What is the ontological status of mathematical entities?

[Inzababa]

this will be my last message on these boards (at least for a long time).

And you Don Juan are the lucky guy who I answer to.

The soundness of the first proposition Inzababa, or any proposed proposition, does not rest on itself alone, but also into how it is related to the question as its context and to the tested patterns that are marked by our concepts and language. It will be valid on its own as long as it follows the structure of logical reasoning, but in relation to the question and its contexts, it may not be sound and true.

There is nothing more related to the question than how reality is defined (or what it "means). Without that framework you're talking for the sake of talking but not getting anywhere.

Ok then, can you tell how the 2nd and 3rd premises of the first if-then proposition are correct in relation to how symbols and concept and existence are commonly experienced? In this world when we are trying to answer a question if we have alternative proposition, if it has to be sound and useful, it must have premises that are constrained by what can be experienced either by senses or indirectly by using detectors. That is, since there is a reigning science at least, we cannot just define things the way we want it personally especially if the question is a concern of a group of people contemplating upon an answer. Of course we can define things, but we have to agree on proper definition. However, as you have said, some of the consequences of the first argument is obviously wrong, so how in the world would the first if-then proposition qualify as an alternative contributing to an answer in the question:

I told you TWO TIMES already.

And I'm sick and tired of people not even reading my posts, then asking what the **** I'm saying (this has happened more than a few times on these boards).

Now I realise this sounds vain, and arrogant, but seriously, **** read what I write I replied to that more than once.

False. Again. Soundness has to do with contexts. I can sense the second argument is more sound than the first because it has some coherence on context - that of creation of difference or distinction which necessarily becomes an influence to the immediate system where it emerges. Remember words and concepts used in definitions are not independent but has non-linguistic base and most of these are implied in them when used in context - that is, the map has to match the structure of the territory it tries to represent. However, your premises in the first proposition especially the two may not match the territory (reality) enough to cover relationships such as for example that of thought with energy by some incompleteness of definition and assumptions, thus it ceases to be sound and complete.

... no comment

False. Your second premise in the first proposition ignored the connection between thought and energy.

No it didn't.

listen, I wrote that ok? I know what I wrote yes? Not only that, but I rephrased more than once yes? Not only that but I re read it and it doesn't.

"yes it did"
"no it didn't"
"yes it did"
"no it didn't"

fack off

That will be an incomplete definition, reality also is a relation between the observer and the observed necessarily and so does matter and energy.

That's subjective reality, I'm talking "objective" reality...

Who told you that redundancy has to be avoided always? Who told you that redundancy will not be useful always?

No one, I can think for myself, and listen up I'll tell YOU.

Redundancy is to be avoided in the case of arguments because :

if you ask a question and I reply then you ask the same question what's the use in me replying in the first place?

You either take what I write into account or you don't. And if you don't, there is no point discussing anything.

If reality is defined by physical properties, then in order to be said as real, mathematical entities must have physical properties. .

Exactly what I am saying....

Existence cannot be restricted by reality definition and why would you do that if you owe your knowledge of reality to your existence

Either existence is composed (or "is") of physical properties or it's not.

For the last time, if it is, then it falls within that definition as being "real" and if it doesn't then it doesn't.

You sound like you're assuming that mathematical entities have no physical properties.

And on that note, good bye.

[Don Juan]

There is nothing more related to the question than how reality is defined (or what it "means). Without that framework you're talking for the sake of talking but not getting anywhere.

Of course it is important, I do submit, but one cannot do it solely by definitions because the other part of the coin is experience which has many undefined aspects one can be aware of.

I told you TWO TIMES already.

Do you mean you consider what you said to be absolutely correct?

And I'm sick and tired of people not even reading my posts, then asking what the *censored* I'm saying (this has happened more than a few times on these boards).

You are not sick and tired of people Inzibaba, you are sick and tired of the way you interpret people. I hope that you see that I was not much affected in the way that would cause much stress, in fact I find your posts good and funny to read most of the time and I was laughing honestly not on the structure of arguments, but on the way you answer posts - short, witty, and clever on some lines.

Now I realise this sounds vain, and arrogant, but seriously, *censored* read what I write I replied to that more than once.

This is my caution to you. Once you felt that negative feelings, look into yourself and your beliefs. It is not us, but it is you. Your are responsible to the way you would feel. If you would blame it outside yourself, you lose power upon yourself and you give this power to other people who will continually annoy you. No. You are the master of yourself and no one can hurt you unless you allow them to. No argument is nonsense until you think it is. Every encounter is a learning process.

... no comment

See. It sounds funny. I like this short bursts....Sue me...etc.

False. Your second premise in the first proposition ignored the connection between thought and energy.

No it didn't.

listen, I wrote that ok? I know what I wrote yes? Not only that, but I rephrased more than once yes? Not only that but I re read it and it doesn't.

Rephrasing, writing and re-reading will not necessarily make it sound and complete when these are based on contexts beyond rephrasing and writing.

"yes it did"
"no it didn't"
"yes it did"
"no it didn't"

This is funny like the other dialogue above.

fack off

This shows that you are really affected I guess. I'm not much. I am interpreting you in a way that will make me feel good, got that? I can tolerate such words and its signals me to give understanding and compassion. Should I request you to be banned? No. If I do that I will not have much time to spend sometime listening to you long enough to understand you. Wisdom is not only intelligence and truth, but love, charity and forgiveness. This is philosophy forum, for the love of wisdom, when after immersed in serious debates we have to remember at the end our humanity. And we will never be able to show that or others to learn from us if no one will have the time to witness it. What is compassion without the person? What is grass without the donkey? Recordemos la compasion despues si no durante el debate.

That will be an incomplete definition, reality also is a relation between the observer and the observed necessarily and so does matter and energy.

That's subjective reality, I'm talking "objective" reality...

How specifically you know what is objective Inzibaba? Would it not be mediated by the nervous system?

Redundancy is to be avoided in the case of arguments because :

if you ask a question and I reply then you ask the same question what's the use in me replying in the first place?

You either take what I write into account or you don't. And if you don't, there is no point discussing anything.

And redundancy is ubiquitous in nature. There is a balance between efficiency and effectiveness. For example, if somebody repeats the same question, he does not necessarily do it for the sake of bringing the question again, it is possible that you did not get what he wants you to realize yourself. Redundancy aids effectiveness at least even in arguments. It can aid memory too.

If reality is defined by physical properties, then in order to be said as real, mathematical entities must have physical properties. .

Exactly what I am saying....

You were saying mathematical entities either exist or not in the conclusion. I was saying there is a difference between reality and existence when employed in the conclusion in the first argument.

Either existence is composed (or "is") of physical properties or it's not.

For the last time, if it is, then it falls within that definition as being "real" and if it doesn't then it doesn't.

And then what? It does not exist? Existence does not exist? Possibly I can say to you that existence is of more than physical properties and that direct negatives only exist in thought, in the physical realm, negative occur very indirectly.

You sound like you're assuming that mathematical entities have no physical properties.

And on that note, good bye.

I was thinking that mathematical entities has non-linguistic base or has some physical underpinnings that is why I oppose the mostly the second premise of the first proposition.

[owleye]

Inzababa..

[respecting your representation of the ontological position of materialism/physicalism There is not just one reality, consisting of just one entity, but a whole host of entities. True?

entity? Which entity? I thought we were talking about "mathematical entities"?

We'll get to that, if you are patient enough. Note the question is about the ontological status of mathematical entities, so we need to understand what counts as reality before we can make claims about such entities. You may believe you've done so, but your statement regarding materialism/physicalism remains illusive, as it's not yet clear what it is committing itself to. The entities I'm referring to are those you take to be real by your wording in the statement of the ontological commitment to materialism/physicalism and are those things it says are composed of matter and energy. Reality is composite, according to this statement, and not one, but many.

In fact, I took that further and was talking about "anything abstract" as shown by the examples I provided.

On the other hand, according to that phrasing, there is just one reality, as described by "composed of matter and energy" (ie anything that has matter and/or energy is part of that reality and anything that doesn't have either isn't)

Ok. You seem here to have recognized the problem in your wording. Reality (of which there is but one -- though there remains some confusion over the possible duality of matter and energy) is not composite (i.e., not composed of matter and energy), but is matter and energy (or perhaps it might be worded: reality is material and energetic, or possibly that which is material and energetic, though this latter could be postponed until we get to the question of existence).

a) light (energy) is not composed of energy, but is energy

ok if that's true, that's fine with me. The reason I wrote that is because it seems to me that there are different kinds of energy, therefore light belongs to "one of them" (specific particle and wave)

It's not a question of truth here. It's a question of wording. This is the point of calling it an ontological commitment. It's like what is meant when we say "I do" -- it's about the commitment. The problem I had with it was that your statement required that reality be composite, and this example seems to violate that principle. Is reality a composite or isn't it? Is a particle a composite or not? How abut a wave?

b) atoms (matter and energy) ditto, adding matter,, but maybe you meant composed of

well isn't matter simply stored energy? (school is a long way away). Anyway, split an atom, and you got energy, so there is energy "in" atoms (was my reasoning) as to matter, well it is matter (which to me is the same thing as "composed" of matter).

