OK the SRH is gonna to need what I feared: a full theory of thinghood. My faith in Buddha's Enlightenment means that I already know that "object" does not exist in any fixed reality - this is the teaching of anatta.
The idea of a material object is a material mechanism to explain identity. Buddha says this is just an idea with no reality.
So we have the famous issue of Hesperos and Phospheros, respectively the morning and evening stars, that were thought in antiquity to be separate heavenly beings. Then a theory of orbiting planets showed that a single object Venus could explain the phenomena of Hesperos and Phospheros: when on the west of the sun Venus would rise before the sun (i.e. what we call morning) and when on the east of the sun Venus would set after the sun (what we call evening). Being inside the orbit of the Earth, Venus never follows the full trajectory of the Ecliptic, going around the Earth like the other wandering bodies. Simple. Case closed.
But just because we now have only one phenomenon why should this be any the less solid than the case of two phenomena? These kind of obvious question always troubled me as a teenager. Why is it obvious?
It is because in the case of two phenomena we have the opportunity to show that they are caused by a single object which shows that they are the "really" the same. We thus attribute "reality" to Venus as the object which lies behind the appearances of Hesperos and Phospheros.
Now Hesperos and Phospheros still exist. You can see them all the time. What has changed is our understanding of them. The morning star is still never the same phenomenon as the evening star because one is in the morning and one is in the evening, exactly as in times of old, but we now call them both Venus and imagine a single entity out there in the heavens instead of two. The point is we imagine.
Now protest the materialists. I will prove to you there is a single entity and we fly into space and orbit Venus - which indeed reveals itself as a single globe. But what is really happening is that the materialist is massing more and more evidence (and phenomena) to support his "idea". The point is that he can't show me his idea in raw form, or Venus as a material object uncloaked from all the phenomena. Seeing this in terms of light is easiest. I will always be looking at light which has bounced off and object, never at the actual object. Now my argument isn't quite right there, but neither is the materialists! The truth is actually beyond me at the moment... I discussed before the stream of cause and effect involved in seeing and that seeing "involves the whole stream" not the arriving of impulses at some homunculous who then sees (this is explaining seeing in terms of seeing). The brain as I argued all those years ago at school doesn't "see", because it is supposed to be the explanation of seeing! This is the SRH in action again.
Taking images as our metaphor, never-the-less, even in the case of the single Venus in the sky this is just an image of the "real "planet. Just as the disk we are orbiting in our space craft is just an ever changing image of the "real" planet beneath, in whose gravitational field we are grabbed.
This is the kantian problem of Noumenon - the object that lies behind all the phenomena. To recap: we believe in a noumenon because it unified all the different phenomena. We would have a real problem if every second we saw Venus orbiting to a new place in the sky we thought it was a new thing! But Buddha doesn't urge us down this path he urges us to stop thinking it is a thing at all and just accept the phenomenon as the "reality". It is upon this reality that we use language to group things and the rules of that are what we call "object". So we don't have a different name for Venus for every hour of the day, and we don't anymore have a different name for Venus when it is present in the morning and when it is present in the evening (tho I still like to think of it like this), we just call it Venus - the language has changed.
What the new language gives us the advantage of is making sense of that feature of this group of phenomena which must have interested the ancient astronomers that the morning and evening stars never occur in the same sky. A clue one would have thought for the new language rules for this event. Why have two names, when you can just have one and use it in the morning and in the evening like we do today: Venus is visible soon after sunset - where it was just called Phosperos before.
It is this contraction of the language which we understand as "suggesting" that there is just one thing there called Venus. But Venus is still a baggage word for an indefinite number of phenomena including gravity measurements, visible phenomena etc etc.
It is so convenient for the mind to invent a phantom entity which "joins" all these phenomena so that they are caused by the "same" thing that we like to think it is real. It is just the way our minds work. The reality is the phenomena only (which as we experience them we can't deny).
The irony here is that I have put together a great "theory" of my own to explain "behind the scenes" the operation of the mind - this must not be my intention! It is simply to undo the conception that there are "real" things behind the scenes beyond our own mental workings.
