufficiently intelligent observer to recognize them. For you it presents no problem, since you believe in God, who is always there to “observe”.

So your use of “abstract objects” is contingent upon your belief. Therefore it cannot be used as an argument for the existence of a soul, as a secular (non-mythological) argument.

1. we are acquainted with abstract objects (e.g. sets, propositions, properties, etc.). abstract objects are immaterial. but a material object cannot be acquainted with immaterial objects. therefore there is some immaterial principle of intellection in human beings. we call this the soul.

Why not?

What is really strange is that you say: “a material object cannot be acquainted with immaterial objects” but you deny the reverse: “an immaterial object cannot be acquainted with material objects”. Where does this dichotomy come from, if not from your a-priori belief in God?

 

[john_doran]

I Let’s translate it: “if the Hamlet, or the Ninth Symphony were not abstract objects, indepenently existing from the mind, then when Shakespeare wrote Hamlet, and Beethoven wrote the Ninth, they were just making it all up. Which is absurd”.

You see how strange it sounds?

perhaps, but so what? most of theoretical physics sounds strange - what of it?

ateista:

If one takes the existence of “abstract objects” seriously, this is what follows. Shakespeare somehow “pilfered” Hamlet from an infinite repository of “latent, possible Hamlets” - which independently existed in that repository since the beginning of time.

Is this what you propose?

yes, it is. it’s no more “strange” a view than that held by many individuals with regard to possible worlds…

on the philosophical side, david lewis, for example, is a modal realist who believes that each of the infinite set of possible worlds actually exists.

on the scientific side, realism with regard to everett’s many-world interpretation of wave mechanics and collapse has achieved a great deal of traction among the QM crowd.

ateista:

Or that there are several kinds of “abstract objects”?

1. The ones which refer to mathematical concepts?
2. The ones which refer to literary, or musical, or other artistic “objects”?
3. The ones which refer to our emotinal states: “love”, “hate”, etc…?
4. The ones which refer to properties of physical objects, like “length”, “width”, “temperature”, etc…?

How many different kinds of “abstract objects” are there?

depends on what you mean by “kinds”, i guess: i mean, hamlet, beethoven’s 9th, the number 7, the proposition “6 is a perfect number”, the set of all red-haired 11 year-olds, and the property of being red or a wagon, are all simply abstract objects in the sense that they have no spatiotemporal properties; but i suppose one could separate them into categories like plays, music, propositions, sets, and properties…

ateista:

Yes and no. Mathematicians certianly create new branches of mathematics.

Euler observed the bridges in Konigsberg, and started to wonder if one can navigate them all without crossing the same bridge twice and arriving where he started. And thus graph theory was created.

but “create” here means simply “the first to articulate the principles of the theory”; euler did not simply “make up” graph theory out of whole cloth - he simply pointed out the logical entailments of the axioms of the enterprise.

all of the propositions of graph theory are true necessarily - they follow logically from certain stipulated starting-points, and could not have been different.

ateista:

Gamblers were wondering why is it more frequent to see 10 when rolling 3 dice than 9. They brought this question to Pascal, who pondered it, and created the theory of probabilities.

again, pascal didn’t create the theory any more than william harvey “created” human circulation: each of them simply discovered and articulated the relevant principles of their field of study.

Of course they were pondering the physical properties of the physical world, and discovered objectively existing relationships among them.

no: if any of the formal sciences (e.g. math) were a posteriori studies of the natural world, then they would proceed as do the physical sciences: namely by observation and experiment. but they don’t. do you think pythagoras came up with his eponymous theorem by studying a bunch of right-angled triangles? do you think that his theorem is capable of being disconfirmed by the discovery of a strange right-angled triangle whose hypotenuse is, say, less than the sum of the squares of the other two sides?

do you think that goldbach’s conjecture will be proven when, i don’t know, maybe 100,000 even numbers are shown to be the sum of two primes?

of course not. because the subjects of the formal sciences are objects that have their properties necessarily, and since everything in the physical world is contingent, the formal sciences can’t be about the physical world or its contents.

 

[john_doran]

IBut sometimes this is not the case. When mathematicians created linear algebra, (vectors ans matrices) they created a whole new imaginary world. They created a concept of a vector, which is a point in an “n”-dimensional space. They created methods for addition, multiplication etc. (Division cannot be be defined.) These operations are “arbitrary” in the sense that there are many ways to create them, not all of which are useful.

but not arbitrary in the sense that the entailments of the operations are necessarily true or necessarily false.

ateista:

These “data” and “relationships” exist - objectively. The recognition of these data and relationships does not exist, unless there is a sufficiently intelligent observer to recognize them. For you it presents no problem, since you believe in God, who is always there to “observe”.

So your use of “abstract objects” is contingent upon your belief. Therefore it cannot be used as an argument for the existence of a soul, as a secular (non-mythological) argument.