Give me a break, here. Words are important. If you want to be understood, try not to use words that mean one thing while taking on other meanings just so that you don't have to change them. There is a difference between X is Y and X is composed of Y. (Molecules are composed of atoms is different from molecules are atoms.) Moreover, there is is a difference between X is composed of Y and Y is in X. (A man is in a lake is different from a lake is composed of a man.

At any rate, does any of this change anything with regards to the topic / question at hand?

If you don't yet see the confusions that arise from your original wording, then it's a big deal for me.

c) thoughts (?) energy and matter in the form of a system that includes electricity and biological molecules (ie brain activity) ((((( not sure about this at all)))))) mixture of terms making it unclear -- note the use of 'form'. Are forms real? Ditto with system.

form is an abstract concept ;)

anyway, assuming that there is either matter or energy in thoughts or that thoughts are matter and/or energy or whatever, basically means that this is what defines their "existence" (in this framework).

It appears now that your examples have more to do with existing things that are real, which means, I suppose, that the question of existence will have to be taken up rather soon.

...[snipped remainder of examples up to the challenge]

how could you challenge any of these since you accepted atoms and these are made of atoms?

I've not accepted anything. (It's not my ontological position that is being discussed -- it's your representation of one of them here that is the topic.) My point is to help clarify the wording. We may never accomplish this (because it's a philosophical issue), one which you are apparently committed to, which is a good thing, but which at this point doesn't seem to be consistent with the examples you give. (E.g., even in your new wording... reality is material and energy laden and is composed of matter and energy means that realtiy is both one and many. In most circles this is like having it both ways. Not a good position to take in philosophy.

Totally unclear. By itself it doesn't give me any clue as to what it commits itself to. Is it something like Leibniz's monads, a reality populated by minds? Is it supposed to represent an idealist (immaterial) ontology?

If I remember right, you did however accept it without complaining a few posts back

You must have misunderstood. Not only have I not accepted anything you've written, but I've no intent to being persuaded by anything you've stated. My more recent posts have merely been to guide you on your philosophical pursuits. I've the strong impression you aren't well schooled in philosophy and might not even be philosophically inclined enough to realize how difficult the problems are that philosophers attempt to respond to.

Anyway there is no commitment to it except for the existence (and evolution) of "you" (by any definition).

And it is this what I'm troubled by, where I offered one possible interpretation in the monads of Leibniz, which if you're not familiar with them will make the task even more difficult as I will have to explain Leibniz.

I'm afraid these examples don't help me understand the position any better. For one thing, I don't see the examples being different from those in your first ontology. Secondly, some of these are concrete, while others are abstract and I can't be sure this is a mistake or intended.

No problem, I'll specify

a) dreams

"you" evolve in dreams yes?

Don't know what this means. Ditto for the rest.

I'd imagine that's easy to understand ; wherever "you" go if you go insane.

[/quote]

What is it that's supposed to be real here (with respect to any of these examples)? I have no concept of "you" in which this makes sense, unless, that is you are talking about some sort of consciousness, or state of mind, something that is wholly different from that which is associated with the physical world, which in this ontological position I'd have to anticipate would not be real. And if that is what this position commits itself to, then it does begin to resemble the monads of Leibniz, where reality is manifold, consisting of ideal entities (ideal "you's" each of which are equally real. To elaborate a bit, Leibniz's monads are windowless and isolated. (Note that chairs and mountains would exist as monads, according to Leibniz, but these would be monads of a simpler sort than those like you or I.)

James

[Positor]

Reality (of which there is but one -- though there remains some confusion over the possible duality of matter and energy) is not composite (i.e., not composed of matter and energy), but is matter and energy (or perhaps it might be worded: reality is material and energetic, or possibly that which is material and energetic, though this latter could be postponed until we get to the question of existence).

I don't quite understand your distinction; perhaps you can enlighten me. If matter is in any way different from energy (which it is), and reality "is" matter and energy, how can reality not be composite?

What is the difference between, for example, "The United Kingdom is England, Scotland, Wales and Northern Ireland" and "The United Kingdom is composed of England, Scotland, Wales and Northern Ireland"? How does the first of these statements make the United Kingdom non-composite? It obviously doesn't mean "The United Kingdom is England and it is also Scotland" etc; it means it is the totality of England, Scotland etc. Therefore it is composed of them, isn't it?

Would it help to say (in a materialist ontology) "Reality is the set having (only) the two members 'matter' and 'energy'"?

[owleye]

Reality (of which there is but one -- though there remains some confusion over the possible duality of matter and energy) is not composite (i.e., not composed of matter and energy), but is matter and energy (or perhaps it might be worded: reality is material and energetic, or possibly that which is material and energetic, though this latter could be postponed until we get to the question of existence).

I don't quite understand your distinction; perhaps you can enlighten me. If matter is in any way different from energy (which it is), and reality "is" matter and energy, how can reality not be composite?

What is the difference between, for example, "The United Kingdom is England, Scotland, Wales and Northern Ireland" and "The United Kingdom is composed of England, Scotland, Wales and Northern Ireland"? How does the first of these statements make the United Kingdom non-composite? It obviously doesn't mean "The United Kingdom is England and it is also Scotland" etc; it means it is the totality of England, Scotland etc. Therefore it is composed of them, isn't it?

Would it help to say (in a materialist ontology) "Reality is the set having (only) the two members 'matter' and 'energy'"?

The context of my comments should be seen as an assessment of the wording Inzababa uses in stating his representation of a particular ontology -- an attempt to clarify it by indicating what I believe it is committed to. Respecting the matter and energy duality, I chose to put that aside for now as I think it is a secondary issue to the problem of the multitude of composite objects which his statement of the position represents. (In effect I'm going after the problem that is easier to resolve.)

As to the interesting ideas you suggest, first I'd say that the United Kingdom is probably better defined as some sort union or unification of England, Scotland, Wales and Norther Ireland (to use your list). To put its definition in terms of an "is" would suggest it is more like a set, having these four members. I wouldn't want it to be considered a set because that implies not being able to add or take away members without it being a different set. Yes, it would have changed, but it might not be enough to change what it means (i.e., its defining characteristics). With respect to being a composition, I suppose this could work, it having more generality than a union. One might also say the UK consists of .... However, saying something more general, while not wrong, might not be what we're after. It depends on the context. In the context here, if reality is composite and manifold, then on the face of it, it is not one thing, but many things, that is, unless, there's something about the composition that makes the composition merely something in name only. Which is the better representation of reality? What needs to be emphasized? The composition or the union? Do we move toward Parmenides "One" or toward Democritus' many (atoms)?

As to the hard question of what's real, despite that I'm a physicalist myself, I'd probably want to reserve that discussion to be in a different context. One of the points of saying I'm a physicalist (rather than a materialist) is to avoid the problem of figuring out the distinction and relationship between matter and energy. If pressed, I might say that energy is a property of matter, but for now, I'll beg off.

James

[Positor]

Thank you. I will ponder your comments further. These distinctions are quite subtle.

[Don Juan]

Although we now know that the universe began some 14 billion years ago, we come to know this because of another beginning – when our nervous system and its senses started to develop. There is then the world out there according to our objective experience, but we cannot discount the influence of our nervous system by which processes we view the universe. Our view of ontology then will have at least two huge frames coming together as a seamless whole – that which unfolds from the beginning of the universe and that which emerges from our own beginning as individuals and interconnected groups. When we emerge in the universe, the universe is our context. But our emergence created a difference and we become the context of the universe in this difference. (This paradox is a unity just like the algebraic expression x=-1/x). Through this difference we can claim that “the universe began some 14 billion years ago”. This difference is something unique or distinct from the rest of the universe because aside from experience of actual things, it has also experiences of abstract “things”. Where then one should base ontology? Should he ignore thoughts and accept the concrete as the only things that exist to which conclusion he arrived by thought? Or should he accept that our view of ontology is a two-faced Janus –one, “the world out there” and the other, “the nervous-system-influenced view” laid together and a part of which seems to fit well? Or should he accept only the nervous system-influenced view of the universe and deny existence of concrete things independent of the observer?

