EVERYTHING we do here is dependent on language; this is the sine qua non of all philosophy.
In the specific context of a site dedicated to scientific research, what we can offer as philosophers is an awareness of the rôle of language (and of the intuitive assumptions dependent on or underlying language use) in any interpretation of theory.
THis is so evident that it often goes wothout saying - but then again, philosophy is the investigation of what 'goes without saying' ;-)
mm aren't you afraid of getting mired in the 'linguistic turn' in philosophising? people over here at Bristol want to get past that era
Haris - as far as I'm concerned, it's the people at Bristol who are stuck in the past - I'm talking about a neo-linguistic turn. My comments are 'radical', in the sense that we CAN'T do philosophy without using language - and if the good folk at Bristol think they can, I'm all ears (or eyes, or nose, or whatever medium they're using).
As you know, the analytic approach to philosophy presupposes a certain degree of sophistication and skill in logic - I'm just remarking that we should have a similar sophistication & skill in our understanding of language in general (cf. the remarks on Sider in my reply to Charles).
Truth and falsehood are of propositions. Any proposition may be represented as a finite sequence of symbols called 'letters' drawn from a finite set called an 'alphabet.' As a consequence it follows that it is possible to list all propositions. One would simply list them in alphabetical order.
The 'real numbers' may be represented as infinite sequences of symbols called 'digits.' It is impossible to order the real numbers to form a list.
Mathematicians say that the propositions are 'countably infinite' --- meaning that they can be arranged in a list --- while the real numbers are 'uncountably infinite' --- they can not be arranged in any such list.
Physics, of course, appears to measure many quantities in terms of real numbers. Time and space, clearly seem to be measured by real numbers.
Thus it would appear that there are *** not enough *** propositions in a set-theoretical sense to describe the world of physics. Thus it would seem that, *** strictly speaking, *** there can be no truth or falsehood regarding some aspects of the physical world. Reality just is what it is. Man's knowing is therefore inherently limited to an approximation of reality.
This conclusion has been rather troubling to some. It is not troubling to me. It merely suggests to me that there may be some vision of reality that transcends and encompasses propositional truth. This vision is sometimes represented symbolically in the owl who sees what is before it without speaking.
"I do not say that John or Jonathan, that this generation or the next, will realize all this; but such is the character of that morrow which mere lapse of time can never make to dawn. The light which puts out our eyes is darkness to us. Only that day dawns to which we are awake. There is more day to dawn. The sun is but a morning star." ~ *Walden* / Henry David Thoreau
dear Bill, i have a little question for you. in the two-line paragraph about physics, you seem to be implying that measurements are propositions whose 'letters' are numbers. but this contradicts your first paragraph. could you please elaborate a bit on this?
dear david, isn't that what Bill means by 'countably infinite' though? that they are infinite, but in principle you can make a list of them?
You're quite right - I misread Bill. The offending message has been taken away and shot.
Apologies to all.
I am a bit confused by the previous posts. I seem to be missing something. Perhaps that is what has been "taken away and shot?"
My point is that one may distinguish between simple vision and discursive reason. As I indicated, above, there are some who are troubled by the limitations of discursive reason. I have in mind those who would imagine the world to be merely a set of 'mutually compossible propositions.'
I first discovered this in reading *A New Cosmological Argument* by Richard M. Gale and Alexander R. Pruss. See http://bearspace.baylor.edu/Alexander_Pruss/www/papers/NewCosmo.html. To me the whole concept seemed absurd. The world I live in is clearly nothing like a set of propositions, but of real objects interacting with each other.
The whole argument collapses upon itself if one can show that there is anything that would necessarily fall outside the bounds of mathematical logic. Certainly, if the world is in any sense measured by real numbers, it can not be a set of propositions. Such a world may be *** approximated *** mathematically by a set of propositions. But it can never *** be *** such a set. QED.
dear Bill, i'm confused. is all knowledge propositional? is there not knowledge which is non-propositional, like for example knowledge of face-recognition? or of walking? and i don't think that anybody has argued that the world is a set of propositions, not even Professor Ladyman and the structuralists hold such a view, to the best of my knowledge. what do you think?
HS:
Clearly truth and falsehood primarily refer to propositions. A proposition is either true or false --- meaningless statements being understood to be false. So your question seems to be whether we can properly *** know *** something which is not in fact *** true. ***
I would think we must say any such use of the term is *** strictly speaking *** metaphorical in nature.