So to Frege. We may have two names for the same thing. "The cloaked man" is a name for someone who may also be called Peter. When we find that Peter is the cloaked man we are linking phenomena together. It is customary to take Peter as the name of the "person" and we tend to think of a "person called Peter" at the name of teh object which we called "the cloaked man". But why do we prefer that name? It is I presume because we like a face to our people since this is the biological way of recognising people. But we would dump Peter and keep the name "the cloaked man" for our hypothetical "thing". Maybe it turns out in the future that Peter is really Paula in disguise and so it can go on forever with our minds endlessly trying to uncover a "real" identity. Infact any of these will do - our point is to separate Peter/Paula/"The Clocked Man" from "other" people and that is a central feature of our social life. But as many other threads illustrate this is not a "reality".
Now based on this discussion I maintain that a "thing" cannot have a relationship with itself because there is only name and no thing. We can say that two names (Peter and Paula) name the same person but this is just to say that A = X amd B = X so A = B. X is still a name.
So in predicate logic where we say that
(Ex) x is a person & x is Peter
we are not actually creating an entity x, we are simply saying that x is a new name for the descriptions "a person" and "Peter" and so it says that these two descriptions are correct for x.
(Ex) x is a rabbit and x is horned (interesting Buddha used 'hare' while English logicians use 'rabbit')
x is never a thing. Even when we say "The horned rabbit hopped." we are not creating an ontology where there is a horned rabbit, we are simply saying that there is another name for a rabbit which also has a horn (call it x in Predicate logic).
Think this sorts this problem out pretty much.
p.s. rabbits never have horns (tho they can have tusks I think).
===
Doesn't this solve a big problem: does the number 1 exist? In English "one" can be an adjective (predicate), a noun or a pronoun.
(Ex) x is a horse and x is one i.e. there exists a horse
(Ex) x is a horse and x is five i.e. there exist 5 horses!
seems a bit odd but actually I think it is correct. Doesn't this take the existential nature of x away? The suggestion that "x" is in some way "existing" is unnecessary.
In ancient times the separation between existence and essence was noted. We may know and discuss the essence of a unicorn (a horse with a horn) but to say whether such a thing "really" exists is an entirely separate issue. What was made clear was that "existence" is not an adjective or predicate that one can say of something; if we allow this then what is it that takes the predicate of existence? Yet in reality existence becomes "essentialised" so that what exists depends upon how you describe things. A page of writing is a single thing, unless you wish to describe the letter graphemes (essence) in which case there are many existing things here. Existence and essence is an indecisive distinction in this view, not the absolute ontological observation that was intended*! So in the examples immediately above it should be of no supprise that "x" has nothing to do with existence.
*Hard Existence - by which I mean solid absolute existence - is a form of fascism. What! Politicising ontology? Yes! Consider: when we ask, what "exists", we are saying what is "real" or "true" and what is worthless and to be ignored. Thus to obtain recognition of existing for what we believe is to have the power to reject other view points. Thus (at root) the argument about whether God exists - it is little to do with ontology really.
What then of "one" as a noun? This is the actual question and in the normal view of nouns we are led to believe that something real exists... but then we realise that we have never met the number one (except in Sesame Street maybe) nor will we meet the number One. So does it exist?.. and weponder on at least I did. In the current view, it doesn't exist because nothing exists - exist is just an idea that we project because of the feature of language for using the same word (name) to refer to different phenomena.
The expression:
"1+1"
we realise when we do maths is another name for "2". And "2" is another name for "1+1+1-1". Here then I agree completely with the development of logical syntax to seeing logic as simply the manipulation of symbols which has led us to computers (which do this). Consistency then is teh feature that we like about good languages which means that we only use certain names in certain situations and this consitency is what leads us to believe that something "solid" exists. Why do we always use the name Bonny for our pet dog, who is the dog at home, who is only ever one dog, and who always looks similar? It is because of consistency in our use of language, not down to some imaginery invariant entity that lies behind the experience of Bonny that ensures we use the name right! A child learning the language makes lots of "mistakes"; if Bonny was a real entity why does the child make mistakes? Doesn't the absolute nature of Bonny ensure that the child always knows it is Bonny?