If the universe will be our basis for existence at least, since we exist in the universe and thoughts emerge from the physical activities of the nervous system interacting with the world out there, then thoughts – including mathematical thoughts and entities- exist. Abstract and concrete things exist for the reason that they occur in and are the products of the universe. I would take then the two-faced Janus view of ontology. In my point of view Russell’s idea of how to know what exists is correct. The second argument of Inzababa is also partly correct because the consequence of existence is influence (at least by serving as constraints of any kind), at least to the immediate context. Taking this view of ontology, I will now try to notice what constitutes reality. The created difference due to our existence creates another difference emerging from the comparisons between mental part and the actual part. We assign the concept of reality more to the group that happens actually in contrast to those happening mentally. Are mental entities not real? Mental entities exist at two levels, as an activity of the universe and itself as having contents. As far as they are activities of the universe, they are real – referring to that part of mental entities constituting their basic makeup. As far as they have contents, the contents are not real. But we use mental entities to represent what’s happening actually and so if they faithfully match what they try to represent can we say they are real? They cannot be real in the sense of reality referring to a verifiable concrete event, but they can be “real” in a shift of meaning of the word referring to matching between the mental entity and what is described out there that is actually happening. So mental entities can be actually happening in their basic makeup and thus are based on concreteness but their content (the elements and relationships), as they are, may not be. For example, the thought of a moving car, is actually happening as a physical process, but the content, the moving car is occurring as a mental entity at the more specific, nonessential end and thus is not real.

For me, mathematical entities exist; they are real as far as the (general) essential part of their make-up is concerned; and the nonessential aspect of their existence is not real though this aspect can be used to capture the relational structure of actual things.

There are two questions posed by Positor in the second page:

1. Do abstract concepts (all or some of them) influence reality in one way or another?

Having physical makeup, character, origin, constraints or base, abstract concepts do influence the immediate, actual event they are in by at least serving as constraints. In an actual event, an entity cannot NOT influence. The mere presence is an influence especially in a tight highly dynamic interrelated system.

2. Is it true that if they do not do so, they do not exist?

Actual events cannot have a direct negative, they always do so influence one way or another.
These are my answers because in addition the relationships of patterns occurring in the universe are so tight, and that they are so tight that “no-influence” at larger patterns can occur. This occurrence of no-influence partly compels us to say “if they do not do so influence….” The very question at number 2 emerges from the tightness of relationships.

By this line of thinking, unreal entities can influence real entities and vice versa, one way or another, by the tight circuits connecting them.

In the third page Positor has also another interesting question to Owleye:

If matter is in any way different from energy (which it is), and reality "is" matter and energy, how can reality not be composite?

It seems to me that this question focuses at least on the relationship between energy, matter and mass. From observation, we have developed conventional definitions of these concepts. If we would reflect upon the definitions and those corresponding common observations, we can notice that energy is an aspect of mass and mass of energy bounded by ranges established by change. Einstein’s E=mc^2 may point to non-composite nature of both energy and mass (so matter). Energy seems like a gradient of mass or mass a gradient of energy, a major influencing factor of the gradient being the speed of light. It is also like saying the United Kingdom is England, Scotland, Wales and Northern Ireland having fuzzy boundaries separating each other. The United Kingdom is the whole ranges of them - the boundary of Wales is the boundary of the United Kingdom and so is England, Scotland, and Northern Ireland. One way this can happen is if the distinction between them is not territorial but based on concentration of people calling themselves English, Scots etc. Thus reality has whole ranges of matter (mass) and energy which cannot be created or destroyed at the basic level.

[jules]

Don Juan is right to emphasize the difference between an idea and the content of an idea. An idea is a physical event, whereas the content of an idea is an abstract semantic entity.

However, I suspect the reason people are inclined to doubt the existence of the latter and affirm the existence of the former is an unjustified attachment to things that are natural. People are suspicious of semanic entities (sentences, equations, etc.), because we made them up, rather than discovering them in nature.

But does anyone doubt the existence of laws (or at least probabilistic rules) that govern the behavior of matter and energy? Because those laws are not composed of particles either.

[mtbturtle]

And no that is not physicalist you troll.

*clearing throat* I've enjoyed many of your posts and your enthusiaism, but please a little restraint.

[owleye]

...
If the universe will be our basis for existence at least, since we exist in the universe and thoughts emerge from the physical activities of the nervous system interacting with the world out there, then thoughts – including mathematical thoughts and entities- exist. Abstract and concrete things exist for the reason that they occur in and are the products of the universe.

I think I know what you mean here, but I believe something needs to be cleared up (which you attempt to do below, but get side tracked in what immediately follows this). What I find confusing in the above, is the use of 'entities' here, because the term is a more general one than thoughts, and shouldn't be used in a side by side way as is done here. Had you used the term 'thoughts' throughout, it might have been clearer. Within the category of thoughts, there are other words that could be used, to include ideas and imaginings. Concepts might also be used here, but my placement of it in this category would probably be restricted to its use in, for example, a concept car, or in "what a concept!" -- what we might achieve in a conceptualization. The ordinary usage of concepts, I think, would be in how they are used in the activity of thinking. Ideals might be a different category as well, probably belonging to the content of a thought, something you bring up later. (Note that mathematical 'entities' are at least sometimes thought of as ideals.) Notwithstanding, I suspect you use entities below to refer to any of the products of mental life, possibly including perceptions and feelings.

...
Are mental entities not real? Mental entities exist at two levels, as an activity of the universe and itself as having contents. As far as they are activities of the universe, they are real – referring to that part of mental entities constituting their basic makeup. As far as they have contents, the contents are not real.

One difficulty here, in referring to the entities in this front face of Janus (which I'll follow along with, despite that I think it's a bit of stretch), is that it makes it difficult to account for biological functions, a distinguishing feature of biology. It's possible this was an unintended lapse in your ontology, but if not, I might assume that function is not a real property of the universe. (Note that biologists speak of function as a product of the structure of an object. The structure of DNA not only reveals its function (reproduction), but wouldn't make sense, absent its functionality. But, I suppose, one can debate this. Much discussion goes on in the thread Lincoln opened up about the meaninglessness of the universe. (Note that something similar can be said about the concept of information, or a least that portion of it that makes it about something -- something that makes it than mere data.)

But we use mental entities to represent what’s happening actually and so if they faithfully match what they try to represent can we say they are real? They cannot be real in the sense of reality referring to a verifiable concrete event, but they can be “real” in a shift of meaning of the word referring to matching between the mental entity and what is described out there that is actually happening.

In describing mental activity -- thereby referring to the mind in some objective sense -- should require avoiding "we use" just to avoid the subjectivity involved by doing so. Note how "we use" above could mean what we do when we build or design cars. Probably better here would be "our mind uses". Given this slight alteration, then, what you seem to be saying in the above is that perceptions (these being the mental entities nearest in their proximity to the external world) may (sufficiently) represent reality. This is not the extent of you want to say, of course, but it should be pointed out that in the way you differentiate the content of a thought from the thought itself, here the representation would be real. After all, representations are mental entities. The question I would think you want to get at is whether or not what it is a representation of is real or not -- it is the content of these mental entities that is the subject of the enquiry. Which is what you conclude in the following.

So mental entities can be actually happening in their basic makeup and thus are based on concreteness but their content (the elements and relationships), as they are, may not be. For example, the thought of a moving car, is actually happening as a physical process, but the content, the moving car is occurring as a mental entity at the more specific, nonessential end and thus is not real.

But now you begin to drift.

For me, mathematical entities exist; they are real as far as the (general) essential part of their make-up is concerned; and the nonessential aspect of their existence is not real though this aspect can be used to capture the relational structure of actual things.

I think the problem here is that although you are, by the use of 'entity', probably referring to the thought of (for example) a number, say '12', and claim it has some real existence because thoughts exist, I'm pretty sure the mental activity involved in having this thought is not exactly the topic under consideration. Moreover, even though there might be some sort of 'representation' of the number '12' that exists as part of that thought, the number itself, that which is being referred to regardless of how it is represented, is what is under consideration.