Thus, when we speak of a man 'knowing his wife' we are speaking metaphorically. The same would be true of the examples you gave.
Aristotle has been interpreted to mean that one can only *** know *** abstract propositions. Thus concrete facts are not knowledge, but experience. So if one follows Aristotle one would not accept experience as knowledge --- even if it is expressed propositionally. Before one can know a thing the *** understanding *** must abstract its first principles from sensory phantasms. Those first principles, and not the sensory phantasms, then are the basis for *** knowledge. ***
Being a pragmatist at heart, I'm not completely satisfied with that interpretation. But being a realist, I think we certainly should distinguish propositional knowledge from simple vision.
So saying, I do agree with David Hirst... "EVERYTHING we do here is dependent on language..." Some of what we do here, however, is *** metaphor. ***
Yes, but didn't you write of it in words, joined together to form sentences?
I understand.
What we do here... Is it meditation? Are we all sitting in *** zazen? *** Or are we writing? Are we, in fact, using language?
Bill - I've started writing a few comments on Pruss (with whom I've had run-ins in the past): I'll try and get 'em finished. It's about time for a discussion on possible worlds...
Why not? Anyone, in some world I already have...
There's too much bloody nonsense of the Lewis kind going on; SOMEONE's got to take a stand
DH:
Thanks!!
My only interest in what Dr. Pruss had to say is regarding the question of whether it makes any sense to imagine that the world is some sort of set of propositions. I have no particular interest in the Ontological Argument. Even Scholastic theology rejected it.
DH: "There's too much bloody nonsense of the Lewis kind going on; SOMEONE's got to take a stand"
It is nonsense. But there is no reason to lose sleep over it.
Who's losing sleep?
As to 'why' he thinks the world is a set of propositions, that depends on the Possible World explanation :
1. A PW is a maximal, compossible conjunction of abstract propositions.
2. The actual world is a possible world
3. Therefore, the actual world is a a maximal, compossible conjunction of abstract propositions
His error is, I think, to be found in his understanding of (2)
I believe there are many errors in his thought but do not wish to discuss him in his absence. Perhaps I could invite him to join the site, but perhaps others would not want that.
In any event it is the idea that I object to. I absolutely object to the idea that this little world I happen to exist in is anything like a set of propositions. That, I think, is the primary mistake.
I see the world somewhat the way Bernard d'Espagnat has described it. We are like the men in Socrates' Myth of the Cave. I know it may offend certain *** scientists *** out there, but our understanding of the world is but a shadow of the world as it really is.
Perhaps we need *** something like zazen *** to remind us of who we really are?
HS: "please don't start a discussion on possible worlds and modality"
Indeed, why not? Quantum Mechanics has taken up the battle cry so we must as well.
I'd rather go with Haldane (I believe) - "the world is stranger than we CAN imagine"
QM has many interpretations.
In my humble opinion, the world may constantly split into many worlds. But their waves quickly collapse back into one.
DH: "Hmmm. As always, the temporal element is fundamental"
Hmmm. I am sure you are right. But what do it mean?
Or, to be more precise, how is it that the temporal element is fundamental?
"the world may constantly split into many worlds. But their waves quickly collapse back into one."
This presupposes thhat time 'flows' in a particular 'direction'
dear bill, what do you mean by 'their waves quickly collapse back into one'? what waves are you talking about? you mean the wave-function of the universes?
DH: "This presupposes that time 'flows' in a particular 'direction'"
Not really. Creation and destruction are inverse operations. Thus one could reverse the two and still come up with the same picture. That sort of thing happens in Feynman diagrams. A particle flowing backward in time appears to be destroyed before it is created. But if you reverse the terminology you end up with the same diagram. The only difference is in the description of what you see.
The question of the 'arrow of time' really only comes up when you start looking at biological systems. We *** know *** that birth precedes death. We know that because we experience life. We know that actions have purposes and that purpose refers to the future; experience refers to the past.
Do subatomic particles have purpose? I really don't know. In some sense I think they do. But I doubt they understand purpose in the same terms we understand it.
HS: "could you please explain a bit the physics of that?"
No. I am not a physicist. I am a simple computer jockey. As such, I have no equations to offer.
Thus I wrote "In my humble opinion...."