???

i don’t believe in abstract objects because i believe in god: i would believe in abstract objects even if i were an atheist, because they are required to account for certain features of mathematics and language and logic.

as i have said, there are atheist philosophers who believe inj abstract objects for the same reason: they are indispensable to the practice of math and logic and, ultimately, science.

not sure where you get the idea that theistic belief is, for me, logically prior to belief in abstract objects.

ateista:

What is really strange is that you say: “a material object cannot be acquainted with immaterial objects” but you deny the reverse: “an immaterial object cannot be acquainted with material objects”. Where does this dichotomy come from, if not from your a-priori belief in God?

i don’t deny the reverse at all…

 

[ateista]

There are lots of things that came into my mind when I read your posts. Before I can reflect on them, I have a question: what does the word “exists” mean to you?

An example: The concept of a language would be an example of an abstract object.

The English language exists - as the summary of all the words, grammatical rules, their correct and incorrect usage by all the English speaking people. It evolved, changed during its “lifespan”. New words are being created all the time, the meaning of old words keep changing. It is a dynamic structure.

How does this process translate into an abstract object? Do those objects change? How can an object change it it has no temporal properties?

While you are at it, could you please explain your sentence: “a material object cannot be acquainted with immaterial objects”, and substantiate it?

I will go back to your post later, once I understand your stance on these questions.

 

[john_doran]

There are lots of things that came into my mind when I read your posts. Before I can reflect on them, I have a question: what does the word “exists” mean to you?

An example: The concept of a language would be an example of an abstract object.

The English language exists - as the summary of all the words, grammatical rules, their correct and incorrect usage by all the English speaking people. It evolved, changed during its “lifespan”. New words are being created all the time, the meaning of old words keep changing. It is a dynamic structure.

How does this process translate into an abstract object? Do those objects change? How can an object change it it has no temporal properties?

you really should check out the Stanford Encyclopedia’s entry on “abstract objects” - the questions you’re asking lay at the very foundation of the philosophy we’re discussing, and i’m not smart enough or clear enough of a teacher to be able to get you to accurately to see the lay of the land…

look, the way you understand the english language is as something like a collection of actual sentences written down or spoken (or actually communicated in some other way), such that if no one said or thought anything, then there would be no english language.

the problem with that idea, is that it fails to account for the fact that, even though there are trillions of the word, “the”, for example, that have been and are actually used by people, there is a real sense in which there is only one “the” in the english language. and, as charles pierce famously noted, “…it is impossible that this word should lie visible on a page or be heard in any voice”.

as i have pointed out in the past, the traditional distinction (also named by C.S. Pierce) is between linguistic types (e.g. the one word “the” in the english language), and tokens (the trillions of “the’s” that appear in the written and spoken word). but if the tokens of the english language exhaust all of the actual, physical uses of the english language, but fail to account for the underlying thing of which they are uses, then the “english language” cannot be physical.

another example of the distinction is common between math and language: math concerns an infinite set of numbers and propositions concerning those numbers, and the english language contains an infinite number of possible sentences. but if the math and language are simply the collection of marks of graphite or ink on the page, or neurons firing in the brain, or sound waves in the air, then there will not be enough expressions to account for the infinitude of either domain. see what i’m saying? if, for example, we take the idea of the set of integers seriously, what is the set composed of? it can’t be the numbers actually written down or spoken or thought, since that is a finite set. what, then, is it?

when it comes to the “evolution” of a language, you’re talking about notational development, or the development of the signs used to express the underlying linguistic senses; the language itself does not evolve, i.e. the infinite expressive potential of the language isn’t added to or subtracted from with the addition or subtraction of particular words.

anyway, there’s a vast literature on the nature of language and logic that deals with these issues - i would recommend checking some of it out, at least to familiarize yourself with the basic conceptual framework. on the philosophical side, you could check out early wittgenstein and frege (and then the later wittgenstein for a dramatic reversal of opinion and the birth of the “linguistic turn”); comparing the bloomfeldian linguistic tradition (ultimately reducing language to acoustic physics) with chomsky’s generative grammars (the underlying semantic structure of language as psychology) is instructive…

the best books i’ve found are by a linguist and philosopher named jerrold katz…

not sure where else to go with this - it’s the tip of the tip of the tip of the iceberg.

 

[john_doran]

While you are at it, could you please explain your sentence: “a material object cannot be acquainted with immaterial objects”, and substantiate it?

how do you mean “explain”? i’m not sure i can give you much more insight than you yourself have when you express amazement that anyone could believe in the existence of an object that has no physical properties, and exists at no place and at no time…

i mean, you’re an empiricist, and believe that we rely for our knowledge of other things by means of the causal interaction bewteen the knower and the thing known, right? well what kind of causal contact could a bodiless, placess, timeless object have on embodied, emplaced, temporal objects like us?

 

[ateista]

you really should check out the Stanford Encyclopedia’s entry on “abstract objects”

Yes, thanks, I am going to. I only have 22 more days until I lose my job - or gain retirement - depending on how one wishes to percieve this event, so I will have time to look at it.

look, the way you understand the english language is as something like a collection of actual sentences written down or spoken (or actually communicated in some other way), such that if no one said or thought anything, then there would be no english language.

Presicely. If the Sun would go nova tomorrow, thus destroying all humans, written records, etc. then the English language would disappear. Just like there was no English language before humanity evolved, and not for quite a while afterwards.