The task being faced might better be understood by considering the example of a triangle, often taken as an example mathematical entity. Supposing one had some sort of representation of a triangle in whatever form it might take in a sense in which it could be a concrete reality. It could be as it is drawn on a blackboard, written out in accordance with its defining mathematical language, or a symbol that stands for it, or even in the form of a mental image. The question arises, then, whether or not it refers to anything in the real world. If you are a Platonist, it does. Basically such triangles, numbers and other mathematical entities (those things that are referred to by any of its representations) exist in Plato's heaven. There's a reasonable case for Platonism merely based on how mathematicians use the term in actual practice. They use these terms as if they existed outside their own mind in some abstract world they may have invented, though Platonists would argue that it was a discovery). In any case, if you are speaking of a universe in ways other than Plato's heaven, -- i.e., you are not an idealist nor a rationalist, then you will have your work cut out for you if you want to contend that mathematical entities exist (apparently you are not contending this, which is the usual position taken by materialists. Lomax will give you a well-respected version that some pragmatists (Quine, for example) take, which gives them some sort of reality. xcthulhu seems to have taken a liking to it being a social construct -- I have the defining book on my shelf for this position. I also have books that adopt a rationalist and a naturalist position on the subject matter.)

James

[Don Juan]

I think I know what you mean here, but I believe something needs to be cleared up (which you attempt to do below, but get side tracked in what immediately follows this). What I find confusing in the above, is the use of 'entities' here, because the term is a more general one than thoughts, and shouldn't be used in a side by side way as is done here. Had you used the term 'thoughts' throughout, it might have been clearer. Within the category of thoughts, there are other words that could be used, to include ideas and imaginings. Concepts might also be used here, but my placement of it in this category would probably be restricted to its use in, for example, a concept car, or in "what a concept!" -- what we might achieve in a conceptualization. The ordinary usage of concepts, I think, would be in how they are used in the activity of thinking. Ideals might be a different category as well, probably belonging to the content of a thought, something you bring up later. (Note that mathematical 'entities' are at least sometimes thought of as ideals.) Notwithstanding, I suspect you use entities below to refer to any of the products of mental life, possibly including perceptions and feelings.

There is a sense of parallelism that is organic in nature when we start to compare and contrast levels of organizations side by side like cells and organelles. My philosophy has inclinations towards levels of organizations comparing not only those of the same levels, but also those of different levels. In a fractal structure, the self-repeating structures allow for a parallel comparison between the high level and low level members. The universe exhibits fractal structures so that the structure suggested by the more general word entity has some similarities to the structure which one can find in thought during abstractions. Essentially we are talking about relationships, information and mapping. Mathematical ideas are of some special case because it can capture the structure of reality (in some sense and for some mathematicians, we discover mathematical entities), at least a part of it, more efficient and effective than language. Mathematical entities go with structures but they do not necessarily describe the whole process or context upon which they exist [in a way, mathematical entities seem to be like “objects” of mathematical thought, however they are not physical (in the sense of having directly the properties of matter and energy) but relationships and structures – towards the informational aspects of reality (but this is the tip of the iceberg)]. Mathematical thought consists of the different (mental) operations and (mathematical) structures employed to arrive at structures which in turn improve and expand mathematical thought. It is an iterative process producing complexity with a spirit of simplicity in the underlying relationships. It has at least three inputs – distinctions coming from the mind, from what is out there, or from the both viewed as a whole.

One difficulty here, in referring to the entities in this front face of Janus (which I'll follow along with, despite that I think it's a bit of stretch), is that it makes it difficult to account for biological functions, a distinguishing feature of biology. It's possible this was an unintended lapse in your ontology, but if not, I might assume that function is not a real property of the universe. (Note that biologists speak of function as a product of the structure of an object. The structure of DNA not only reveals its function (reproduction), but wouldn't make sense, absent its functionality. But, I suppose, one can debate this. Much discussion goes on in the thread Lincoln opened up about the meaninglessness of the universe. (Note that something similar can be said about the concept of information, or a least that portion of it that makes it about something -- something that makes it than mere data.)

Remember that systems are always a part of a larger system and has also sub-systems in it. That is why a system is a two-faced Janus. Meaning, we care considering multiple contexts here provided by the higher system, the lower subsystems, the system itself and their relationships and influences upon each other – there is a sense of transition, not only linear but also non-linear. System boundaries are determined partially by control. A larger system does not necessarily control (at least not directly) its subsystems. Now function is a result of the two-faced Janus nature of systems. Function depends on presence of a hierarchy – a higher level and a lower level. So in thinking about these things we have to consider at least of two levels. If you think about a cell and its function, you have to think of its higher contexts, and the subcontexts within it. So then applying the context-content frame to biological mechanism will have unique distinguishing character in contrast when you apply it to abstract entities because the levels become part of the constraint in addition. In the biological mechanisms, both levels are at least about physical entities. In the abstract entities, there is a quantum leap of difference greater than that of biological mechanism levels, because one of the levels is leaning towards the physical end and the other leaning towards purely mental end. It does not necessarily follow then that using this frame to abstract entities will have the same effect to biological entities because one has to consider the network of ideas and facts which forms the context of the entity being studied.

In describing mental activity -- thereby referring to the mind in some objective sense -- should require avoiding "we use" just to avoid the subjectivity involved by doing so. Note how "we use" above could mean what we do when we build or design cars. Probably better here would be "our mind uses". Given this slight alteration, then, what you seem to be saying in the above is that perceptions (these being the mental entities nearest in their proximity to the external world) may (sufficiently) represent reality. This is not the extent of you want to say, of course, but it should be pointed out that in the way you differentiate the content of a thought from the thought itself, here the representation would be real. After all, representations are mental entities. The question I would think you want to get at is whether or not what it is a representation of is real or not -- it is the content of these mental entities that is the subject of the enquiry. Which is what you conclude in the following.

Why do I have to avoid subjectivity when I believe it is equally important as objectivity? Remember that I began with two beginnings in mind – the beginning of the objective world and the beginning of a subjective one and how we use the subjective frame in order to know the objective content – how the process of the nervous system facilitates your knowing of the universe. It is possible that when we think, we do it at the level of the subconscious which is a mind-body operation, just like in “autopilot” activities which some part of the information comes from reading, self-deduction-induction or any abstraction which become constraints to the “autopilot” behavior and making representations is not necessarily voluntary. When you say representations are mental entities, you are both referring to its content, general character and the process by which it exists (because they are dynamic entities). Whether it is a representation of a real object, there is a processes involved and this process leads to a transformation so that instead of dealing with purely matter and energy we are now dealing with structures and relationships when we are talking about mental entities.

But now you begin to drift.

I still hold in this part the two sided-character of mental entities just like I did in the previous.

I think the problem here is that although you are, by the use of 'entity', probably referring to the thought of (for example) a number, say '12', and claim it has some real existence because thoughts exist, I'm pretty sure the mental activity involved in having this thought is not exactly the topic under consideration.

Do you mean to say reality is necessarily arranged in topics and those tools of subdivisions employed by thought? In as much as meaning does not rest in the word alone, mental entities do not rest in itself alone. Remember that no man is an island and that the world is an interconnected whole. Do not reify the members of a set as if they are independent from the set that bounds them. They have never been independent and the set describes a character of the members in a form that would suggest (at least implicitly) that the member has other characters other than that expressed by the set. The product of distinction is always a twin at least but we still have to take note where the division was made because divisions are employed in aspects and not in whole and this applies to sets too.

Moreover, even though there might be some sort of 'representation' of the number '12' that exists as part of that thought, the number itself, that which is being referred to regardless of how it is represented, is what is under consideration.

Well there is no stopping you if you would prefer that way. But the universe does not work that way. An entity is always situated and this implies context, both coming from its higher levels and from its lower levels. An entity is a relationship of contexts with fuzzy boundaries and in multi-plane and nonlinear conformations. If we are trying to understand natural phenomena we cannot restrict the topic to our preferred fixed boundaries and still be correct. Of course we are trying to avoid wandering off, but we are not restricting our exploration. There has to be some balance and this will be decided upon by what is in nature, not us in this sort of discussion.

The task being faced might better be understood by considering the example of a triangle, often taken as an example mathematical entity. Supposing one had some sort of representation of a triangle in whatever form it might take in a sense in which it could be a concrete reality. It could be as it is drawn on a blackboard, written out in accordance with its defining mathematical language, or a symbol that stands for it, or even in the form of a mental image. The question arises, then, whether or not it refers to anything in the real world. If you are a Platonist, it does.

The one which allows us to say that this example 1 is a triangle and this example two is another triangle is a pattern of relationship of points, lines or spaces or any sort having the same boundaries resulting to the shape. This pattern is a point of focus subject to our thresholds and habits of perception and its extensions (the devices we use). The figure drawn in the blackboard is just is, but our interaction with it and similar relationships makes it a triangle. A pattern is a relationship between the observed and the observer (they are attractors of thought as one contemplates about the world). We are partly responsible as observers in deciding upon the boundaries of a triangle, if not consciously then unconsciously. At higher levels, that is, at the level of mathematical entities, part of this pattern will be representation because the information coming from the examples is received by the senses and processed by the nervous system and situating it in its memories and projections (because the brain is at least basically a memory-prediction system, it needs both data and the process that completes the circuit to get and provide feedback). As a pattern, a triangle is a “hybrid”, a result of our interaction with what is out there. It has physical and mental bases connected by a whole process. If a triangle refers to anything in the real world, then we have to look at the context and notice what “refer” implies. It implies the observer and the process by which he claims the triangle to refer to a thing in the real world. In the end, it is the activity of the observer interacting with what is out there that forms the basis of a triangle. Does it exist, yes it does. Is it real? Part of it yes, part of it no, this is so because the question of its reality refers to a process having emergent properties that goes beyond or different from those involving matter and energy.

