Philosophy - PHILOSOPHY FOR EDUCATION

Philosophy f o r Education has two quite distinct modes: (a) to understand the nature of education (teaching, learning, curriculum, assessment, etc) and the obstacles preventing it from being delivered in schools, (b) to contribute towards a renewal of general intellectual optimism and sense of progress. Teachers need to believe in the future ---if their words and values are to get through to the students. The historians of the 22nd century may judge the barren managerial years since around 1980 as mainly caused by the collapse of general intellectual confidence which occurred in the 1970s. By the 1970s the pessimistic message of Thomas Kuhn ---that science was irrational--- had reached far beyond the academy. Feyerabend and others had lost their faith in physical science's capacity ever to be able to reach an understandable resolution of its paradoxes. At about the same time Imre Lakatos demonstrated that Pure Mathematics' olympian image was based on a ruthless presentational agenda, rather than an honest resolve 'to say it as it is'. For seventy years it had been the received wisdom that physical reality is mathematical in character and that the mathematics appropriate to the microworld of fundamental physics must be highly abstract. Around the world thousands of the brightest and the best pure mathematicians had been labouring to create an abstract mathematical mindset commensurate with the problem. It became clear in the 1970s that something had gone badly wrong. Hardly any of the millions of hyper-abstract theorems discovered during this period had, it turned out, any relevance to physics. People began to wonder if it had all been a wild goose chase. Faith in the power of "merely human" intellect collapsed ---for some, who called themselves 'post-modernist philosophers'. A dark cloud of gloom settled over intellectual life of all kinds, especially in education, which must, of course, be built on |hope| if it is to get through to the young.

This page offers some general philosophical themes the Editor, Chris Ormell has developed in PROSPERO and PER NEWS. A brief summary is set out here. These theses are offered as contributions towards the rebuilding of intellectual confidence and thence of renewing the zeitgeist of education.

Their underlying motif is that we must look for ideas which lead to |constructive agendas| for the future.

EXISTENTIAL BASICS

A We did not choose to be born. We were pitchforked into this strange world by our parents. To try to make sense of it we can only use reason, logic (clear thinking) and the things we know best.

B We c a n' t k n o w what is not yet known ---what will happen in the future. All worldviews which try to look ahead ride on faith in credible agendas. The best we can do is to find an agenda which is consistent with what we know best and with scientific knowledge. The problem today is that science is clinging to a discredited, truncated epistemology (Cartesianism, with the Mind side discarded) and a deep pessimism has settled onto the quest to understand this strange universe. (Some publishers have found that they can make money by pretending to an optimism in cosmology, but this should not distract us.) The stakes are very high. Many aspects of today's organisation are in disarray, e.g. capitalism, critics of capitalism, politics, critics of politics, US politics, critics of US politics, education, the EU, the Arab world... This is today's existential crisis, the mother and father of all existential crises.

C Abstract modelling is the logical and synoptic way to try to understand the universe. But timeless models (=mathematical models) can never give an adequate account of us or biological vivacity. They are not just static, but necessarily static. We can only build a cogent model of the universe if we incorporate an element of The Other ---that which is actively outside our control.

D We can only attempt to maximise the cogent qualities of the type of model we use to understand the universe. This is all we can do. It will be a form of scientific research programme a la Imre Lakatos (metaphysics is not on ---metaphysical statements fail to make sense : they can no more make sense than a bird can fly in a vacuum ---Wittgenstein's metaphor). We need to incorporate The Other and this, reduced to its simplest form, is.... random vivacity.

MODELLING DESIDERATA

1 We need an a n t h r o p i c o n t o l o g y, this means an ontology which is consistent with our existence as conscious beings with freewill. It must also be consistent with the scientific quest to understand the universe. ('Ontology' = a theory of what ultimately exists.)

2 The present Official Story is that what ultimately exists are mathematical abstractions. But these abstractions are forms. Something must h a v e the forms, the stuff of the universe. To say that this stuff is mathematics is like saying that what cast a shadow was ----another shadow. This Official Story won't do. Mathematics is also only able to offer models of c h a n g e by treating time as a dimension and then asking the reader to imagine a 'Now space 'moving through the structure. But if we ask: "At what speed is this Now space moving?" we see at once that we have stepped into an absurdity. There can be no such second-order time. The model needs the extra-model imagination of the reader to make sense. This simply won't do: it fails the anthropic condition. (The alternative is spacetime as a timeless reality which totally contradicts what we know best ---that we can make choices, act creatively, make interventions, etc.)

