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The idea of a sequence of causative steps breaks down, since nothing alters another thing without itself being altered; and, as I suggest, there are no wholly separate ‘things’ in any case.
Note that in conveying these two ways of understanding mathematics, Weyl contrasts one that is ‘continuous’ or ‘topological’, suggestive of the right hemisphere, with one that is made up of serial ‘operations’ (procedures) carried out on ‘algebraic’ signs (abstract discrete entities), suggestive of the left hemisphere.
This has something to say to the nature of reason, namely that it needs to transcend its intrinsic limitations in order to be able to operate rationally.
We cannot abstract philosophy from the happenstance of the physical being that dreamed it up.
Philosophy is not, then, purely a matter of impersonal reason, but living: bound up in the temperament, character and history of the person who expounds it.
Philosophy still has to learn that it is made by human beings and depends to an alarming degree on their psychic constitution.
We cannot divorce the philosophy from the philosopher.
Now that I know how foolish we all are, I am happy to be just another human being.
In sum, we expect our truths to be something which we casually designate ‘literally true’; anything that isn’t ‘literally true’, we tell ourselves, isn’t true at all.
myths are not to be taken literally, but nonetheless exist to express truths that everyday language is too limited, too narrow, too precise to convey, are like people who would dismiss Shakespeare’s King Lear on the grounds that, according to the chronicles of Geoffrey of Monmouth, the historical Leir (as he was known prior to Shakespeare), fled to France, and with the help of Cordelia and her husband, overthrew his other daughters and sons-in-law, and was restored to the throne.
A fact is presumed to be true independent of context. But no human knowledge is ever independent of context, even if only that it is human, and derived from experience.
Or as Einstein put it succinctly: ‘As far as the propositions of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.’
Logos (‘reason’) was the pragmatic mode of thought that enabled people to function effectively in the world. It had, therefore, to correspond accurately to external reality. People have always needed logos to make an efficient weapon, organize their societies, or plan an expedition. Logos was forward-looking, continually on the lookout for new ways of controlling the environment … Logos was essential to the survival of our species.
Myths may have told stories about the gods, but they were really focused on the more elusive, puzzling, and tragic aspects of the human predicament that lay outside the remit of logos … When a myth described heroes threading their way through labyrinths, descending into the underworld, or fighting monsters, these were not understood as primarily factual stories. They were designed to help people negotiate the obscure regions of the psyche, which are difficult to access but which profoundly influence our thought and behaviour … When Freud and Jung began to chart their scientific search for the
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In other words, myths were archetypal, not incidental, truths, reflecting eternal patterns that we could recognise, but which could not, without diminishment, be translated into the everyday terms of logos.
‘Words, words, words …’ This would certainly fit with Mercier and Sperber’s view that logic was invented in order to win arguments, not to take us closer to the truth.
Although language is indeed the tool required for philosophy,193 it is nevertheless a limited servant that should never become the master.
The left hemisphere may add – and it adds enormously much – but what is added must be returned to the world that is grounded by the right hemisphere, or we misconceive the nature of reality.
‘the metaphor is far cleverer than its author, and so it is with many things. Everything has its depths.’
We know that the mind is not a tabula rasa, a blank slate on which experience inscribes itself from scratch, but comes, as it were, prepared for the encounter it is to have with the forms of the world, including, but by no means limited to, the forms of language.
The beauty and power of art and of myth is that they enable us, just for a while, to contact aspects of reality that we recognise well, but cannot capture in words.
The more important something is, the more we have to struggle in the attempt to reduce it to language. We would be lost without words, but sometimes it is wisdom to be lost for words. Words are always a representation in terms of something else. The work of art exists precisely to get beyond representation, to presence, even if that presence is itself composed of words, as it is in poetry.
It returns us from the ‘presencing’ of the world in language (right hemisphere) to its ‘re-presentation’ in language (left hemisphere). We do not use metaphor to decorate, and therefore obscure, something best conveyed literally (although that would be how the left hemisphere sees it), but to bring to life a deeper and broader set of meanings than could be conveyed by literal language.
Without a language one can rely on, there is no way of establishing common truths. But a language that is not sensitive to context is dangerously unreliable.
This is the old temporal causation problem: in reality it’s not a linear relationship, but a betweenness. There is a never-ending reverberative loop set up between the experience and the metaphor, in which neither can be said to have precedence. It is not one of steps, or progress by parts, but one of the co-creation of a new whole.
One important difference between mythos and logos is that, according to logos, knowing how or why something happens appears to exhaust its nature; whereas according to mythos, the nature of something is precisely what cannot even be approached by logos.