Bill - if we leave to physicists the task of relating theory to our intuitions & experience of the world, you end up with "A Brief History of Time" and the Copenhagen Interpretation... I think we really do have a duty to intervene.
what's so bad about the brief history of time?
dear bill, i wasn't looking for equations, since i wouldn't understand them. i was just looking for an elucidation of the terms used, to be able to comment on you idea.
I've never had much interest in Hawking. Half of the interest in him is, of course, is due to his ALS and half to his thoughts.
I've never read the book, so I can not comment on it.
I can only comment on my 'intuitions & experience of the world.'
The 'dalek voice' can ONLY be an affectation - and why on Earth did he accept a speech synthesiser with an American accent? Rather a shame in a Lucasian Professor of Mathematics...
mm, true, i'd never thought of the implications of Hawking's chosen accent on national pride :)
DH: "The 'dalek voice' can ONLY be an affectation - and why on Earth did he accept a speech synthesiser with an American accent? Rather a shame in a Lucasian Professor of Mathematics..."
It is certainly true that voice synthesizers have improved over the years. He ought to upgrade. But I guess he has grown attached to it.
Skaro? (by the way guys, should we throw in some new topic? most topics have dissolved by now)
You really DON'T know your classics - the Daleks come from Skaro (as in Doctor Who?)
i know doctor who, but in the last series i watched there was no mention of this bit of classical commonly held knowledge :)
Bill: "I guess he has grown attached to it".
My God, he IS Davros!
(that's enough of the elitist nerdery from Mr Hirst. Shall we get back to propositioning Sophie?)
propositioning Sophie does seem like a dirty remark, though i can't pinpoint the dirtyness. should we start a new thread? what would be a good thing to argue about?
should we discuss paradoxes of rationality or logic? (dunno dutch books, liar paradox, whatever)
hmmm - about 1.2s if timed from the examples given in the TV show. I'd say that each syllable corresponds to a 'time' (probably a matter of processing semi-discreet phonemic segments). There's probably a degree of 'temporal blurring' between the segments when the utterance is heard...
guys please let's get serious, and let us not start with time again!!
Name one philosophical problem that isn't impacted by time and space...
The recognition of two, rather than one, of some thing probably requires spatiotemporal separation and certainly requires a certain way of individuating regions of spacetime.
The term "transcendental" has a number of senses - which sense did you have in mind?
DH: "The recognition of two, rather than one, of some thing probably requires spatiotemporal separation and certainly requires a certain way of individuating regions of spacetime."
Two things, neither of which is bound by space or time, are not separated by space or time.
DH: "The term "transcendental" has a number of senses - which sense did you have in mind?"
So you pick transcendental?
I'm sorry, could you give me an example of something that is 'not bounded by space and time'?
If you tell me what you understand by 'transcendental', I'm game. Are we talking Kant, phenomenology, or Sartre?
"Quantity and the transcendental --- that's two... take your pick"...
Ahhh: the Problem of The Many.
...Time and Space, transcendance, etc...I would believe that even Philosophy is humbled in the ultimate question of interpreting 'Reality'.
NvR: "I would believe that even Philosophy is humbled in the ultimate question of interpreting 'Reality'."
It seems to me that Haris is humbled by your presence...
DH: "I'm sorry, could you give me an example of something that is 'not bounded by space and time'?"
Of course you are. But we need not go into personal matters...
Space is not 'bounded' by time. Mathematics is not 'bounded' by either space or time.
"Space is not bounded by time"
I find this rather puzzling. Is it some kind of neo-Newtonian account? ;-)
I see you're a realist about mathematics. If one holds that mathematics depends on *doing mathematics*, then the temporal element is present in the process of 'doing'.
On the other hand, we could put the question another way: what is the status of atemporal propositions, such as "2 + 2 = 4"?
We are all humble before the Divine Beauty of Aphrodite...
Doing mathematics is not mathematics, but is a sort of doing. Scientists use mathematical constructs to describe objects that seem to have existed long before anyone was doing mathematics. For example, we are told that the universe is billions of years old. I see no reason to doubt the validity of such numerical techniques merely because they refer to things which are understood to have existed before any mathematician was around to validate them.