3 Something has gone wrong with this view that mathematics is the final language of physical reality. Mathematics has proved its usefulness in physics during the last four centuries, over and over again, but it does not follow that it is fitted to be the language of the end-game in physics. (It still has a major role to play, but it is as the meta-language of actimatics, see below.)

4 We need to rethink the role mathematics has played in human history: see mathsrenew.co.uk.

5 Unfortunately higher mathematics w e n t e x o t i c around 1900 when it accepted the existence of infinities beyond infinity. This was considered a paradise by leading mathematicians. They let their critical guard down, because they forgot that mathematical objects have to be precisely defined ---this is the heart of maths as a discipline. There are only a finite number of symbols available to make these definitions, so there c a n' t be more than an infinity of possible, definable mathematical objects. But lots of mathematicians were/are so intoxicated with the notion of infinities beyond infinity that they went into fantasyland and started accepting indefinables as mathematical objects (real numbers). To try to "save" infinity beyond infinity they accepted that you can 'define' a real number as an i n d e f i n a b l e decimal! It is difficult to think of a more palpable, brazen contradiction.

This mistake has had extremely unfortunate consequences. For a hundred years it allowed higher mathematicians to live in a bubble of triumphalism and self-congratulation ---in effect, an ivory tower--- when they were urgently needed to confront and make sense of the bizarre discoveries of quantum physics. They went round saying that "mathematics is an end-in-itself" knowing that mathematics' reputation was so high that they could get away with it. But a hundred years have passed and this capital (mathematics' reputation) has gradually been spent.

KEY POINT: No one found a satisfying explanation for Russell's Paradox (1901) so they eventually accepted in the 1920s Zermelo-Fraenkel's restrictive set theory (ZF set theory) as the basis of mathematics. This was a fudge. A proper explanation can be found in Ormell's Some Varieties of Superparadox (1993), which can be read on the internet. It shows that the artificiality introduced by ZF set theory is not needed. ZF set theory had the side effect of introducing a general attitude of artificiality into mathematics. There is a perfectly sensible commonsense solution.

6 Scientific explanation depends on the principle of spatial deconstruction. If we start with the human body ---which is the most complex and mysterious thing ever observed in the universe--- we can deconstruct it progressively into body parts, organs, cells, DNA and other massive protein molecules, Amino acids, atoms, protons, electrons etc and quarks. This is the "explanatory chain" of science.

As we go down the levels the behaviour becomes simpler: the entities on level n are e x p l a i n e d as a logical consequence of the behaviour of the entities on level n+1. It is because the entities on level n+1 have simpler behaviours that we feel that an explanation has been provided. So what would count as a final level of entities? It can only consist of active entities which have no 'pattern of behaviour' at all. Thus the only viable candidate for representation of the final |stuff| of the universe is absolutely random sequences. These are l i v e sequences of marks (tallies). They are not timeless. A jumping sequence is one where there is a change of tally-type each time. The simplest possible unit is an absolutely random jumping sequence of three tallies \ | / because if there were only two tallies \ and / it would be predictable \/\/\/\/\/\/... etc.

7 Absolutely unpredictable sequences can be fully and clearly conceptualised. They are logically possible, they can be experienced as a live, on-going reality, but they are not mathematically definable. This conclusion follows from a mirror image of Descartes' Cogito argument. See Ormell's series of six articles 'A Modern Cogito' in the journal Cogito 1992-94.

8 A new post-cartesian modelling discipline ('actimatics') can be created by applying definitions and constructive fiats to live absolutely unpredictable sequences (ultimate units UUs). This research programme is being developed in Prospero Vols 17/18/19/20. This follows from the fact that mathematics has grown for more than 2,000 years by adopting definitions. Definitions reflect resolutions to attend selectively towards special bits of fields of abstract objects. (Abstract objects are objects of attention which make no initial reference to anything in the real world.) They come to seem to be extremely real, because they are there, unchanging, whenever you go back to them.

