CONCEPTS & METHODS & MATHS

The P E R Group is predicated on a conception of philosophy as a clarification activity using various methods:
Linguistic analysis ---light touch Brunerian simplification
thought experiments concept formation.
Light touch linguistic analysis ---linguistic analysis needs self-evidently quickly to clarify what it addresses, otherwise it becomes otiose and self-defeating. It is a like a joke which needs to be self-evidently funny. If it has to be 'explained' it is no longer funny.
By 'Brunerian simplification' we mean intellectually honest forms of simplification, which do not distort the overall role of a concept or theory. Of course to be able to use Brunerian simplification one needs to cultivate a multi-angle approach to problems. Essentially the simplification stage applies to problems. One is aware of a generalised conceptual unease. It is like a pain which seems to lack a precise location. This is like Peirce's concept of 'irritation'. Simplification helps to bring into focus the precise source of logical confusion.
Thought experiments use creative imagination to explore possible solutions to problems.
Concept formation can be the clinching step in making something previously unclear, clear. It functions like a signpost in a fairly nondescript landscape.
The meaning of words is rooted in their use in the discourse of the society. So there is no future for fabricating new portentious jargons. Philosophy for education must work with ordinary language of the clearest, plainest kind --- if it is to exert leverage in the political arena (see the page on Values and Culture). Mystification is out.
Chris Ormell's use-expectation account of meaning was set out in a publication The Meaning (circulated privately in 1996 to a group of twelve philosophers including Antony Flew and Paul Hirst) and was also sketched in his six Cogito articles 1992-94. It argues that while the meaning of a word or phrase is a social fact (=its actual usage by a circle of users) its 'use' qua function is to convey and share expectations of experience ---what to look for when you go somewhere and/or do something--- with others. It can only achieve this function, though, when a good level of trust obtains between speaker/writer and listener/reader.
The key concept of 'education' has been overrun in the last three decades by managerialists who have continued to call their pressured learning establishments 'educational' institutions. (They dare not signal to the public that their regime is now targetted on a different thing.) Their approach may be described as 'quasi-educational credentialism' because it appears to conform to traditional educational aims. The curriculum is fairly similar in a broad way to traditional curricula. The difference is that now the official aim is not preparing youth for life, but for a job, and the process puts all its eggs in one notoriously unreliable basket, the marks obtained in stereotyped examinations. Previously, exam and test results were treated with circumspection by experienced, responsible people. All sensible observers knew that cramming for exams and "teaching to the exam" were to be deplored, because they were a superficial way to get marks which had no "long term educative effect". They misled the examiner but worse still, they misled the candidate, who tended to suppose that she/he now "knew the stuff" and had reached a staging post in education. Things crammed were typically forgotten within days after the exam. Teaching-to-the-exam meant that the background picture, which gave the content of the curriculum meaning, was omitted.
'Education', though, means the transmission of the enduring culture of a society to the rising generations. This raises the novel question "How do you interpret this when society has largely ceased to recognise what used to be its enduring culture?". We can reconstruct the 'score' of this enduring culture, while recognising that the 'score' is not the music. Only when there is a partial return in society to the full enduring culture (=music) can we expect that a few schools might be set up to transmit this culture. We need a 'movement of the educated' to begin to move in this direction. This is the long-term aim of the P E R Group and PROSPERO.
The Total Epistemology unveiled in PROSPERO 18-1 offers a vivid new approach to philosophy across the board. It is based on the Anthropic Ontology developed in Annexes in PROSPERO since Spring 2011. See page 5 PHILOSOPHY.

BSB (Basic Secular Belief) consists of five principles or precepts:
The Trust Precept (1) may be stated:
<<Genuine Caring is what makes the human world go round. Ties created by genuine caring and trustworthy behaviour are what holds relationships ---and hence groups--- of all kinds together. Our happiness depends on such groups and relationships, so Genuine Caring is an imperative for living. We should cultivate it as much as possible.>>
The Golden Rule Precept (2) may be stated thus:-
<<The Golden Rule is the only basis for moral sustainability: something can only be ‘right’ if it is capable of being adopted as the universal rule. This follows from the fact that homo sapiens is an incorrigibly copying animal. Whatever we do which is not capable of being universally adopted, will be copied endlessly and its unsatisfactory consequences will grow and grow. We should always act in a way which will not create socially harmful consequences if widely copied. This might be described as the ‘principle of moral sustainability’ in modern language.>>
The Contribution Precept (3) may be stated thus:-
<<Everyone is the beneficiary of past contributions made to the common good by others. Most of the ‘furniture’ of the modern world came about in this way. It is our duty to make our own contributions to the common good ---commensurate with our ability and resources--- in recognition of this bounty.>>
The Renewal Principle (4) may be stated thus:-
<<The moral world is in constant flux and anyone who has fallen down on (1), (2) or (3) can make a fresh start, and by means of single-minded determination can establish a new track record on these things which will eventually outshine any previously unedifying track record. The ‘constant flux’ referred-to here arises from the average person’s short memory span in relation to personal judgments, which probably became a biological necessity once typical human populations grew to many thousands. >>
The Measured Response Principle (5) may be stated thus:-
<<One should not return evil for evil. This sets a qualified limit to the ‘copying sentiment’ associated with the Golden Rule. It is needed to prevent the possible formation of vicious circles of tit-for-tat. So there is a qualification, namely that retaliation to deter future offence is justified when it is likely to have that effect, but not when it will simply provoke more offence.>>
(This secular moral code is supported existentially by the Total Epistemology mentioned above.)
Perceptive readers will notice that this set of Principles mirrors some of the main features of traditional Belief, but without any theological or transcendental overtones. They are not untried, woozy, unrealistic or "New Age" tenets. They were handed on faithfully from generation in the past, essentially because they worked.

PHILOSOPHY OF MATHS CORNER
1 The 20th Century crisis in maths came in 1901 when Bertrand Russell discovered his paradox.
2 The crisis turned into a catastrophe when Russell gave up trying to understand the paradox and switched to banning it by introducing enforced stratification (language levels).
3 Stratified set theory was accepted by the international maths community in the 1920s.
4 A set was no longer defined by its membership criterion because some membership criteria were met by their own set.
5 This was a remarkable exercise in a method known as "sweeping a problem under the carpet".
6 The problem was solved in 1993 when the present Editor Chris Ormell published his monograph Some Varieties of Superparadox. It was acclaimed in a review in the Maths Gazette and by individuals such as W. W.Sawyer. OTHERWISE IGNORED

Does it Matter?
Yes, the Official Story about truth, validity and meaning in maths are a mess. The fudging of Russell's Paradox left the subject in a state of muddle, ambiguity and artificiality.
This problem has not been addressed.

It affects school maths because the subject has been left to drift since The Cockcroft Report (1982).

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