C. S. Peirce in his essay, ***On a New List of Categories*** wrote...
"The terms 'prescision' and 'abstraction,' which were formerly applied to every kind of separation, are now limited, not merely to mental separation, but to that which arises from attention to one element and neglect of the other. Exclusive attention consists in a definite conception or supposition of one part of an object, without any supposition of the other. Abstraction or prescision ought to be carefully distinguished from two other modes of mental separation, which may be termed discrimination and dissociation. Discrimination has to do merely with the senses of terms, and only draws a distinction in meaning. Dissociation is that separation which, in the absence of a constant association, is permitted by the law of association of images. It is the consciousness of one thing, without the necessary simultaneous consciousness of the other. Abstraction or prescision, therefore, supposes a greater separation than discrimination, but a less separation than dissociation. Thus I can discriminate red from blue, space from color, and color from space, but not red from color. I can prescind red from blue, and space from color (as is manifest from the fact that I actually believe there is an uncolored space between my face and the wall); but I cannot prescind color from space, nor red from color. I can dissociate red from blue, but not space from color, color from space, nor red from color."
I think that in general all affections are located somewhere. I can not imagine red or hot or hard or painful without imagining some spacial context for the affection. On the other hand, I can imagine empty space without any affective content.
I find also that I can not imagine time except in the context of some affection --- and therefore in the context of space. On the other hand, I can imagine affection without any temporal context. For example, I can imagine an unchanging red sphere.
Time therefore seems to be 'bound' to affection and to space in the sense that it always has both an affective and a spacial context. Yet it is far from clear to me that space is necessarily 'bound' to affection or time in quite the same way.
Is that what is meant by a "neo-Newtonian account?" If so, then I am guilty.
I believe that there are six 'categories:' quantity, space, affection, time, action and material form. In addition, there are transcendentals which can not be defined in terms of the categories --- for example, the word ***category*** can not be defined in any of the six categories, since it applies to all six of them.
I have in the previous postings explained what I mean in regard to quantity, space, affection and time. The last two categories deserve special consideration. Just as I can not imagine space without quantity or affection without space, or time without affection, I can not imagine action without time.
Material form refers to that which persists in so far as it persists. Action refers to that which is transient in so far as it is transient. Thus there is a degree of opposition between the two concepts.
Material forms are, of course, 'substances' in the sense that Aristotle used the term. I do not, however, simply equate the two terms. For I do not claim to know precisely what is substance. Newton, of course, held that space and time were absolute. As such, they would seem to be substances. On the other hand there are those who view Einstein's idea of space and time as substance --- space and time give rise to other phenomena through the curvature which they exhibit.
I prefer the term material form to substance simply because it sidesteps such issues. There is another reason I like the term... it emphasizes the distinction between matter and form. Believing, as I do, in what I call 'Hierarchical Hylomorphism' I find the term most pleasing.
I am, indeed a realist. Bernard d'Espagnat, winner of the 2009 Templeton Prize sees Quantum Mechanics in terms of a 'veiled reality.' Like the men in Socrates' 'Myth of the Cave' we see the world only through shadows. Personally I do not doubt that the shadows do represent --- no matter how imperfectly --- the world in which I live.
It seems to me that --- in evolutionary terms --- the senses have survival value for us only to the extent that they tell us about the way things really are. Philosophical theories which deny that reality seem difficult to justify.
Many philosophers have argued that relative terms such as father and son or half and double should be placed in a category by themselves.
I would identify Sophroniscus' son with Socrates, a material form. The fact that ***son*** is relative does not change the fact that son refers to a material form.
Since relative terms exist in each of the six 'categories' I interpret relation as a transcendental concept.
Many philosophers have argued that qualification ought to be a separate category. I do not see it that way. It seems to me that things are qualified precisely in terms of the six categories I have named --- or else in some transcendental sense.
For example, 'fast' and 'slow' qualify actions. They do not qualify quantity, space, affection, time or material form except as metaphors. Thus we might say that a cheetah is fast, meaning that it runs quickly. 'Fast' and 'slow' are not actions, but they qualify action and are ***attached*** in some sense to that one category.
In a similar way, 'intense' qualifies affection.
Many philosophers have argued that passion should be a separate category. I would simply see it as the flip side of action. Cain killed Abel. Abel was killed by Cain. The two are logically equivalent ways of saying the same thing.
Many philosophers place state and position in separate categories. Unfortunately there seems to be no good definition of the terms. Aristotle gave examples of what he meant by the terms. He did not explain what he meant beyond those examples.