9 SOME EARLY RESULTS It turns out that we need a f o u r tally system to represent three dimensions. Consider a field of all possible four tally absolutely random jumping sequences (UUs): a proto-universe. They are utterly separate objects. Space does not exist. But |we| can impose a metric onto these absolutely independent sequences and thereby "club" them together into a connected, three dimensional space. A relativist metric is the simplest way. (This is not metaphysics: we need to find structure-types which fit the empirical evidence and which also allow (logically allow) the system of higher objects described below.) These UUs have a maximum speed of separation because the most they can do is keep producing different tallies from each other. For example the UU which currently looks like this:

\_/\|_/|\/\/\_/|/_\/|/\/\/|/\|\/\_...

and a second UU _/\|_\/|\/|\_/|\|/_\/|\/|\/|/\_|\/\...

have been diverging for the last five jumps, because their tallies in these positions differ. They can't "differ" more quickly than this. This is invariant whatever metric one imposes on them. (There is an infinity of possible metrics.)

They have stochastic spin, which is relatively stable.

CRUCIAL POINT Each UU can be checked for stochastic spin on six different bases (=permutations of | \ / _). If m i n d is in the loop, we can associate each UU with its t o p s p i n which is about 4.5% more than one would statistically expect. This, replicated over untold numbers of UUs provides a vast pool of organisational energy.

For every UU there is a tertiary equivalent sequence of 1s and 0s together with a starter tally (\ | / or _). It follows that if we add a recurring tricimal b to any UU (call it X) we get another UU (call it Y). (Otherwise one could subtract b from Y and the result would be wholly predictable. But this "result" is X! So Y must be another UU.) Hence, by subtraction of X from Y we can get any form of recurring pattern whatever. This shows very clearly that the sky's the limit for building reliable dynamic structures using jumping random sequences as the basic units. This substratum or proto-universe contains as much potential for generating predictable, reliable pattern as one could ever want.

10 The essence of Total Epistemology is this: it is reasonable to suppose that we can eventually construct an amazing dynamic cybernetic system (ADCS) which will model the human brain. This is 'reasonable' because we know what is possible with modern constructions (computers) using micro semi-conductors. But because jumping random sequences are slippery, this is likely to be possible only in conjunction with a mass of by-products. (We can only produce a specific local pattern by creating a mass of lesser by-products elsewhere.)

11 The postulated ADCS will be far more powerful in terms of parallel recognition-power than the best modern computer. But once an ADCS exists, it can take over the burden of making the definitions needed to sustain its own existence! It can apply the selective attentions needed to make itself real. The definitions will produce by-products: other ADSCs, higher animals, lower animals, plants, inorganic objects... This is a neo-Kantian universe. Kant was the first person to see that the laws discovered by science are necessary because they are |preconditions for our existence|. If they did not hold, we would not be here to see them. The discovery of actimatics turns this Kantian premonition into a scientific research programme. One has to accept an entire universe of by-products to create a human being (=many human beings).

This explanation of why the universe exists differs from religion and modern cosmology because it does not look for the explanation in the extremely distant past, but here and now. (It is, in effect, a reverse Copernican thought revolution because it puts humankind back at the centre of the universe.) The past is an unknown country which gets mistier and mistier the further you go back. At the limit any temporal quest to explain the universe ends up with total whiteout.

12 Each ADCS creates its own universe, but we are saved from solipsism by symmetry.

13 So the message is: Yes our brains are a kind of machine, but machines with freewill because they create themselves... (We are products of our own feewill, but we are also aware that we operate on automatic for a lot of the time ---so we have a machinelike side. Much of the drama of ordinary life occurs on the cusp where freewill meets automatic response.) This is e x t r e m e l y counterintuitive but necessary.

14 Corollary 1 is that genuine "artificial intelligence" is hardly likely to be produced, if it takes an entire universe of by-products to create a small region with ADCSs ---out of the neutral clay of a proto universe of jumping random sequences. Corollary 2 is that if living things are found on a distant earthlike planet, they are likely to be like us. Corollary 3 is that there will be superminds in the future who will look back and judge us. (If not earlier, at John Barrow's Omega Point. These superminds take the role of "God" in earlier ontologies.)

15 Another corollary: we are all very closely related to each other. This leads to Basic Rooted Belief, a secular residue of previous Belief. The universe conceptualised like this has a kind of spiritual quality. (See page 3 CONCEPTS/METHODS.)

COMMENT The view of the universe we get from this inquiry is quite ferociously counter-intuitive. But so is modern quantum physics. The new view meets the demands of logic and rigour without succumbing to fudges or wishful thinking.

16 It is startling to the nth degree. All bets are off. A new era beckons.

NOTE: this is a bald summary. For details see PROSPERO 20-4, available from PO Box 16916, London SE3 7PH, UK price $8 + postage.

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