Basically such triangles, numbers and other mathematical entities (those things that are referred to by any of its representations) exist in Plato's heaven. There's a reasonable case for Platonism merely based on how mathematicians use the term in actual practice. They use these terms as if they existed outside their own mind in some abstract world they may have invented, though Platonists would argue that it was a discovery). In any case, if you are speaking of a universe in ways other than Plato's heaven, -- i.e., you are not an idealist nor a rationalist, then you will have your work cut out for you if you want to contend that mathematical entities exist (apparently you are not contending this, which is the usual position taken by materialists. Lomax will give you a well-respected version that some pragmatists (Quine, for example) take, which gives them some sort of reality. xcthulhu seems to have taken a liking to it being a social construct -- I have the defining book on my shelf for this position. I also have books that adopt a rationalist and a naturalist position on the subject matter.)

My position is that mathematical entities exist, but in terms of reality they are products of the interaction between the observer and the observed, bounded by a whole process part of which is towards mental leanings having unreal parts (the contents), while another part is towards physical and therefore real. Every triangle is a dynamic stable interaction between the observed and its observer. It calls forth the appreciation of structural relationships, not purely material alone, neither purely mental alone, but both as parts of a whole.

[Don Juan]

I think there is something I have to add about biological function.

One difficulty here, in referring to the entities in this front face of Janus (which I'll follow along with, despite that I think it's a bit of stretch), is that it makes it difficult to account for biological functions, a distinguishing feature of biology. It's possible this was an unintended lapse in your ontology, but if not, I might assume that function is not a real property of the universe. (Note that biologists speak of function as a product of the structure of an object. The structure of DNA not only reveals its function (reproduction), but wouldn't make sense, absent its functionality. But, I suppose, one can debate this. Much discussion goes on in the thread Lincoln opened up about the meaninglessness of the universe. (Note that something similar can be said about the concept of information, or a least that portion of it that makes it about something -- something that makes it than mere data.)

It seems to me that biologist speak of the fit or correlation between structure and function, but knowledge of the structure does not immediately reveals function. This condition exists because in biology the same structure can have different functions and different structures can have the same function, especially when we are talking of protein structures. When Watson and Crick discovered the structure of DNA several contextual factors were already in place for example scientists already know that there is a relationship between genes and proteins, that genes are most likely composed of the DNA, that genetic recombination exists, that genes are carried by the chromosomes and are replicated faithfully and so on. The chromosome theory of inheritance suggest that the DNA in genes undergo replication but how specifically? This question then is answered by the discovery of the structure of DNA and the consequent experiments on DNA replication. The history proceeded that way and not the other way around discovering the structure of DNA then wallah one already knows the function. Function is a product of both the structure and its context and sometimes as it happened in history of the discovery of the structure of the DNA, the idea of the function comes first and then we look for the structures and configurations which perform that function. In correlating function and structure, biological context immediately relevant to the structure is implied. In information theory it is like this, the specific function of a missing letter in a discourse can be revealed by the discourse without the letter, but if you only have that missing letter without the discourse, it is much more difficult to know the specific function.

[owleye]

I think there is something I have to add about biological function.

It seems to me that biologist speak of the fit or correlation between structure and function, but knowledge of the structure does not immediately reveals function. This condition exists because in biology the same structure can have different functions and different structures can have the same function, especially when we are talking of protein structures. When Watson and Crick discovered the structure of DNA several contextual factors were already in place for example scientists already know that there is a relationship between genes and proteins, that genes are most likely composed of the DNA, that genetic recombination exists, that genes are carried by the chromosomes and are replicated faithfully and so on. The chromosome theory of inheritance suggest that the DNA in genes undergo replication but how specifically? This question then is answered by the discovery of the structure of DNA and the consequent experiments on DNA replication. The history proceeded that way and not the other way around discovering the structure of DNA then wallah one already knows the function. Function is a product of both the structure and its context and sometimes as it happened in history of the discovery of the structure of the DNA, the idea of the function comes first and then we look for the structures and configurations which perform that function. In correlating function and structure, biological context immediately relevant to the structure is implied. In information theory it is like this, the specific function of a missing letter in a discourse can be revealed by the discourse without the letter, but if you only have that missing letter without the discourse, it is much more difficult to know the specific function.

Well, yes, though I'd used DNA structure as an example of my broader point. Obviously, teleological thinking has a long history. Indeed, so does form. The two were linked in Anstotelian philosophy. We understand that arms and hands are tools that function in certain ways and from that we can say that shape (the form it takes) has a lot to do with it. However, my point was that function can be reduced to structure (a physically endowed form) while equally expressing the idea that function emerges from structure. It was an example that I used to make a case for the existence of function itself, a teleology, so-to-speak. (The argument, however, cannot be extended beyond the reach of the genes. There's no reason to think that genes have higher purposes beyond what its structure reveals. Or, organisms, themselves, have no purpose beyond what their genome has laid out for them.) Despite this argument, however, there are some who don't believe functions exist at all. Their argument is that functions are merely mental projections. We are, in effect, anthropomorphizing when we say that the shape and flexibility of flagella serve to help the sperm reach the egg in the medium it swims in.

The reason I'd brought up the point was to examine your statement about physical existence, particularly as it might relate to emergent properties, something that biologists are keen to admit into their ontology. If they are included in your idea about what's real, would that mean functions exist?

James

[Don Juan]

Well, yes, though I'd used DNA structure as an example of my broader point. Obviously, teleological thinking has a long history. Indeed, so does form. The two were linked in Anstotelian philosophy. We understand that arms and hands are tools that function in certain ways and from that we can say that shape (the form it takes) has a lot to do with it. However, my point was that function can be reduced to structure (a physically endowed form) while equally expressing the idea that function emerges from structure. It was an example that I used to make a case for the existence of function itself, a teleology, so-to-speak. (The argument, however, cannot be extended beyond the reach of the genes. There's no reason to think that genes have higher purposes beyond what its structure reveals. Or, organisms, themselves, have no purpose beyond what their genome has laid out for them.) Despite this argument, however, there are some who don't believe functions exist at all. Their argument is that functions are merely mental projections. We are, in effect, anthropomorphizing when we say that the shape and flexibility of flagella serve to help the sperm reach the egg in the medium it swims in.

The reason I'd brought up the point was to examine your statement about physical existence, particularly as it might relate to emergent properties, something that biologists are keen to admit into their ontology. If they are included in your idea about what's real, would that mean functions exist?

James

At best I think we can think of function in biology suggesting an intention-like character. As you may notice the changes in the DNA may be random but conformational changes in a protein for example follows a certain pattern and some of which have a certain range of activity and the whole system in which it is in may have some form of redundancy that when this particular protein is expressed at low levels, some changes occur to compensate and aid the survival of the organism for a certain period. Possibly evolutionary changes occur that way. When environment poses constraints on the organism, it undergoes somatic changes long enough for the random changes in the genetic information bring about the characteristics contributing to economy of survival releasing the somatic parts the burden of stretch or further strengthening it, etc. Somatic change and random changes in the genetic material then can be seen as working as a unit and behaves in an intentional-like manner. Function in biology however means what a structure does given two directions of influences, coming from the lower context (the elements of the structure) and the higher context (the environment of the structure). It is not about purpose. Function in biology, in this sense, exists. However, does function which implies purpose exist? Of course it does at least as an idea or sets of relations. This is because my idea of existence is not restricted to physical objects but extends to mental experiences. My fundamental elements for existence is not only matter and energy but also information.

[owleye]

At best I think we can think of function in biology suggesting an intention-like character.

"Intention" is probably a stretch here. I'd prefer restricting its use to conscious experience. Though I'd used 'purpose' in my account, I was wary of doing so, as this, too, gets me into a bit of trouble. My reason for using it was due its relationship with 'serves'. In ordinarily language, performing a function is the same thing as serving a purpose. However, in expressing it this way, I think I'm saying too much about it (function). What seems to be true is that functions are hierarchical. We have basic functions and higher level functions. And it is only within the top-most system that 'purpose' comes into play. And when we reach this top-most layer, the hierarchy turns to mush -- well what it turns to (or rather returns to) is the builder -- which can be said to be the genes, which is where functioning beyond the structure imposed by DNA ends.