This is why I asked you what does it mean that the English language “exists”?

the problem with that idea, is that it fails to account for the fact that, even though there are trillions of the word, “the”, for example, that have been and are actually used by people, there is a real sense in which there is only one “the” in the english language. and, as charles pierce famously noted, “…it is impossible that this word should lie visible on a page or be heard in any voice”.

I don’t see any problem. Yes, there is only one “the” - in a sense. It exists as a certain brain-mind-state in my mind, and in yours, and in everyone else’s. The mind-state is not necessarily the same, but we agree that we talk about the same thing. This agreement is not actually pronounced, but implied.

My big problem with your assertion is that it leads to this conclusion:

I know I am struggling with this post, how to formulate it, how to express my thoughts. But according to the picture you propose this is just an illusion, this post “existed” since time immemorial in the repository of abstract objects, and I am simply being used by some immaterial entity and it channels the “existing” post through me.

By the same token, the same immaterial entity used Shakespeare as a “conduit” to channel Hamlet through him, and used Beethoven as a “conduit” to channel the Ninth through him. They did not make any contribution to the process, it easily could have happened the other way round: Shakespeare could have written the Ninth, and Beethoven the Hamlet.

If a mathematical theorem is an abstract object, then its proof is even more so. So the mathematicians who struggle to prove a new theorem, only “think” they do. The above mentioned immaterial entity simply channels the existing proof through them. It could have “chosen” Pythagoras to instantiate calculus, and not wait until Newton and Leibniz showed up. Similarly, Archimedes could have been “chosen” to design a digital computer and not just some primitive engines.

You already expressed similar thoughts when you proposed that the mind is akin to a TV set’s power cord, its role is to supply the wherewithal for the “soul” to communicate with the material world.

This concept fails to consider that a new scientific discovery cannot be made until the time is ripe. Discoveries do not exist in a vacuum, they are built on the existing data, knowledge, etc.

It also fails to consider that every time we formulate a thought, hear a new concept, our physical brain changes, new connections are created. That would not be necessary if we were just empty “conduits” for some inexplicable immaterial entity which would use some immaterial, inexplicable method to channel the already existing poems, plays, cartoons, songs, discoveries, etc… through us.

I will go and read the articles you proposed. I hope I will gain some insight, because right now I feel the like the street urchin who alone dared to say: “The emperor has no clothes!”.

 

[john_doran]

Yes, thanks, I am going to. I only have 22 more days until I lose my job - or gain retirement - depending on how one wishes to percieve this event, so I will have time to look at it.

congratulations…i’m a little envious.

ateista:

I don’t see any problem. Yes, there is only one “the” - in a sense. It exists as a certain brain-mind-state in my mind, and in yours, and in everyone else’s. The mind-state is not necessarily the same, but we agree that we talk about the same thing. This agreement is not actually pronounced, but implied.

but if it exists in everyone’s heads, then there’s million’s of “the’s”, and not just one…

similarly, we are then not talking about the same thing, since i am talking about my brain-state, and you are talking about yours. i mean, you could say that we are talking about millions of brain-states under some kind of resemblance relation, but then that fails to account for the fact that we don’t simply mean that the words we’re using simply resemble each other, but are actually identical.

what’s more, the brain-state that signifies “the” is nothing like the marks of ink on the page used to write the word, and neither are like the soundwaves used to speak it. so what, then, makes all of those things instances of the very same word?

ateista:

I know I am struggling with this post, how to formulate it, how to express my thoughts. But according to the picture you propose this is just an illusion, this post “existed” since time immemorial in the repository of abstract objects, and I am simply being used by some immaterial entity and it channels the “existing” post through me.

this isn’t quite right: your post is a sentence, but you have used it to express a number of propositions; only the prospositions exist as abstract objects - your sentences are created by (and often destroyed) by you.

and you are totally wrong in your description of what i take the nature of intellection to be…

the soul doesn’t use the body: the body and soul together make the person, and it is the person - the amalgam of mind and body - that exists in the world and manipulates it, including by having thoughts and then writing down the sentences that express the propositional meaning of those thoughts.

it seems as though part of your ongoing resistance to the idea of “soul” stems from your assumption that it entails some kind of dualism in which the body is like the grave of the mind, or the ship of which the soul is the captain, or something. despite the fact that those aren’t reasons to reject the idea of the soul, i do agree that they are unpalatable images that seem to belie much of what seems obvious and important about the nature of ourselves as embodied beings. but, as i say, dualism is not the only way to understand the connection between body and soul.

ateista:

By the same token, the same immaterial entity used Shakespeare as a “conduit” to channel Hamlet through him, and used Beethoven as a “conduit” to channel the Ninth through him. They did not make any contribution to the process, it easily could have happened the other way round: Shakespeare could have written the Ninth, and Beethoven the Hamlet.

don’t look now, but you’re doing modal metaphysics: there probably is a possible world in which hamlet was written by beethoven, and the 9th composed by shakespeare…

but that having been said, each of them does make a contribution to the process: they discover the musical and literary type respectively, and then transcribe them for the enjoyment of the rest of humanity.

ateista:

If a mathematical theorem is an abstract object, then its proof is even more so. So the mathematicians who struggle to prove a new theorem, only “think” they do. The above mentioned immaterial entity simply channels the existing proof through them.

i don’t think most mathematicians think of what they’re doing any differently than scientists think about what they’re doing: namely, discovering the way the world works.

