(first part aimed at Paul Geddes)
In order to deduce mathematics; one first has to learn numbers, so your relation would fundamentally have to be based on how a person learned numbers? as how are we first taught numbers?..by relating them to something are we not? e.g. in terms of apples or cows and further more basic fractions are taught sometimes using things like pies.
so which ever way anyone learns any mathematics, there is always relation involved, of any kind.
so, because our mathematics is fundamentally based on a relational education structure we cannot say that mathematics does not have to relate to the outside world.
my point is (as i know I am not the most coherent arguer) that we can think of mathematics/equations without a relation, but only after we have initially learned mathematics which is fundamentally relational. so in this instance (mathematics) is not the best example of 'consciousness is not necessarily relational.'
the problem i think is - that as humans we have experience, and as such we learn things from a very young age, and sub consciously we carry this knowledge through life until we understand our knowledge, so one might argue that every part of our consciousness could be relational to something we have experienced previously. The only thing i could think of that does not require relation or previous knowledge is actually sex, as this is one of the most basic human things - to procreate. nowadays we have education to tell us what to do, but what would happen is that education was not there? e.g. early human history, how did early humans find out about sex? i think in this instance, it is one of the few things that our consciousness 'Just knows' because of the fact that consciousness just 'is,' and natural human identities like this do not require relation to know how something is or how it is done. What do you think about this paul?
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the problem i am having is that.. 'Consciousness is'...so it has 'being,' consciousness, therefore is the fundamental 'groundstate' of all being and all knowing,
if this is the case how can consciousness ever be objectified? as surely consciousness is always the subject? therefore surely consciousness is actually unitary?
has anyone any thoughts on this?
Terence Nabbs
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Tez. I think you have provided a very good example of the initial point I made to Paul. The point is that if our consciosness of mathematics is abstract then we would have mathematical ability at birth. I guess we do not see many babies with the mental acuity to think complex mathematical equations. If we think of what we do when we cognize mathematics, even when we imagine mathematical concepts, consciousness is itself orientated beyond itself. E.g if we we are doing cordinate geometry we have to imagine lines and numbered coordinates. Consciousness does not get these from either experience or whether they are inbuilt. Instead, consciousness itself automatically relates to something other than itself, thus demonstrating the phenomenological point.
ReplyDeleteI think that we should more clearly mark the difference between mathematical ability and and demonstrating use of mathematical language because I think the two can be confusing.
ReplyDelete1. Mathematical ability is something you have to posses to tackle even the simplest mathematical problems.
2. Demonstrating this ability is found in experience.
In much the same way, we are all conscious but we need to refer to something else (ie. a computer) to demonstrate the ways in which we are conscious.
I think what I mean to say is that explaining, understanding and knowing are relational but being is not. I'm not sure if it's coming across but I don't particularly like Merleau-Ponty.
I think this idea that mathematics has never been 'pure, abstract mathematics' and has always held physical objects (at least when learning the basics) in mind when learning of numbers is a pretty good idea and some good historical evidence can be used to advance this argument.
ReplyDeleteFor instance the ancient Sumerians had a sexagesimal number system based on the numbers 12 and 60. They thought about numbers in this manner as they used the knuckles of the fingers of one hand to count with i.e. the four fingers of a hand have three knuckles each therefore counting up to twelve whereas we, because we learn counting initially using all the digits of both our hands, have use the decimal system with the base number being ten.
This gave the Sumerians a much different understanding of mathematics than we have now and we have inherited some of this number system in our time-scales whihc is why there are 60 minutes in an hour and not 10 or 100 etc.
The relational structure of number to physical objects is quite clear in this example and shows the different paths an understanding of the same discipline can take when abstract-physical relations differ between the thought-systems.
To take this idea further (at the risk of it falling apart) is there not something implicitly Foucauldian in this phenomenological argument in which the nature of a person's understanding of reality is tied directly to certain sets of discourses or, to say it differently, the power/knowledge structure of a given society (power as in puissance not pouvoir)and, as we have seen in the differences between the sexagesimal system and our decimal system, the nature of thought (or at least the way people think) differs when understood through different certain sets of relations?
ReplyDeleteIf phenomenology does uphold this, then does it not also have to take on board all of the epistemological baggage that Foucault himself spoke of?
I really enjoyed Dom's example.
ReplyDeleteThe discourse of numbers is outside of 'tabula rosa', therefore maths is relational and applied within the power structure.