[...snipped explanation of how evolution works and making a case against purpose and a case for information] This is because my idea of existence is not restricted to physical objects but extends to mental experiences. My fundamental elements for existence is not only matter and energy but also information.

Though you rule out purpose, and somewhat discount 'intentionality', given how I characterize these two in my comments above, are you also discounting 'function'? With respect to your idea about information, I would agree, but in doing so, we might actually be in disagreement because we don't mean the same thing by 'information'. In terms of biology, which includes humans, information is always information about something; it doesn't stand alone. What that information is about is the thing itself, it having discernible properties that can be extracted from how these properties come into contact with us (the organism), and in particular how it affects the evolutionary success of the genes. This is to say that the DNA encodes information about the (its) environment that have a bearing on its successful reproduction. (It may also encode what might be called data -- it having little or no information content about the current environment.) Is this the sort of thing you had in mind, or are you thinking of information as negative entropy? If so, I believe I can understand your position better when you describe is as matter and energy where information is but a property of matter and energy (in the form of negative entropy). However, in gaining this I lose the reason why you would introduce it as a third category -- matter, energy, and information.

James

[Don Juan]

"Intention" is probably a stretch here. I'd prefer restricting its use to conscious experience.

If you would notice that the whole word is “intention-like” and not exactly “intention”. I am referring to a part of the concept of intention, that part that suggests direction, specificity (but allowing a certain range) and consistency of action in a given context that draws us into thinking that it serves a purpose. The usage is somewhat metaphorical.

Though I'd used 'purpose' in my account, I was wary of doing so, as this, too, gets me into a bit of trouble. My reason for using it was due its relationship with 'serves'. In ordinarily language, performing a function is the same thing as serving a purpose. However, in expressing it this way, I think I'm saying too much about it (function). What seems to be true is that functions are hierarchical. We have basic functions and higher level functions. And it is only within the top-most system that 'purpose' comes into play. And when we reach this top-most layer, the hierarchy turns to mush -- well what it turns to (or rather returns to) is the builder -- which can be said to be the genes, which is where functioning beyond the structure imposed by DNA ends.

I can use ‘purpose’ for both perspective – ordinary language and in scientific description, noting either my subjectivity if I would like to keep the common meaning or keeping in mind a difference in meaning if purpose means an end arrived at without intention but with consistency and specificity. This is because just as there are two points of beginning I was referring to, there are also at least two ways of description. One can describe an event in a very objective manner and the words that maybe used are not necessarily technical but common words whose meanings become technical according to the specific context. In this sense, function can mean what a part does devoid of any purpose. One can also describe in a subjective manner taking into consideration even at least unconsciously the connection between the observer and the observed. In this sense, function can mean the same part and activity but seen as serving a hierarchy. In some ways, this also refers to the two focuses of cybernetics – the first-order and the second-order. The first-order refers more to objective descriptions, while the second-order takes note of the context where the described first-order relationship is situated – the subjective landscape. The second-order basically says that the feedback relationships in nature described objectively is within the feedback relationships between nature and observer, or in other words, the observer is a participant in the description of nature. By virtue of the second-order disposition he often unconsciously inserts a purpose to the first-order events he describes. This is not to say that purpose does not exist, but this is to say that purpose exist because of the difference created by the emergence of the observer.

Though you rule out purpose, and somewhat discount 'intentionality', given how I characterize these two in my comments above, are you also discounting 'function'?

I hope that you see that I do not discount intentionality, purpose and function, but I strive to know where their meaning should properly be when considering contexts. When we are focused on objective description of biological processes, then an objective meaning of function (the one which does not imply purpose) has to be followed. If we are focused on an almost objective description but that which is within the confines of subjectivity, then function can shift meaning into that one which suggest purpose. The second kind of description, objectivity embedded in subjectivity, cannot be ignored if we want a complete description because in order to set experiments, record data, discuss data and interpret, make conclusion and act, one has to employ a nervous system or similar system. This does not require us however strictly to be this complete and we can discuss things in biology in an objective manner. So with regards to your question, I believe in at least two meanings of function depending on context and what is required is to know what it means when used in context. That is to say also that we cannot have a single meaning of ‘function’ and generalize it to every instances of specific, consistent activity in context. ‘Function’ is not discounted, but situated.

With respect to your idea about information, I would agree, but in doing so, we might actually be in disagreement because we don't mean the same thing by 'information'. In terms of biology, which includes humans, information is always information about something; it doesn't stand alone. What that information is about is the thing itself, it having discernible properties that can be extracted from how these properties come into contact with us (the organism), and in particular how it affects the evolutionary success of the genes. This is to say that the DNA encodes information about the (its) environment that have a bearing on its successful reproduction. (It may also encode what might be called data -- it having little or no information content about the current environment.) Is this the sort of thing you had in mind, or are you thinking of information as negative entropy?

When we are to describe biological processes objectively (in the first-order), the patterns that are present in the process are not necessarily about something, they are just is – they are what they are. In its simplest form or unit, information is what it is, a difference that makes a difference. But since description no matter how objective presupposes an observer (the relevance of the second-order), then the patterns we notice in biological processes become about something. Information as about something is a (conscious or unconscious) point of view from the second-order frame. That is why in our discussion elsewhere, I said you are referring to information occurring in a higher order. The higher order point of view enables as to ask “The DNA encodes information about what?” Our objective description creates a sort of redundancy in terms of information to what is already in the system we describe. In some sense information does not have to be a consciousness “thingy” you know.

If so, I believe I can understand your position better when you describe is as matter and energy where information is but a property of matter and energy (in the form of negative entropy). However, in gaining this I lose the reason why you would introduce it as a third category -- matter, energy, and information.

Information is a difference that can enter and be transformed in the feedback circuitry of a system. It is a communicational distinction which networks of systems and subsystems process to articulate with each other. Information is different from matter and energy because it is of zero dimensions and thus cannot be located in the manner we locate matter and energy.

[owleye]

If you would notice that the whole word is “intention-like” and not exactly “intention”. I am referring to a part of the concept of intention, that part that suggests direction, specificity (but allowing a certain range) and consistency of action in a given context that draws us into thinking that it serves a purpose. The usage is somewhat metaphorical.

The interesting topic we are discussing (function) falls within the category of the existence of emergent properties. More specifically, the ontology being presented is based on a physicialst interpretation (using the concepts of matter and energy as its basis) Biologists are keen to using the term 'function' to describe (and explain) certain activity encountered in living organisms. Humans use the term for the parts they use to construct tools or perhaps even technology itself. Absent a human purpose (or humans, generally), the construction can be said to lack it. For this reason it is reasonable to say that purpose and intention are not included within a physicalist ontology if humans (or other intentional creatures, those with human like properties of consciousness) exist. Note: they may be reintroduced in consideration of attributing these mental properties to having some physical basis.

Now, purpose, or intention, though excluded here, could be what gives the construction its "direction'". So reducing 'function' to structure even in the context you are setting out, having a direction doesn't by itself clear things up. Assuming it reasonable to conclude that parts of things are functional even when they are not constructed with something in mind (some intention or purpose), let me proceed to ferret out what you might mean by direction, something you also do in what you subsequently write, but I'll be taking a different tack. (Note that though we are having a discussion, my general thinking on having them on a board such as this is that it is principally a tool we use to improve our own understanding -- i.e., what we write is principally for our own benefit.)

Mathematically, function can be seen as a kind of transformation of something into something. When "executed" it might have the appearance of being directional, and we might say that if there's something physical to support it all, that while it may be a construction or a destruction, depending on the flow of energy, directionality could be attributed to having a temporal dimension. In this way of thinking about function, function puts a temporal direction to the spatiality associated with its underlying structure. A part that is not useful is said to be dysfunctional. This informs us that its use depends on the function (temporal directionality) of the activity of the role played by the structure in that activity within in the context (a term you often use) of its environment. What it does (i.e., the function or use it has, or what it is designed to do) based on its structure, over time, under certain circumstances, is the direction it takes.