What we know of them is that they refer to verb forms. Unlike verbs which express action, they express states of rest. Position refers to such things as 'standing' and 'sitting.' Thus they denote states of rest following the actions, to stand and to sit. State refers to such things as 'shod' and 'armed.' Those are states of rest following passions. Thus the shoe is put on the foot, rendering it shod. The armor is put on the man rendering him armed.
It would seem that position is to state as action is to passion. I believe that such terms should be understood simply as qualifications of material forms.
Quantity is the stuff of mathematics. Each of the other five categories is ***somehow*** measured quantitatively. Thus space is measured by distance. Affection is measured by force. Time is measured by duration. Action is measured by momentum. Material form is measured by mass.
Yet such measurement is not quite what the categories refer to. For example, thought seems to be a sort of action. Yet it is difficult to measure it alongside such actions as running or jumping.
In a similar way, women tend to weigh less than do men. I would not say, however, that a woman is any less a material form than is a man.
And it is difficult to compare affections in terms of forces. The light that strikes my retina exerts but a slight force against it. Yet that minute force is as evident to me as other affections which exert far greater force.
I hope these musings of mine shed some light on my odd view of these matters. I am sure that a real philosopher would find innumerable flaws in what I have written.
All I can say is bring it on...
Bill : "Doing mathematics is not mathematics, but is a sort of doing".
This is an opinion. The implication is that mathematics would somehow be 'real' even if there were no thinking beings capable of doing mathematics. This could be seen as a form of ‘magical thinking’, albeit a rather sophisticated form : the putative entities exist *under the form presented by the modelling system*, even in the absence of the modelling system. For my money, it’s as naïve as stating that “nature would exist even if there were no human beings”.
Mathematics can be described as a *language*, Bill, not just as the manifestation of an ontologically-dubious ‘ideal realm’; intuitionism and formalism are entirely reasonable counter-positions to Platonism about maths.
Of course, I’m sticking my neck out as I’ve done almost nothing on the philosophy of maths in itself – but there are enough similarities with the philosophy of logic (which I have done) for me to venture an opinion. Anyway, Brouwer and Hilbert are almost classical now…
Bill : "Is that what is meant by a "neo-Newtonian account?" If so, then I am guilty."
What's with all these Peircophiles on RG all of a sudden - and where were you when I was trying to defend the old bugger as the Third Man in the Frege-Russell axis?
Anyway, Peirce is water under the bridge - the only interesting AND original work he did was on semiotics; all the rest (relations, quantifiers etc.) were 'dans l'air du temps' and his contribution has been fully integrated. As a metaphysician, he's a washout.
It's a neo-Newtonian account because it postulates 3+1 dimensions, rather than the four dimensions of Einstein-Minkowski spacetime.
Bill : "the distinction between matter and form" ... "Socrates is a material form"
Is there some kind of historical re-enanctment group going on here ? The referent of "Socrates" is (perhaps, if he existed) the contents of a certain region of spacetime. There's a degree of arbitrariness in such delimitations introduced by the pragmatic ends of our discourse - ANY region of spacetime, however discontinuous or gerrymandered, constitutes an entity; certain entities seem to 'carve reality at the joints' better than others, but what constitutes 'better carving' depends on what criteria we adopt. If we're talking about Socrates and his son, we're obviously discussing a concrete process (think about it).
BTW, and despite the 'hole argument', I think the substantivalist-relationist division can be deflated (though this is perhaps because I tend to substantivalism)
I postulate distinct 'categories' for space and time. And as I pointed out before, even the greatest modern physicists, speak in terms of two categories. So one might say that the categories are of expression and not being. The distinction is very old. Is that not the way Porphyry justified Aristotle's Categories against Plotinus' criticism?
I have been a 'Peircophile' for far too many years. But as time passed, my application of his thought has become more selective. As to 'the Frege-Russell axis...' I know of Frege and Russell only as a mathematician would know of them.
Which "greatest moden physicists" would those be?
I was nearly rather impolite over your comments on Frege and Russell, but I'll tone myself down to remarking that I'm no longer surprised that your philosophy seems so... 'personal'. It's like meeting a physicist whose knowledge stops at Galileo.
Metaphysical categories : I listed the buggers somewhere, but I can't remember where... somewhere in a discussion with Charles (with whom, Bill, you seem to have more than a few points of agreement)
Yes, Socrates is a material form. I am a material form. So are you. Another way of describing us is as processes.