The idea of reason has at least two main meanings: a rigid, abstract, linear mode, prizing precision and certainty, and owed to the left hemisphere; and an embodied ability to hold in suspension knowledge of various kinds justly, and to evaluate them in the context of lived experience, where reason is not in any sense at war with feeling or imagination. This mode is more dependent on the right hemisphere: and is, like the right hemisphere’s understanding of science, in my view more fruitful than the alternative that is often served up in its place. And it is vanishing and dying.
The first sense is this: that in the deep (though, clearly, not the superficial) structure of reality opposite truths do actually coincide, and we must therefore accept both.
was the distinction between the two sorts of truths, profound truths recognized by the fact that the opposite is also a profound truth, in contrast to trivialities where opposites are obviously absurd.
But what is the second sense? This concerns the structure of the mind and brain: the distinct versions of the world made possible by either hemisphere. As the reader is aware, these have complementary, but contradictory, properties.
This has consequences for apparent contradiction, since a statement and its denial can often be true in different degrees and different contexts.
In essence, this involves a sophisticated mathematical estimate of the change in probability added by the new evidence, obtained by contrasting ‘prior probability’ (before taking into account the new evidence) with ‘posterior probability’ (after taking the evidence into account).
It entails acceptance of the fact that if you set the bar high enough, we can never be said to know anything. Knowledge is a matter of degree: our standards for ‘knowing’ anything change with context.
Sensitivity to matters of degree, and to context, are both areas in which the left hemisphere is handicapped by comparison with the right.
It can potentially be analysed ad infinitum, but it cannot be created ad infinitum.
A finite distance is achieved in a finite number of steps: ‘the illusion that it is infinite is due to mathematicians who confuse their mathematical representations with what is represented.’8 Or as I would put it for clarity’s sake, who confuse the representation with the presence, the left hemisphere’s take with that of the right.
Analysis is a (1) fragmentation into (2) static instants of a (3) ‘re’-presentation, by definition ‘after’ the fact and (4) in an abstract realm; it has all the hallmarks of the left hemisphere about it. By contrast our intuitive understanding takes as an (1) indivisible whole (2) the nature of motion as it is (3) present within (4) embodied experience, and has all the hallmarks of the right hemisphere about it.
Note that all the ‘building blocks’ of the experiential world – space, time, depth, and, I would add, consciousness – are clearly different in kind from anything else, are irreducible, and therefore require a leap: they cannot be approached incrementally.
‘What Zeno shows’, as philosopher George Melhuish puts it, ‘is that continuity cannot be composed of discrete elements even if there is an infinity of them.’12 It has to be inhabited whole; it cannot be composed from without. Flow is an irreducible, not an emergent, element in the universe.
There might be a message here that co-operation leads to logically superior results at the global level, even if competition gives the appearance of doing so at the local level. We saw this in the case of biological evolution. And once again, the right hemisphere is better able to see both the overview, and the worth of co-operation compared with simple competition.
Here what seems to be happening is that the left hemisphere, dealing with representations rather than experience, finds itself in a hall of mirrors, in which a representation is represented by a further representation, which is represented by a further representation, and so on.
The left hemisphere world is hermetic, so one ‘hits one’s head on the ceiling’, so to speak, and can go no higher. But, according to the right hemisphere, to which all frames of reference are open, there is always another level to which one can go to ask a question that transcends the frame of reference.
There are a number of self-referential paradoxes, most of which resolve if one is clear that distinct levels of language are conflated. To make a statement A about a situation, and to make a statement B about the language in which statement A was made, are two different kinds of thing.
To understand infinity we have to make a leap: you can’t get there by continuous movement from here.
I would suggest that the leap is from the incremental, computational (Newtonian), left hemisphere-compliant universe to an intuitive, non-incremental, non-computational (Planckian), right hemisphere-adapted universe.
The process is never-ending, but the thing is finished. We therefore need the symbol for practical purposes. As Hermann Weyl remarked: ‘mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is, finite means.’37
Because, if it is true, the cosmos is not composed of entities that exist in their own right, influencing one another, but of patterns that are reflected in reciprocal movements of what only come to look like entities when they are observed by us.
The automatic system handles huge amounts of information in almost no time. Only the end result is propelled back to consciousness as an intuition. Consequently, in appropriate contexts, institutions should in principle see to it that decision-makers trust their intuitions.
individual decisions are made in the brain. Human brains, however, are closely interconnected with, and embedded in, the distributed networks of culture from infancy … Humans are collective thinkers, who rarely solve problems without input from the distributed cognitive systems of culture.
Analytical decision-making seems to interrupt the intuitive processes that serve experts well.