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.This demonstrates, according to Plato, that all people, of whateverintellectual or social status, have an innate knowledge of an absolutely realmathematical world.All that is needed is a reminder to enable them to recall and‘see’ this world.Indeed, the word ‘theorem’ is derived from the Greek yevreinmeaning ‘to look at’.Plato’s argument is not particularly convincing to us now.Even if it were true thatgeometrical ideas are implicitly present in all human beings, this could be telling usmore about human beings than about ‘reality’ – a vital point which, as I will describe,would be taken up much later by Immanuel Kant.Plato’s claim was credible at thetime, however, because it fitted in with a generally current notion of a ‘heavenly’repository of truth to which we might have access, as expressed, for instance, by hiscontemporary Parmenides (1986).Plato saw these absolute truths (called, in English translations, ‘ideas’ or ‘forms’)as ultimate reality.Furthermore, he felt there was some truth in mythologicalaccounts that described the human soul coming from this realm of reality to beincarnated, and this was what enabled the soul to remember, like Meno’s slave, thetruths that it had previously known.So Plato’s realm of ideas had two aspects, which we would regard as opposed.Onthe one hand, it was the source of abstract ideas, both statements about geometry andgeneral concepts like ‘Cat’, which we think of as rather ordinary.On the other hand,it was associated with reincarnation and the divine which we would link withspiritual/mystical experience (or with delusion, depending on our approach).ForPlato or his character Socrates, there is always an air of mystery and ‘numinosity’about all aspects of this realm.We can note that, although modern thought isconcerned with distinguishing rational ‘factual’ mathematics from numinous (andpossibly delusional) spirituality, Plato classes them together and is concerned withdistinguishing both from the mere ‘appearances’ of the material world, though wewould regard the latter as ‘reality’! We shall see in what follows how subsequentphilosophical developments resulted in Plato’s ‘ideas’ being seen as humanlyconstructed rather than (divinely) ready-made, and undermined his distinctionbetween reality and appearance.Knowledge and Reality117Reality Through RationalityAlthough Plato’s views were to last for the next 2000 years, an alternative school ofthought immediately started to emerge in parallel with Plato’s from the work of hispupil Aristotle.He lacked Plato’s mystical streak and so had no time for a separaterealm of reality.For him, reality was in the here and now.He continued anddeveloped, however, the tradition of careful logical analysis started by Socrates andPlato.In particular, he codified the rules of logic and developed a system forclassifying the words used for talking about things into logical categories (such as,‘substance’, ‘quantity’, ‘place’ and so on).He proposed that by using these one couldanalyse people’s ideas and discover the truth by proceeding from a generally agreedstarting point to reliable conclusions (Aristotle, 1989).Although Aristotle rejected Plato’s notion that universal ideas like Cat (as opposedto Tiddles, a particular, solid cat on a particular mat) occupied some special absolutereality, he did assume that there was a real property of ‘catness’, so to speak, that was contained in actual cats.Plato’s ‘ideas’ (or universals as philosophers now call them)were still there for Aristotle, but they had been brought down to earth in the form ofproperties of actual objects.By the middle ages, however, the reality of suchuniversals started to be questioned.In 1087, the French theologian Roscellinus(D’Onofrio, 2008: p.140) taught that universals like this had no reality, but were justwords that we chose to attach to things, a view called nominalism that graduallygained acceptance amidst much controversy.The picture that progressively emergedin the early middle ages on the avant garde side was one in which the ordinaryphysical world of things was real, but we then classified things arbitrarily by attaching words to them.The more conservative side, however, held to a more Platonic view,holding that the ideas had an absolute reality, a view termed realism.We can compare this with the interacting cognitive subsystems (ICS) modeldescribed by Isabel Clarke in this volume (p.107ff.) which makes a distinctionbetween two ways of knowing: one way using language in its Western form ratherthan its older form (described here by Klotz and Lancaster) and relying mainly thepropositional subsystem, and the other way going beyond constructs or relyingmainly on the implicational subsystem.These two ways of knowing loosely corre-spond, respectively, to Aristotle’s logical, categorising approach and the numinousaspect of Plato’s ‘ideas’ which Plato sees as expressed through myths.As Neil Douglas-Klotz has emphasised in his chapter, whereas Semitic languagesheld together the different aspects of existence represented by these subsystems,Western language has divided them [ Pobierz całość w formacie PDF ]