I would not say that any region of space and time is a material form, however. I would say that any non-empty region of space at a given time contains material forms, be they mere particles, atoms, molecules, cells or organisms. How should we 'carve reality at the joints?' To some extent that is a question for Quantum Mechanics to address. At that level we are dealing with ***veiled realities*** as Bernard d'Espagnat might put it.
There's also pluralists and constructivists in maths, from what i remember. as regards these material forms, since when have we decided to go back to Aristotle? and what would this 'deflation' of the substantivalist-relationist debate consist in?
The distinction between matter and form goes back at least to Socrates.
I would emphasize the hierarchical nature of my understanding of hylomorphism. As such I assume Atomism. Aristotle --- on the other hand --- rejected Atomism.
I seem to remember someone's writing... "EVERYTHING we do here is dependent on language; this is the sine qua non of all philosophy."
If as it has been asserted, language is the ***sine qua non*** of all philosophy; then it seems to me that it is the ***sine qua non*** of the 'categories.' As such it hardly makes sense not to interpret the categories to refer to expressions rather than to being. Certainly we must address the categories of expression before we consider categories of being. Indeed, is it even possible for men to know 'being' per se? For knowledge is of propositions --- of the true and the false --- while being seems to transcend propositional knowledge.
Now I suspect that even David Hirst, for example, makes appointments by stating the time and the place where he is to meet people. So perhaps we should start by asking why such a thing might be...
But who am I to say?
DH: “A good subject for discussion? Why, 'time', of course!”
That fits in well with our discussion of the Lord of Time.
Plotinus discusses time in the Seventh Tractate of the Third Ennead...
“Would it, then, be sound to define Time as the Life of the Soul in movement as it passes from one stage of act or experience to another?
“Yes; for Eternity, we have said, is Life in repose, unchanging, self-identical, always endlessly complete; and there is to be an image of Eternity-Time-such an image as this lower All presents of the Higher Sphere. Therefore over against that higher life there must be another life, known by the same name as the more veritable life of the Soul; over against that movement of the Intellectual Soul there must be the movement of some partial phase; over against that identity, unchangeableness and stability there must be that which is not constant in the one hold but puts forth multitudinous acts; over against that oneness without extent or interval there must be an image of oneness, a unity of link and succession; over against the immediately infinite and all-comprehending, that which tends, yes, to infinity but by tending to a perpetual futurity; over against the Whole in concentration, there must be that which is to be a Whole by stages never final. The lesser must always be working towards the increase of its Being, this will be its imitation of what is immediately complete, self-realized, endless without stage: only thus can its Being reproduce that of the Higher.”
http://classics.mit.edu/Plotinus/enneads.mb.txt
Plotinus' remarks resemble a very primitive version of perdurantist four-dimensionalism - a person is extended in four dimensions, having both spatial and temporal parts. The 'person' is the mereological sum of those parts. Plotinus' distinction is made between the temporal stages of the 'person' (its proper parts) and the sum.
However, the relation is part-whole and atemporal. No part can 'tend towards' the whole, it just 'is' part of the whole. A subregion of a region doesn't 'tend towards' its participation in the greater region. The spiritual mumbo-jumbo is just another whacked-out generalisation from (misunderstood) local conditions.
Of course I make appointments in time AND space - the appointments take place in particular spatiotemporal locations. The spatial component is, of course, only locally relevant, though I should imagine that GIVEN THE TEMPORAL coordinate we should be able to work out the 'real' spatial coordinates within a larger framework (the position of the solar system with respect to to the galactic centre, for example).
MB: "What is time without space or space without time? Are the two completely separable?"
I certainly can imagine space without time. It is more difficult to speak of time without space.
For example, I can imagine a red sphere. The words, 'red sphere.' do not seem to me to predicate any time frame at all. Nor yet, do they predicate eternity.
I am not sure I can imagine time without presuming some sort of space. Yet I can certainly speak of time without predicating space. For example, 'July 4, 1776' states a time without predicating any particular space. I would admit, however, that the expression, 'July 4, 1776' does imply some sort of spacial context, since time does seem to be locally defined. Perhaps that is what David meant by the "'real' spatial coordinates."
As I see it, the six 'categories' I have outlined are hierarchically related to each other. Material Form is the most concrete category. Action is more abstract than is Material Form. Time is more abstract than Action. Affection is more abstract than is Time. Space is more abstract than Affection. Quantity is more abstract than Space. And beyond Quantity there are the Transcendentals.