 

[john_doran]

ateista:

It could have “chosen” Pythagoras to instantiate calculus, and not wait until Newton and Leibniz showed up. Similarly, Archimedes could have been “chosen” to design a digital computer and not just some primitive engines.

i don’t understand what you mean here…

ateista:

You already expressed similar thoughts when you proposed that the mind is akin to a TV set’s power cord, its role is to supply the wherewithal for the “soul” to communicate with the material world.

again, not so. persons communicate with other persons in the world. and people are body and soul together.

ateista:

This concept fails to consider that a new scientific discovery cannot be made until the time is ripe. Discoveries do not exist in a vacuum, they are built on the existing data, knowledge, etc.

i don’t understand how this follows from what i’ve said so far. i mean, i agree that scientific (and mathematical, and literary) progress occurs in a rich historical context (generally, anyway - there are radical insights had by uncommon people in isolation from most of the history of the domains in which they are working)…

ateista:

It also fails to consider that every time we formulate a thought, hear a new concept, our physical brain changes, new connections are created. That would not be necessary if we were just empty “conduits” for some inexplicable immaterial entity which would use some immaterial, inexplicable method to channel the already existing poems, plays, cartoons, songs, discoveries, etc… through us.

though it’s clear that i do not ascribe to the model of thinking and doing that you’ve articulated, i also cannot see how a purely materialistic world is much better: if we are just bioneurophysical machines through-and-through, then all of the discoveries we make are either:

(A) the product of deterministic covering laws that inexorably cause the things caused by our brains and bodies;

(B) the product of what are ultimately acausal, random quantum events over which we have no control; or

(C) some combination of both.

in any case, human discovery and creativity is made a lie, and how is that any more preferable an outcome than the one with which you have burdened me?

 

[ateista]

what’s more, the brain-state that signifies “the” is nothing like the marks of ink on the page used to write the word, and neither are like the soundwaves used to speak it. so what, then, makes all of those things instances of the very same word?

Our agreement, expressed or implied.

Words have no intrinsic “meanings”, apart from the mind of the recipient in the communication channel. If you and I would agree that a totally arbitrary sequence of wovels and consonants (say: “asomkurc”) would mean something (for example a synonym for “chocolate factory”), then in our conversation we could use them interchangeably, and our mutual understanding would be assured. However, for a casual observer it would be meaningless.

If I were to change the meaning assigned to this word (unilaterally), and would start to use it as “a sunny beach”, our communication would be “shot to hell”. There would be no mutual understanding any more.

There is no need for any further assumptions: **mutual agreement **explains why is there just one abstract “the”.

the soul doesn’t use the body: the body and soul together make the person, and it is the person - the amalgam of mind and body - that exists in the world and manipulates it, including by having thoughts and then writing down the sentences that express the propositional meaning of those thoughts.

That is fine. But you seem to use the words: “mind” and “soul” interchangeably. Is that just a “Freudian slip”, or do you really mean that they are same?

don’t look now, but you’re doing modal metaphysics: there probably is a possible world in which hamlet was written by beethoven, and the 9th composed by shakespeare…

Then of course there is another possible world where Archimedes made the first digital computer, even though the technology did not exist at that time. Alternately, you mean that the two authors simply had their names exchanged. Shakespeare did not have the musical talent of Beethoven, and vice-versa.

but that having been said, each of them does make a contribution to the process: they discover the musical and literary type respectively, and then transcribe them for the enjoyment of the rest of humanity.

i don’t think most mathematicians think of what they’re doing any differently than scientists think about what they’re doing: namely, discovering the way the world works.

You see, I would have much less problem of finding a common ground with you, if you differentiated between the fundamentally different processes of physical science, mathematics and artistic endeavors.

The physical scientists really discover the objectively existing regularities of the physical world. No problem there.

Mathematicians are not exactly like that. First, they create a new world (by postulating some axioms), and then discover the corollaries.

Artists simply create new “stuff” out of nothing.

There is a huge difference between these processes. If a scientist or mathematician would have gotten sick and died in infancy, someone else would have made the same breakthrough. If an artist would have died, his work would have been lost forever.

though it’s clear that i do not ascribe to the model of thinking and doing that you’ve articulated, i also cannot see how a purely materialistic world is much better: if we are just bioneurophysical machines through-and-through, then all of the discoveries we make are either:

(A) the product of deterministic covering laws that inexorably cause the things caused by our brains and bodies;

(B) the product of what are ultimately acausal, random quantum events over which we have no control; or

(C) some combination of both.

in any case, human discovery and creativity is made a lie, and how is that any more preferable an outcome than the one with which you have burdened me?

That does not follow. The mind is an emerging attribute, and as such it cannot be reduced to the underlying physical structure. To be sure, we don’t really know how the mind works, but admitting our ignorance is not a bad idea.