In addition to the emergence of function, another concept which function depends on, one that biologists think of in consideration of living things as organisms, is that of systems and their subsystems. Some of these systems include control subsystems, others, perhaps, better understood as information processing systems. Some of the control systems are feed-back related, others less so. Organisms are said to be open systems having a specific kind of relationship with their environment. With respect to ontology, then, the same question respecting the reality of systems occurs as it does functions. The usual way of adopting a system into an ontology is to think of it in thermodynamic terms. A system exists essentially because the sum of its parts don't make up the whole. It emerges as an entity because there is some main thing it is in which its constituent elements act in some manner as random variables that in their interaction, coupled by influences outside it unify it into a single entity -- a system of the way its constituent elements (systematically) play in making it what it is. One usually puts a boundary on a system such that there is an inside and an outside, so-to-speak. However, the existence of boundaries is better associated with a deeper ontology, and so would require a deeper understanding of reality. One question that arises from this analysis is, is the universe a system (or even something that is more than the sum of its parts) or is it merely a name we give to the collection of parts?

I can use ‘purpose’ for both perspective – ordinary language and in scientific description, noting either my subjectivity if I would like to keep the common meaning or keeping in mind a difference in meaning if purpose means an end arrived at without intention but with consistency and specificity.

I think I can accept this, but actually would prefer not to use 'purpose' to mean what you have in mind for it in the latter interpretation. Function, to me, suffices. However, I do like your use of consistency and specificity if, by this you allow for it something like "usually consistent" and "usually specific". In physical terms, I doubt you could get away with these terms in their unqualified sense. (On the other hand, you might be able to make use of them at a deeper level, though I'm not sure.)

This is because just as there are two points of beginning I was referring to, there are also at least two ways of description.[/qupte]

I would hope that you would base your interpretation of physical phenomena in such a way that it helps explain it, not merely describes it. I add this because I'm a bit touchy about the limits of use of the term, 'description'.

One can describe an event in a very objective manner and the words that maybe used are not necessarily technical but common words whose meanings become technical according to the specific context. In this sense, function can mean what a part does devoid of any purpose.

Though function can mean this, there is a sense in which 'doing' is already built into what a function means. Nothing is done without having something in mind that it was doing. In a descriptive sense, I tend to draw on the term 'activity' rather than doing, until, that is, I've reached a point in the description where function emerges. Of course 'activity' may not be the right term either, since the term originated from the verb 'to act', which has within some agency associated with it. However, over time 'activity' seems to have lost this, so I don't think it necessary to go so far as to say behavior, or even processing, which has kind of been taken over by information theory.

One can also describe in a subjective manner taking into consideration even at least unconsciously the connection between the observer and the observed. In this sense, function can mean the same part and activity but seen as serving a hierarchy. In some ways, this also refers to the two focuses of cybernetics – the first-order and the second-order. The first-order refers more to objective descriptions, while the second-order takes note of the context where the described first-order relationship is situated – the subjective landscape. The second-order basically says that the feedback relationships in nature described objectively is within the feedback relationships between nature and observer, or in other words, the observer is a participant in the description of nature. By virtue of the second-order disposition he often unconsciously inserts a purpose to the first-order events he describes. This is not to say that purpose does not exist, but this is to say that purpose exist because of the difference created by the emergence of the observer.

Hmm. I might be able to make sense of this in the following way: if the biological organism extends its reach to the world that it brings within its control, creating a boundary that is larger than the immediate boundary encased by its body, something like how seeds developed, creating an environment for reproduction that reliably allowed it be a land-based organism, less dependent on a water environment, then, yes, it might be possible to say that tools have real functionality in the same way that the shape of enzymes have real functionality. However, I'd still prefer to think that the purposefulness and the intentionality derivative of mental activities be placed in a different category, different from how you characterize it -- namely subjectivity and objectivity, the observer vs. the thing itself. The principle reason for this, for me, is that intentionality seems to be more detached from the structure of the world than functionality anticipates, and they can even be obstructions to the problem since we sometimes get confused about the target. Thoughts may exist, but whether their content exists is another question. If what is being sought is a physical interpretation of functions then including intentions as functions is going to make this a much more difficult challenge. My own suggestion would be to restrict the discussion to functions, at least for now, notwithstanding that mathematical entities is the end goal. However, if you're satisfied that functions can exist in a physical sense, then we can move on to intentions and purposes, despite how difficult they are to physicalize. (Of course, ideals, to include mathematical entities, is going to be even more challenging, and I suppose this will lead to the realization they have no physical existence, in the sense in which they are the object of our thoughts, that which is being referenced.)

When we are to describe biological processes objectively (in the first-order), the patterns that are present in the process are not necessarily about something, they are just is – they are what they are. In its simplest form or unit, information is what it is, a difference that makes a difference. But since description no matter how objective presupposes an observer (the relevance of the second-order), then the patterns we notice in biological processes become about something.

I would hope that describing reality doesn't interfere with reality in the way you say it does. I would agree that our descriptions can be anthropomorphic, but that shouldn't be a quality of describing that we should endorse. Information being about something doesn't mean that it is information to an observer. It is information to an observer only for the observer's information processing. DNA holds information about the environment it evolved within, but that doesn't mean that it had to be an observer of some first-order information of the environment. To me, it becomes information when something in the environment ("a difference that makes a difference") is identified in such a way that it can be made use of (has some functionality with respect to it) by something else. Encoding (in its broadest sense) is what creates the information, at least the way I see it. Otherwise, it is merely a difference in the world -- i.e., data, the so-called negative entropy idea.

James

[Danlanglois]

Of course numbers exist. What is the prime number after 3? 5.

I wonder how formally we want to use the term 'exist'. Do fictional characters exist, for example? Of course they do, I say. But, then, do I expect to meet Sherlock Holmes? Am I psychotic? No. I just think it seems trivial, trying to come up with a list of what exists. What are you going to do with that list?

What is the real question about numbers, I think there's an Aristotle quote about this, the question being, according to him, not whether they exist, but how they exist.

[BadBoyofCosmology]

Infinity is a math-only concept that doesn't apply to the reality.

Counting all that physically exists, a property list of the universe, no math per se exists, or time. Math describes the list, and we don't have time, we just move through it.

You suppose God could get arrested, and the universe taken in as property?

[DragonFly]

Nature has regularities to it, and math is very amenable for the descriptions, and so some people may have come to think that math underlies reality. Numbers came about later—to keep track of how many things there were.

[yadayada]

Of course numbers exist. What is the prime number after 3? 5.

I wonder how formally we want to use the term 'exist'. Do fictional characters exist, for example? Of course they do, I say. But, then, do I expect to meet Sherlock Holmes? Am I psychotic? No. I just think it seems trivial, trying to come up with a list of what exists. What are you going to do with that list?

What is the real question about numbers, I think there's an Aristotle quote about this, the question being, according to him, not whether they exist, but how they exist.

I think this is an abuse of the word exist. It is possible to deliberately conceive of numbers as real, within a specified universe of discourse, but exist is usually reserved for things in nutural physical reality. You know, the things we see, grasp, eat, or fall on us.

Within the universe of the book, Sherlock is real, and while reading, the character is subjectively real to me. To say that he exists as described indeed crosses the bounds of sanity.

[owleye]

yadayada...

I think Danlangois is aware of what you are criticizing based on his own response to it -- namely that the criticism goes to how it exists.

In any case, inquiring about the ontological status of anything is to ask how it exists, if it does, so not a whole lot is gained by merely calling attention to it in so far as it contributes to the topic, and my guess is that Dan was merely trying to get the topic back on track. Searle, for example, speaks of social reality, largely based on deontological considerations, particularly that of commitment to what one says about things that we construct in language and take to be convention. Mathematical objects have been argued to have a kind of social existence of sorts. This is the position taken up in a book on the topic ("What is mathematics, really?") which I have in my library. The well-respected xcthulhu (sp?) on this board seems to lean in this direction, I believe on the basis of the arguments therein presented.

James

[yadayada]

I'm sorry if I sounded harsh and critical. That is not my intent.

My point is to draw a distinction between the use reality and existence. Historically, Plato talks about metaphysical types that are more or less real. To him, ideals are the most real, and mathematical models are somewhat less real, but both of these are considerably more real than objects or changing appearances.

Aristotle chose the world of fixed, concrete objects as the topic of philosophy, and these and only these have come to be talked about and thought of as 'existent'.

For example, when I watch a movie or read a book, its characters become more or less real to me, depending on how well I can understand the characters. Yet, in any fiction, no character 'exists'. Numbers are characters in mathematics. The more familiar I am with numbers, the more real they become, yet they cannot exist any more than other, more human fictional characters.

[Lomax]

I think this is an abuse of the word exist. It is possible to deliberately conceive of numbers as real, within a specified universe of discourse, but exist is usually reserved for things in nutural physical reality. You know, the things we see, grasp, eat, or fall on us.

I see it the other way around. Historically, "exist" was not reserved specifically for physical objects, and I see no reason why it should be. In fact it would make the debate over physicalism rather senseless (which perhaps you feel it is).