DH: "It's a neo-Newtonian account because it postulates 3+1 dimensions, rather than the four dimensions of Einstein-Minkowski spacetime."
The basic problem of Time is, in fact, a Newtonian one. One does not have to invoke either Albert Einstein or Hermann Minkowski to see it.
According to Newton's Laws of Motion, the laws of physics are invariant to the 'direction' of time. A body falling through a gravitational field will follow the same course if we reverse the time co-ordinates. Some have described this invariance by saying that there is no 'Arrow of Time.'
Yet it is perfectly obvious that there are irreversible processes. Expose an ice cube to heat and it will melt. Expose water to heat and it will not freeze. The process goes in one direction in any given situation. Newton's Laws of Motion can not explain that. So physicists have invoked a sort of ***Deus ex machina*** instead, proposing completely separate Laws of Thermodynamics which appear to flow from the head of Athena, since there is no way to derive them from the Laws of Motion.
The notion that space and time are somehow equivalent explains nothing. In fact, it makes the problem all the more obvious, since physicists can find no preferred direction in spatial terms which might be analogous to the 'Arrow of Time.'
Without a doubt, physicists are working on the problem.
One of the main reasons to object to the simple equivalence of time and space is that it makes it impossible to understand organic, biological processes. One can not ignore the 'Arrow of Time' and hope to understand biology.
Man is, of course, a biological organism. Man's mind is particularly sensitive to temporal matters. In psychology, intention is everything... everything... everything... And intention is the nothing more than the working of the mind with respect to time. Animals, including --- and especially --- man, intend to do this or that, knowing that the future can be different from the past.
Michael:
Mathematicians prove theorems about spheres without reference to either space or time. By that, I mean without reference to real space or real time. To a mathematician, a sphere is a mathematical conception, not a physical one. Any physical manifestation of a sphere is --- for the mathematician --- a poor substitute for his mathematical conception.
When I say I can imagine a red sphere I am likewise talking about imagination, not physicality. I imagine it without any particular beginning or any particular end. Yet, I would not say it is eternal, either. I would say it is imaginary.
Is some frequency or vibration part of my idea of redness? I think not. Physicists describe physical redness in such terms. But my idea of red is far simpler than that. I believe it is what C. S. Peirce called a 'tone.' In contrast, you seem to be looking for a melody --- or even some harmony or rhythm. Yet none of that enters into the simple conception of red --- pure redness and nothing but redness.
Perhaps you do not know what I mean by red? I can not possibly tell you what I mean. It is a simple affection. One either 'gets it' or not. I know of no way around that.
Ven:
Yes and no. Language is important. But I am talking about definition. How do we define words?
As I see it, there are three essential types of definition...
(1) We define things by example. Children learn this way. Ask a child what a dog is and he may respond "A dog is like Fido." He knows that a his pet, Fido is a dog. It is in his mind, the ideal dog. So whatever is like Fido must be a dog.
Definition by example is generally frowned upon by scholars. Yet there are times when it is ideal: when we list all conceivable examples of a thing we have stated exactly what we mean by a term.
And, of course, we should remember that all definitions ultimately depend on the knowledge of individual beings --- examples, in other words.
(2) We define things by their ***propria,*** that is by properties which uniquely belong to one thing.
Thus a child might define dog by saying that a dog wags its tail and sticks its tongue out. For the wagging tail and extended tongue are properties which he associates with dogs. As he grows older his knowledge of properties becomes more abstract and his definitions mature.
(3) We define things by genus and species; that is, by similarity and difference.
Thus we may define man as Homo sapiens. 'Homo' is the genus, a group of animals similar to each other in certain ways. The species, 'sapiens' identifies what makes man different from other Hominids: man's unparalleled wisdom.
Each category is intended to serve as a highest genus in which things are truly similar. My Latin is a bit rusty, but... they are the ***summa genera,*** the highest 'kind' of being in regard to definition by genus and species.
Of course, there are things that can not be defined by genus and species. I call them 'transcendental.' They can be defined only by example and their propria.
To give an example of what I mean by ***transcendental,*** I would point to the concept of 'category,' itself. Clearly if the categories are what they are supposed to be there is no one category which contains all categories. Thus 'category' can not be defined by genus and species and is transcendental. We can only define the categories by giving examples of what they might be and by stating what is unique to each of them.
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