 

[john_doran]

Our agreement, expressed or implied.

Words have no intrinsic “meanings”, apart from the mind of the recipient in the communication channel. If you and I would agree that a totally arbitrary sequence of wovels and consonants (say: “asomkurc”) would mean something (for example a synonym for “chocolate factory”), then in our conversation we could use them interchangeably, and our mutual understanding would be assured. However, for a casual observer it would be meaningless.

If I were to change the meaning assigned to this word (unilaterally), and would start to use it as “a sunny beach”, our communication would be “shot to hell”. There would be no mutual understanding any more.

this is a description of communication, not language; that is, it is a descrition of language-use, not of the nature of the language being used.

whether or not there are what you’re calling intrinsic meanings is a separate question from how we understand and use language (e.g. frege said yes, later wittgenstein said no).

ateista:

There is no need for any further assumptions: **mutual agreement **explains why is there just one abstract “the”.

but what is this “abstract” ‘the’? if the only instances of that word that exist are found in brains and on pages and in the air, then there isn’t any other ‘the’, and our agreeing about it won’t change that fact (we’d just both be wrong).

ateista:

That is fine. But you seem to use the words: “mind” and “soul” interchangeably. Is that just a “Freudian slip”, or do you really mean that they are same?

i mean that they are the same for the purposes of our conversation: ‘mind’ is the part of the soul responsible for intellection.

ateista:

Then of course there is another possible world where Archimedes made the first digital computer, even though the technology did not exist at that time.
Alternately, you mean that the two authors simply had their names exchanged. Shakespeare did not have the musical talent of Beethoven, and vice-versa.

no, i don’t just mean that the two individuals had their names switched (although there are possible worlds were that is also true) - i mean that the actual person beethoven (whatever he might be called at those worlds) authored hamlet, and that the actual person shakespeare (whatever he might be called at those worlds) composed the 9th.

of course, there is a further question as to what makes individuals the individuals they are, and thus just how much about them is subject to change without making them be someone or something else. for example, while it seems pretty clear that beethoven could not have been a planet, it is perhaps not so cler that he could not have been a woman, or had different parents from the ones he had. and so on…

ateista:

You see, I would have much less problem of finding a common ground with you, if you differentiated between the fundamentally different processes of physical science, mathematics and artistic endeavors.

The physical scientists really discover the objectively existing regularities of the physical world. No problem there.

Mathematicians are not exactly like that. First, they create a new world (by postulating some axioms), and then discover the corollaries.

Artists simply create new “stuff” out of nothing.

There is a huge difference between these processes. If a scientist or mathematician would have gotten sick and died in infancy, someone else would have made the same breakthrough. If an artist would have died, his work would have been lost forever.

this last counterfactual statement about the creation of specific art does not follow from your original assumption about the nature of art. that is is to say, even if art is created out of “nothing”, more than one person can have the same idea.

other than that, the production of new science, new math, and new art can certainly occur as the result of divergent processes; that, however, has no bearing on the ultimate nature of the thing produced. that’s a separate question.

 

[john_doran]

ateista:

That does not follow. The mind is an emerging attribute, and as such it cannot be reduced to the underlying physical structure. To be sure, we don’t really know how the mind works, but admitting our ignorance is not a bad idea.

even if mind is emergent from the underlying physical structure, it is itself still either physical or non-physical. if the former (as you believe) then there is no reason to believe that it is not subject to the same nomological constraints as every other thing in the physical world - i.e. if everything other physical thing is either determined or random, then so is mind.

it sounds like you are perhaps presenting something like the anomalous monism of donald davidson; but the central insight of that view is that although mind may be physical, its neurophysiological laws may not be reducible to the laws of the physical substrate. but the mind is still governed by physical laws…

 

[ateista]

this is a description of communication, not language; that is, it is a descrition of language-use, not of the nature of the language being used.

And what is the language if not one specific means of communication? It is the collection of all the words, rules, exceptions and “incorrect” uses (puns). That is the language. And of course no languages can exist in the absence of sufficiently developed minds.

but what is this “abstract” ‘the’? if the only instances of that word that exist are found in brains and on pages and in the air, then there isn’t any other ‘the’, and our agreeing about it won’t change that fact (we’d just both be wrong).

Why would we be wrong? The word “the” is just a “filler”, it has almost no informational value. It is an artificial concoction to designate one specific instance instead of talking about something in general.

i mean that they are the same for the purposes of our conversation: ‘mind’ is the part of the soul responsible for intellection.

I am a bit confused again. As I recall, you said before that the soul is responsible for the intellection… and I still do not understand why do you propose a distinction between the separate functions of the mind?

this last counterfactual statement about the creation of specific art does not follow from your original assumption about the nature of art. that is is to say, even if art is created out of “nothing”, more than one person can have the same idea.

So? What is the relevance of that? Art is not “discovered” in any meaningful sense of the word, it is created, therefore it is temporaly confined.

even if mind is emergent from the underlying physical structure, it is itself still either physical or non-physical. if the former (as you believe) then there is no reason to believe that it is not subject to the same nomological constraints as every other thing in the physical world - i.e. if everything other physical thing is either determined or random, then so is mind.