Too add something, as humans we are born with the ability to learn about maths; in the same sense Chomsky uses when learning a language. This could go some way in explaining how maths, simlar to words, seems intuitive.
I have been reading through and it seems i've started a massive debate. Going through all the replies a question keeps popping into my head. If there was only my mind in existence and nothing else (an extreme Descartes) then would the concept of mathematics still exist? If so then it is not relational to a 'world' anymore.
ReplyDeleteThen I would say that the concept of 'amount' would be foreign to a solipsistic mind
ReplyDeleteWell...if it's possible for a mind to be conscious of its own consciousness then that could constitute a thing to be conscious off and it could maybe comprehend amount i.e. if that mind was capable of a range of emotions then it would potentially be able to grasp the concept of amount, but I'm just not sure how it would express it.
ReplyDeleteWell my me, haven't we had the busy weekend. Good to see things up and running here!
ReplyDelete@ Everybody. One question I would add, tying Dominic and Paul's question together is this, if consciousness is only self-referential then how does it at all relate to anything. What Derrida famously called 'auto-affection'i.e. a consciousness only affecting itself is an impossibility from its inception since it would not, by definition refer beyond itself, and would thus remain utterly solipsistic.
@ Dom. I think that M-P's importance on Foucault is important. I guess the basic phenomenological point with mathematics is that at base it will require an embodied being. The extent to which this is discursive is up for grabs. So if we took some of the most traditional mathematical notions such as geometry, it would mean that say the conception of triangles requres an embodied perceiver and thus does not exist prior to acquisition. THings like algebra and advanced Reimennian mathematics requres a body in time so as to utilse things like succession, contiguity, differential ratios, next. So rather than being eternal and immune from transformation mathematics is wholly perceptual in the sense that MP understands it. {We will talk about a counterpoint to this a lot more when we get to Badiou!!}
@Paul. Well it is certainly thinkable! Since you thought it. But could you perhaps fill out the contours of what this type of existence would feel like and how it could be conceptualised. It could be a good thought experiment to tease this out a little more.
The problem with the radically sceptical argument is that is based in doubt. There is nothing to cling on to. Even if there isn't anything other than your mind (which is unknowable) it appears that there are other things also. I think this links in to what Michelangelo was saying. We are only capable of dealing with the world in one way (whether it is a solipsistic one or not) and it is an innate talent. This ability is much like the mathematical one I was talking about earlier and precedes the necessity to show that we are dealing with the world.
ReplyDelete@Patrick. I am going to stick my neck out here and say; If we listen to Plato, we already 'know' everything at birth it is just a matter or 'recalling' our already existing 'perfect knowledge,' if this is the case, nothing we know or learn could be said to be relational, as we already know it, thus this must be true for consciousness, as we do not have to be relational, in anything, in order to understand.
ReplyDeleteprobably not a popular idea :)
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@everyone
Consciousness must be able to extend beyond itself because if not, we would not have language, we would not be in a position to interact with anyone. The variables surrounding how people learn are vast and unending, this just shows that consciousness 'is' consciousness of something, no matter where you are in the world does it not? the nature of a person's understanding of reality is tied directly to whatever variables are put upon a person from their birth.
F H Bradley's impossibility of anaysis, i think would be a good read here as he concludes that that qualities and relations depend on each other and yet are incompatible with each other.
if this is the case we could say that, qualities and relations are impossible, and the world only exists of things and their qualities.
Furthermore we could also take into account the ‘unreality of relational structures’ which i beleive was a 'version' of the ‘Eleatic paradoxes’ of Parmenides and Zeno. “relations are not real in themselves, objects connected by relations are ‘illusionary’ and you need a certain abstraction to have two objects in relation. Without this process, you may as well only have one object because there is nothing to connect the two objects in question.
my point is,
If we say that Consciousness 'is'... it is in the world and has being, in order to understand anything there must be some kind of relational structure, However Consciousness is not only self-referential, but is completely extended all of the time, these two are in fact synonymous, it is a case of - things and their qualities, and things in my 'self referential' mind, they are synonymous and incompatible.
(I hope I have made some sense in my writing)
@Rob..I suppose this would mean that the sceptical arguement or the solipstic argument is worldless by definition and from its inception. For Husserl, consiousness is of the world, for Heidegger being-in-the-world, for MP embodied being.