So maths is better understood as a consistent game and our ability to play the game and adhere to rules is what gives things like "one" the apparent feeling of reality and solid-existence.
How interesting this ontological theory links both The One (the quest for the predestined sexual/soul partner) and the theory of meaning and society previously presented.
So what exists then; don't phenomena exist? When a sentence refers to itself isn't that a solid existence:
"This sentence exists"
If it doesn't exist how can it be asserting something about itself? ("This sentence doesn't exist" is a contradiction, which means the one above must be a tautology).
I think the point here is that "this sentence" can be printed a million times. Each time this page is rendered in a browser that sentence will be rendered completely new. So which sentence is it referring to? It is actually referring dynamically to the presentation of the sentence in each moment, and time it is read - and these are in fact numerous phenomena constantly being recreated every time it is read or thought about. Phenomena "exist" in time, and are endlessly evolving and changing. It is the mind armed with language only which tried to order all this endless flux and apply a finite language in what is an infinite space of eventualities - this can only be done with "dogma" and the forcing of situations into linguistic constructs. This I guess is why Buddha amongst so many urge us to step outside language and see the world as it "is" forever changing, fluid and unstructured.
===
A few days to sink in. The suggestion here (and it seems to make sense) is that Mathematics is at root exactly the same as Natural Language. Learning maths then should be the same as learning any other language. Ideas of innate language grammar in humans (Chomsky et al.) thus apply to innate grammar in maths. The questions of how words come to represent "things" are exactly the same questions as how Numerals/Variables/Unknowns etc come to represent numbers. If numbers seem abstract they should be no more abstract than "things"... because neither actually exist. There is a non-linguistic realm but it is the realm only of ephemeral phenomena, of sensory experience. Numbers and Things are things of the mind the result of grammars and "mental" rules (where "mental" is not a process lying behind the appearances, but infront of them which is why we human see them so clearly!!). The interesting question that remains is why these two very distinct systems of rules: maths and language? There are other systems of rules that we learn: morality, customs, culture, sports, politics, legality... these one might group as the third language of Society. The same as above applies to this language also.
So we have the triumvirate of Language, Maths and Society as the governing groups of human consciousness. They are isomorphic and hide nothing from each other that the others don't know. Who is good at language thus has the skills to be good at maths thus has the skills to be good at society... except this isn't true... and what of music? And, if these divisions are true upon what basis are these great divisions based? Why does my mother find language and society easy while she finds maths hard, and I find maths fairly easy and the others I don't leap at? What is the root of these distinctions? By SRH already know we need look for something new outside the widely used theory of rules spread deep in this blog...
=== update 27/11/10
In agreement with Derrida I need to separate spoken word from written word. There are two separate structures here. The reason for the split is that historically marks on clay tablets were the invention of accountants. The first records of writing are simple inventory lists and the first records of numbers are the same (lists of units). It seems that the evolution of written languages (both maths and natural language) come from the requirements of recording quantities and qualities for the purposes of ownership and trade (emphasis on recording). Clearly maths is not a spoken language: it depends upon the recording of equalities and the formulaic transformation of these formulii - this is what formal systems capture and computers are so good at (computers appearing in this analysis as simply dynamic clay tablets). It seems odd however to imagine that spoken language evolved in tandem with written language. Spoken language must have been a fully fledged event long before the relatively recent clay tablets. The problem is that "history" doesn't record spoken sound (directly) so ironically it is silent! Spoken sound gets recorded as a constantly evolving stream - the archeology of what was said yesterday is deeply hidden under what we say today. There is much poetic stuff to say here but time is short. Derrida tries to bring philosophical attention to the written word but I disagree here: it is the spoken word which rule the mind just as maths is not a language for the mind but for the paper. Geometry on the other hand is a language for the mind which happily can be expressed in algebra for the paper. They need to be separated and it is interesting how the difference lies in the nature of the human activity of trade and accounting.
A search for happiness in poverty. Happiness with personal loss, and a challenge to the wisdom of economic growth and environmental exploitation.
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