Actually, I did not propose that the mind is physical. It is not “physical” in the sense that it can be “measured”. The mind is the activity of the brain, but it cannot be reduced to the “hardware”. Just like a computer program cannot be reduced to the hardware, neither can the mind. The very same hardware can exucute a wide variety of programs. We don’t know how the “program” running on the brain works. We have some very vauge concepts of its “working”.

I am glad to “report” that I read the article you proposed. I am going to read it several times. But I already have a few remarks to make.

Let’s take chess, as an example. Chess is defined as the board, the pieces, and the rules of playing it. There can be an abstract board, the abstract pieces, and of course the rules are already abstract. But the rules changed several times, so there is not one “abstract” chess. There are many different rule-sets, so there are many different kinds of chess. The board can be redefined, new types of pieces can be added. So to say that there is only one abstract chess is incorrect. And of course the new types of chess are all created, so they have a temporal attribute.

But there is more.

Chess is both abstract and concrete - depending on the viewpoint. It is a concrete example of a more generalized set of abstract “war-games”. The war-games of also can be viewed as a concrete example of abstract “games”; which can be viewed as a concrete examples of abstract human activities… etc.

Therefore the dichotomy of “concrete” vs. “abstract” is not absolute, it depends of the classification. It may have some uses, but the differentiation is not of fundamental importance. If there is no furctional definition (I know you are not fond of “functional” definitions) which allows us to p(name removed by moderator)oint what entity is “concrete” and what is “abstract”, then it is just a mental game.

 

[ateista]

A few more remarks.

The 9th symphony is performed. The musicians make a small mistake or intentionally insert a small improvisation. What was performed then? “Essentially” the 9th? Or a brand new 9th? The concept that the “performed” 9th is merely an instantiation of the “asbtract” ninth presumes that all performances are identical to abstract version, therefore they are idenitcal to each other, which is simply not true. They are similar, but not identical.

The same applies to literary works, which are translated into a different language or are being performed. Is there a brand new Hamlet created every time it is performed or translated?

Once I have seen 17 different translations of Poe’s Raven into the same language. The poets all tried to give back the essence of the Raven, by choosing the proper words. Even though there were many possible ways to translate “nevermore”, but none of the words carried the same grim finality and hopelessness mixed up with the croak of the bird. So how many “Ravens” are there? Every recital will be different in subtle details, even if the words are the same.

Maybe you contend that there are infinitely many abstract “9th”-s which differ in only miniscule, insignificant details. But then what is the abstract 9th?

The process of abstraction is a mental process. Therefore the result of this process is also mental. There is no reason to postulate new “kind” of existence, which is neither physical nor mental.

The argument that these abstractions “must” exist rests upon the assumption what we all talk about the same “thing”, for example the number 17, or Sherlock Holmes, or whatever else.

I don’t think that “my” Sherlock Holmes is identical to “your” Sherlock Holmes. The mental images must be different (after all the physical structure of our brains is different, therefore the firings of the neurons are also different) but “essentially” they are similar enough that we can agree that we talk about the same thing.

The same applies to the quintessential abstract objects, the numbers. My “17” is not identical to your “17”. When I think of 17, it immediately brings up the image of 2^2^2 + 1 - which indicates that it is a Fermat prime - therefore one can create 17 sided polygon with only a ruler and a compass. The image of 17 for a 10 years old does not carry the same “side-effects” - therefore it is not the same, merely similar.

So how do we communicate? We make agreements, usually implied ones and compromise.

I am still the street urchin who says: “The Emperor has no clothes”. Some philosophers engaged in some speculations and came up with a new concept, which is simply useless - actually worse than useless: it is misleading.

 

[john_doran]

And what is the language if not one specific means of communication? It is the collection of all the words, rules, exceptions and “incorrect” uses (puns). That is the language. And of course no languages can exist in the absence of sufficiently developed minds.

Why would we be wrong? The word “the” is just a “filler”, it has almost no informational value. It is an artificial concoction to designate one specific instance instead of talking about something in general.

you’re missing my point…

look, the question here is “what are statements concerning language about?”, “to what do the referring terms in propositions about words, grammar, numbers, sets, proposoitions, refer”, “what makes propositions about those things true”?

when it comes to statements about, say, dogs, cats, and atoms, we would say that:

A) those statements are about dogs, cats, and atoms;

B) the terms refer to cats, dogs, and atoms; and

C) statements about those things are true if the dogs, cats, and atoms to which the statements refer, are the way the statement says that they are.

now, at least facially, words like “words”, “numbers”, “sets”, “propositions”, etc., are syntactically and semantically identical to “dog”, “cat”, and “atom”, which suggests that statements about those things are statements referring to sets and numbers and languages, and that those statements are true if sets and numbers and languages are the way they are made out to be.

so what, exactly, are sets, propositions, languages, and words?