ReplyDelete@Tez...If we are Platonist, at least in the vulgar sense this would be the case. The slave boy in the Meno was taught Pythagores theorem by demonstration. Does this make sense though? We don't know how to walk at birth, but we might know how to swim. This would at least suggest that somethings are learnt and some are implicit. This however, is beside the point for Husserl for example. Irrespective of ones experience or cognitive faculties, (Husserl would have abjured either of these two options), saying that consiousness is always indexing itself to the world. I can't really go into in detail here as I don't have the space but you should look up his work on what is called the noetic-noematic correlate. The rough idea is that the mental stream of perception and consiosness in all of its phases is dynamically reaching to the world. The distinction between rationalism and empiricism falls down since we can't experience qualities or properties in themselves, and we can't experience or reflect on prior intellectual structures except by positing. This is not to say that they don't exist but if they are there they are not pure and immobile but active, dynamic and directed tot the world.
ReplyDelete@TEZ Had anuther quick read through and would first like to disagree with Tez when he argues that consciousness is in the world. Surely we can argue that consciousness is subjective in the respective that my consciousness is my own and no one elses. I can BE conscious of someone else, but cannot SHARE their consciousness.
ReplyDelete@Everyone. The notion that i placed where we can imagine that my mind and nothing else exists and be expressed by imagining complete darkness and there is only your mind. You have no body so no sense of boundaries would be possible. The point that i was trying to express was that as i am thinking in the darkness and am conscious of it, i would therefore be able to comprehend the possibility of anutha one of my self even if they did or did not exist. Therefore I would be able to comprehend others (therefore more than 1) but would maybe strugle to give a word to it, but the result would be the same. I have done maths without relating to the world, but have related it to only my own consciousness.
Well for Merleau-Ponty a mind wouldn't be able to think on its own as it would not be conscious of anything, it wouldn't have anything to think about. The question of mathematics wouldn't arise in a lonely mind as it would have nothing to attach the idea of number or whatever to, there would just be nothing.
ReplyDeleteI said earlier that maths could maybe arise in a solipsistic mind only if it could experience changes of mood as that would be an example of change and the mind would be able to understand that there are different things and that it would be possible to quantify those different things, however I don't think that a solipsistic mind could experience changes of mood as there would be nothing to change the mind's mood: as Patrick said, auto-affection is an impossibility as there would be nothing to bring about an affect upon the mind, and the mind wouldn't be able to bring about an affect upon itself as it wouldn't be conscious, there would be nothing to be conscious of.
Maybe it's a pretty big claim I'm about to make (I'm not sure if it's really big or obvious...maybe that's just philosophy...)but a solipsistic mind would by its very nature never reach the mirror stage so therefore it wouldn't even be able to affect itself, there's no red dots to pick at in a solipsistic mind.
Change and movement is necessary for thought as it gives something to bear thought upon, and in this solipsistic mind there would be no change or movement and therefore it wouldn't think or be conscious, let alone self-conscious and able to ponder philosophically about other minds other than itself.
Therefore maths (or any thought) would be an impossibility. If you're trying to express that maths is apriori and therefore doesn't need any external input to calculate things then I understand what you're saying, but I think that just because something's apriori doesn't mean that it could be thought out of nothing by a solipsistic mind, it is only via the physical world of embodied thought that we are able to think and to bear thought upon things, so a single mind couldn't think and therefore comprehend, calculate and reason apriori 'facts', or whatever you want to call them.
And this says nothing of the idea that maybe it's only our single body which provides us any coherence in what we would understand as the 'I' and if we didn't have a body (or understand that we have a body) we would not be able to understand that these different experiences/scenarios/affects/feelings have any sort of common reference point (ourselves).
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ReplyDeleteOh My goodness!!
ReplyDeleteThis argument is very complex, I definitely started reading and had to get myself a stiff brew.
I want to ask one thing...what if nothing can be quantifiable at all? What happens if we don't have ten sheep, we just have a collection of ONE (not shouting) sheep. What happens if we didn't have ten pieces of chocolate but ONE collection of chocolate?
This is a thought used by an aborigini tribe, mainly as they believe nothing can ever be owned. Anything they have is not theirs, it is the Earths and they have no perception of amount or mass, everything is one.
There was a survey that was conducted and they could not do simple sums, as to them one+one equalled a much larger one. This in our everyday life would obviously not function but is this not because we live in such a materialistic world? How can we relate this to people who to not quantify things because wealth and belonging are things that they cannot relate to, nor do they care for? I think as we are educated we have been brought up with this knowledge. I think that even someone that had been locked away all their life could understand this, or learn to, but someone who has been brought up understanding values as one and no-one owns anything could not. What do you all think?