[yadayada]

I see it the other way around. Historically, "exist" was not reserved specifically for physical objects, and I see no reason why it should be. In fact it would make the debate over physicalism rather senseless (which perhaps you feel it is).

You are undoubtedly correct, and the vast majority of philosophers agree with you.

That is because history in philosophy is largely Aristotelian. Aristotle collapsed the four classes of metaphysics of Plato into one, so that only one reality remained. This has not changed in mainstream philosophy, which, naturally, is what is taught in school.

http://plato.stanford.edu/entries/arist ... taphysics/

Categories begins with a strikingly general and exhaustive account of the things there are (ta onta)—beings. According to this account, beings can be divided into ten distinct categories. ... They include substance, quality, quantity, and relation, among others. Of these categories of beings, it is the first, substance (ousia), to which Aristotle gives a privileged position.
Substances are unique in being independent things; the items in the other categories all depend somehow on substances.
...
The individuals in the category of substance play a special role in this scheme. Aristotle calls them “primary substances” (prôtai ousiai) for without them, as he says, nothing else would exist.

Existents are derived from Aristotle's primary substances. Does the physical world exist? Of course. By definition, not by argument.

There are many realities, both possible and actual. Geometry, physical mathematical theories, movies, books, our private worlds among them. None of these actually exist.

Consider: Realities are continuous, wide ranging from not very real to very real, while existence is binary. Something either exists or it does not. The logics are different. To force some reality into existents, one would need to split it into dichotomies with the PNC, and the LEM, and Identity. Then categorical logic follows. (Another, independent example of this is Wittgenstein's Tractatus)

[Danlanglois]

To force some reality into existents, one would need to split it into dichotomies with the PNC, and the LEM, and Identity. Then categorical logic follows. (Another, independent example of this is Wittgenstein's Tractatus)

Okay, my guess is that the PNC is the principle of non-contradiction. If I'm on the right track, then the LEM might be the law of the excluded middle. And, also, something is what it is, if we're talking about Aristotle's three laws of thought.

As to whether numbers exist, I imagine, that there is a substantive question, whether the truths of mathematics are grounded in abstract forms, concrete material instances, or human conceptual activity. My problem with debating existence, is that I don't see that anybody is actually primarily concerned with whether numbers exist, or, similarly, whether properties exist, whether meanings exist. I offered, that there is a more traditional Aristotelian view, and I get hit w/all this? Which, could be good.

At the end of the day, Aristotle does not bother asking whether properties, meanings, numbers exist. The way I might put it, is that the whole discussion is about substances (and not, or at least not precisely, like you seem to mean it, '(E)xistents are derived from Aristotle's primary substances'). I tracked down my Aristotle quote, where he does pause to ask whether numbers exist:

it is true also to say, without qualification, that the objects of mathematics exist, and with the character ascribed to them by mathematicians

The 'serious' question about numbers being, whether they are transcendent substances, or grounded in concreta.

The question of 'What is there?' Who cares? I recall Quine gives an answer--'everything'. I'm fine with that answer.

I don't see metaphysics as addressing the question of what exists. What is the task? To say what exists? If that is the task, then the method will be to solve for the domain of quantification required, and etc., perhaps. There are, however, views of metaphysics other than this.

It seems to me that you misread Aristotle (well, you read him intuitively, having hung around american philosophers too much, put it that way?); perhaps my reading of him is more interesting than he actually is? But Aristotle leads into the Metaphysics with this:

we must inquire of what kind are the causes and the principles, the knowledge of which is wisdom

What is the task of metaphysics, here? Also, I think you'll arrive at a different method. I, at least, take a permissive disinterest in such questions as whether there are numbers. You say '(T)hen categorical logic follows', but, consider how Aristotle launches the Categories:

‘Of things said without any combination, each signifies either substance or quantity or qualification or a relative or where or when or being-in-a-position or having or doing or being-affected’’

That is, I take it, a catalog of types of entity. Wouldn't you say, then, that he simply assumes that all such types of entity exist, without need for further discussion?

Again, whence comes any great concern with questions such as whether numbers exist?

What exists, I figure, given that numbers exist, is grounds, and groundings, such as, they might be counted as substances. That's grounds. Or else, how are they grounded? In, that is, the real substances?

Is there anything directly at stake in existence questions, then? No. Is there any harm in positing an abundant roster of existents? No.

What is fundamental?

Interest in questions of what is fundamental, I'd construe as interest in traditional metaphysics.

There are many realities, both possible and actual. Geometry, physical mathematical theories, movies, books, our private worlds among them. None of these actually exist.

I'm positively interested in arguing that a metaphysics that is packaged with a permissive stance on existence, will prove best. Ask me whether possible worlds exist, etc. There is no dictum here, methodological, epistemological, metaphysical, that I am violating or falling afoul of?

Existence questions are trivial, while there are other questions that are interesting. And deep, and unavoidable. Say, that we study substances, and their modes, and kinds, by studying the fundamental entities, and what depends on them. What then, of numbers, in these terms? Terms, of ontological dependence, of priority in nature. What grounds what? What is fundamental, what derives from it?

btw, I'm trying to come up with a comment about your notion of 'wide ranging from not very real to very real,..' I think, that ‘‘real’’ is used flexibly in ordinary English to mark a multitude of distinctions. Existent/nonExistent. Objective/subjective. Basic/derivative. I could actually go on here, there's maybe paradigm/deviant cases--a 'real man'. So I might object. I'm not interested in the shallow question of what exists. Let's get to the deep question of what is fundamental--what little is fundamental, shall we say. That, of course, being the the whole concrete cosmos, see, there's where I blast your Plato. There is only one fundamental entity.


In any case, not much doubt, that the ontological status of mathematical objects is perhaps the most important unsolved problem in the philosophy of mathematics. Can I offer, that there is no agreement on what the mathematical objects generally are. Thought provoking..?

I have sort of a theory. Begin with this, that numbers certainly do not belong to some transcendent Platonic realm. I'm inclined to refer to 'number' as a rule, or general rule. For me, this gets somewhat involved, maybe I'll leave it at that, except that it isn't really 'my' theory, I'm inclined to look closer here, at Kant.

[DragonFly]

The objects referred to by numbers exist, such as pebbles (that are being counted).

[owleye]

The objects referred to by numbers exist, such as pebbles (that are being counted).

I'm pretty sure numbers don't refer to objects such as pebbles; rather in the sense you are driving at they refer to their quantities, if numbers are (refer to) quantities. However, referring numbers to quantities carries implications that they are imposed by the mind onto objects and are not necessarily intrinsic to the objects themselves. In the abstract domain, which is what I thought the topic was about, numbers aren't quantities, despite their possible use as quantifiers in logic. They don't represent anything other than what their formal characteristics tell them they are. They are abstractions, freed of content. (I know, pretty dogmatic. I can be wrong and welcome criticism.)

James

[owleye]

I see it the other way around. Historically, "exist" was not reserved specifically for physical objects, and I see no reason why it should be. In fact it would make the debate over physicalism rather senseless (which perhaps you feel it is).

You are undoubtedly correct, and the vast majority of philosophers agree with you.

That is because history in philosophy is largely Aristotelian. Aristotle collapsed the four classes of metaphysics of Plato into one, so that only one reality remained. This has not changed in mainstream philosophy, which, naturally, is what is taught in school.

Well, I doubt this is the cause. But even if this is the cause, I shouldn't imagine that you would want to invent whole new meanings of the terms just to get around this influence. If you intend for 'existence' just one of its meanings, then we will all be able to understand you, if you can point out which one. Similarly for 'reality'. But if we have to understand you to mean something that is not currently understood as its meaning, then I suggest coming up with a different word entirely. The words we choose usually have some intention behind them but if you are unable to communicate that intention by their use, one that emphasizes it in contrast with something else that isn't intended, it would seem folly for the rest of us to keep on trying to figure it out.

James

[yadayada]

Nope, you got that all wrong. It isn't just my usage. What I am asserting is that
1) the word 'existence' is different than 'reality'
2) confusing existence, reality, being, and various uses of 'is' is a catastrophic philosophical blunder, no matter who the source.

Existents are *derived* from Aristotle's primary substances. Does the physical world exist? Of course. By definition, not by argument.

There are many realities, both possible and actual. Geometry, physical mathematical theories, movies, books, our private worlds among them. None of these actually exist.

Consider: Realities are continuous, wide ranging from not very real to very real, while existence is binary. Something either exists or it does not. The logics are different. To force some reality into existents, one would need to split it into dichotomies with the PNC, and the LEM, and Identity. Then categorical logic follows. (Another, independent example of this is Wittgenstein's Tractatus)