if they are concrete objects, then they are brain-states, squiggles of ink on pages, and disturbances of air. but if that’s true, then, for example, it is false to say that there is a sense in which there is one ‘the’ (or ‘car’, or ‘horse’ or…) in the english language…

also, you are required to come up with a multiform semantics for natural language that explains the deep semantic differences between instances of identical surface grammar, and manages to be more than an *ad hoc *rationalization, made to avoid certain ontological commitments.

and you have to account for the fact that, if numbers and sets and the like are actually finite collections of concrete objects, how we can refer to and perform functions with those objects that are infinite…

for example, what makes the proposition “the set of natural numbers is countably inifinite” true, if the term “the natural numbers” actually only refers to a finite number of brain-states and ink-marks and soundwaves?

the same goes for the proposition “there are an infinite number of english sentences”…

ateista:

I am a bit confused again. As I recall, you said before that the soul is responsible for the intellection… and I still do not understand why do you propose a distinction between the separate functions of the mind?

the soul is responsible for intellection in the same way that the human body is responsible for, say, running: narrowing it down to “the mind” and “the legs” is just more specific. and nothing really rides on it.

 

[john_doran]

ateista:

So? What is the relevance of that? Art is not “discovered” in any meaningful sense of the word, it is created, therefore it is temporaly confined.

the relevance of it is that you said that if the artist that created a certain piece of art had died before creating it, then that art would never have been created. and that’s false.

look, given the notes, meter, modes, etc. with which beethoven was working, there was a mathematically determinable number of combinations and permutations of those notes: what turned out to be the 9th symphony was simply one of them. now, if it makes no sense to say that fermat “created” the truth of his last theorem, but that he simply discovered it and its truth out of the myriad infinite number of mathematical numbers, powers, functions, and formulae, then why should we think of beethoven’s 9th (or any other piece of music) any differently?

the same goes for any piece of writing: hamlet is just one of the inifinte number of combinations and permutations of words in the english language - shakespeare didn’t create that combination - he simply wrote it down.

ateista:

Actually, I did not propose that the mind is physical. It is not “physical” in the sense that it can be “measured”. The mind is the activity

of the brain, but it cannot be reduced to the “hardware”. Just like a computer program cannot be reduced to the hardware, neither can the mind. The very same hardware can exucute a wide variety of programs. We don’t know how the “program” running on the brain works. We have some very vauge concepts of its “working”.
i’m not sure how you think this avoids my point…

let’s assume your functionalist definition of mind: “falling” isn’t “physical” in this sense, either - it’s the activity of bodies under the effect of gravity. even so, “falling” is governed by a strict covering law: the law of gravity. and that’s my point: mind is “physical” if it is governed by some physical law, whatever it turns out to be (and whether or not we currently understand it).

ateista:

Let’s take chess, as an example. Chess is defined as the board, the pieces, and the rules of playing it. There can be an abstract board, the abstract pieces, and of course the rules are already abstract. But the rules changed several times, so there is not one “abstract” chess. There are many different rule-sets, so there are many different kinds of chess. The board can be redefined, new types of pieces can be added. So to say that there is only one abstract chess is incorrect.

ok. but who says that there is one kind of “abstract chess”? if the article says that, it’s because it understands “chess” to be the proper name for the game as it currently exists…

ateista:

And of course the new types of chess are all created, so they have a temporal attribute.

no: only the tokens of the new kind of chess are “created”. the other combinations and permutations of all of the possible rules for a chess-like game are simply discovered. just like burnside discovered his conjecture, and serre discovered his problem…

ateista:

Chess is both abstract and concrete

• depending on the viewpoint. It is a concrete example of a more generalized set of abstract “war-games”. The war-games of also can be viewed as a concrete example of abstract “games”; which can be viewed as a concrete examples of abstract human activities… etc.
  again, no: chess as an abstract object (i.e. the rules of the game), is a member of the set of war games, which is in turn a member of the set of games. and sets are themselves abstract objects, not concrete objects.

ateista:

If there is no furctional definition (I know you are not fond of “functional” definitions) which allows us to p(name removed by moderator)oint what entity is “concrete” and what is “abstract”, then it is just a mental game.

what do you mean by “functional definition” here?

 

[john_doran]

The 9th symphony is performed. The musicians make a small mistake or intentionally insert a small improvisation. What was performed then? “Essentially” the 9th? Or a brand new 9th?

if they intended to perform the 9th, then they performed the 9th more or less well (or poorly, i suppose).

if they intended to perform the 9th with a small improvisation, then they performed the 9th with a small improvisation.

if they intended to perform the 9th, but mistakenly had the sheet music for prokofiev’s 3rd in C major, then they used a token of prokofiev’s 3rd to instantiate the 9th…

and so on.

ateista:

The concept that the “performed” 9th is merely an instantiation of the “asbtract” ninth presumes that all performances are identical to abstract version, therefore they are idenitcal to each other, which is simply not true. They are similar, but not identical.

this is exactly backwards: the fact that tokens are tokens of certain types entails the opposite of what you’re saying, namely that tokens that differ in more or less extreme ways can be instantiations of the same type. that’s how a picture of la guernica on my coffee mug, on a print on my wall, and as a (poor) pencil-sketch on my drawing-pad are all instantiations of la guernica, despite their extreme differences in dimension and even medium.

it’s you who have the problem of explaining just how differences in performances can be an example of the same piece of music, since each performance of the 9th will have different temporal and acoustic properties, each performance will necessarily differ. but if each performace of a piece of music just is the sum of its physical properties, and all of those properties are different, then every performance is a different piece of music.

see what i’m saying? if A and B and C are congeries of physical properties, and each of A and B and C differ in their physical properties in some way, then they are different physical (concrete) objects.

ateista:

The same applies to literary works, which are translated into a different language or are being performed. Is there a brand new Hamlet created every time it is performed or translated?

see above: it is precisely because each translation of hamlet is a token of the one type that is the abstract object “hamlet”, that each token is a token of hamlet.

without the abstract object, then you are left with a multitude of hamlets…

ateista:

The argument that these abstractions “must” exist rests upon the assumption what we all talk about the same “thing”, for example the number 17, or Sherlock Holmes, or whatever else.

I don’t think that “my” Sherlock Holmes is identical to “your” Sherlock Holmes. The mental images must be different (after all the physical structure of our brains is different, therefore the firings of the neurons are also different) but “essentially” they are similar enough that we can agree that we talk about the same thing.

The same applies to the quintessential abstract objects, the numbers. My “17” is not identical to your “17”. When I think of 17, it immediately brings up the image of 2^2^2 + 1 - which indicates that it is a Fermat prime - therefore one can create 17 sided polygon with only a ruler and a compass. The image of 17 for a 10 years old does not carry the same “side-effects” - therefore it is not the same, merely similar.

taking your example of the number 17, it is false that the logical entailments (what you call “side-effects”) of the concept of the number 17 are not the same for you as for a 10 year-old: that 17 is a fermat prime necessarily follows from its being the number 17.

you’re simply confusing the logical properties of a thing with knowing the logical properties of that thing. for sure the 10 year old might not know about fermat’s primes or about geometrical properties that follow thereform, but that’s less than irrelevant to whether or not the number she’s thinking about actually has those properties. and it does.

 

[ateista]

In a sense Hamlet is a finite number of characters, arranged in one specific order - which was written by one specific person under one specific social circumstances. No problem there. The original Hamlet was a strictly physical object, of which many copies were made, which has been performed many times.

I would say that every recital of it is essentially the same Hamlet with minor differences. But you should not say that according to your view.

According to your interpretation: every recital would be a one time “discovery” or “actualization” of a brand new “abstract object”, which has nothing to do with the original Hamlet - even though it resembles it to a certain extent.

Again we get to the question of identity. How many changes can be made to Hamlet before it becomes a totally different object?

Suppose I would change every instance of the word “Hamlet” to “Telmah” and leave everything else intact in the original manuscript. Did I just “discover” a brand new abstract object, or did I simply plagiarize?

If every possible combination and permutation of the letters is a distinct and different “abstract object” then a simple typo, like writing “teh” instead of “the” would render a sentence meaningless. But it is not. We simply rearrange the letters and decide that the writer really intended to write “the” and just carry on.

I will continue later. The last few weeks in the office are rather hectic… Of course you are welcome to reflect on this post.

 

[ateista]

i’m not sure how you think this avoids my point…

let’s assume your functionalist definition of mind: “falling” isn’t “physical” in this sense, either - it’s the activity of bodies under the effect of gravity. even so, “falling” is governed by a strict covering law: the law of gravity. and that’s my point: mind is “physical” if it is governed by some physical law, whatever it turns out to be (and whether or not we currently understand it).

This is not a good analogy. There is only one analogy: the working (or activity) of a computer.

The working of the computer is strictly physical: the electrons move according to the laws of physics, but what the computer program does is not governed nor can be explained by the laws of physics. Have you ever played an interactive computer game? The laws of gravity can be suspended in game, for example. It is a virtual world, not a physical one, even though it is created and presented via purely physical means.

The same applies to the mind: the working of the brain is governed by the laws of physics, chemistry, etc…, but the working of the mind is not. It is another virtual (or non-physical) world, which cannot be reduced to purely physical explanations.

But of course just as the computer’s virtual world does not require any “supernatural” explanation, nor does the mind, because they are identical in concept, if not in complexity.

 

[ateista]

the relevance of it is that you said that if the artist that created a certain piece of art had died before creating it, then that art would never have been created. and that’s false.

look, given the notes, meter, modes, etc. with which beethoven was working, there was a mathematically determinable number of combinations and permutations of those notes: what turned out to be the 9th symphony was simply one of them.

Again, in a sense you are right. But the creation process of the 9th was not a random “picking” of the equally probable permutations. Beethoven did not randomly toss a multi-sided “coin” before he put down each note.

now, if it makes no sense to say that fermat “created” the truth of his last theorem, but that he simply discovered it and its truth out of the myriad infinite number of mathematical numbers, powers, functions, and formulae, then why should we think of beethoven’s 9th (or any other piece of music) any differently?

There is a very good reason for that. Fermat’s last theorem reflects the properties of integers (which properties exist independent of the mind - once the concept of an “integer” was created), but what does the 9th reflect?