laws of physics would be immoral, and (as I remarked in Chapter 4) to imagine laws of physics that would be more moral than the real ones.
The reach of ideas into the world of abstractions is a property of the knowledge that they contain, not of the brain in which they may happen to be instantiated. A theory can have infinite reach even if the person who originated it is unaware that it does. However, a person is an abstraction too. And there is a kind of infinite reach that is unique to people: the reach of the ability to understand explanations. And this ability is itself an instance of the wider phenomenon of universality – to which I turn next.
TERMINOLOGY
Levels of emergence Sets of phenomena that can be explained well in terms of each other without analysing them into their constituent entities such as atoms.
Natural numbers The whole numbers 1, 2, 3 and so on.
Reductionism The misconception that science must or should always explain things by analysing them into components (and hence that higher-level explanations cannot be fundamental).
Holism The misconception that all significant explanations are of components in terms of wholes rather than vice versa.
Moral philosophy Addresses the problem of what sort of life to want.
MEANINGS OF ‘THE BEGINNING OF INFINITY’ ENCOUNTERED IN THIS CHAPTER
– The existence of emergent phenomena, and the fact that they can encode knowledge about other emergent phenomena.
– The existence of levels of approximation to true explanations.
– The ability to understand explanations.
– The ability of explanation to escape from parochialism by ‘letting our theories die in our place’.
SUMMARY
Reductionism and holism are both mistakes. In reality, explanations do not form a hierarchy with the lowest level being the most fundamental. Rather, explanations at any level of emergence can be fundamental. Abstract entities are real, and can play a role in causing physical phenomena. Causation is itself such an abstraction.
6
The Jump to Universality
The earliest writing systems used stylized pictures – ‘pictograms’ – to represent words or concepts. So a symbol like ‘’ might stand for ‘sun’, and ‘’ for ‘tree’. But no system ever came close to having a pictogram for every word in its spoken language. Why not?
Originally, there was no intention to do so. Writing was for specialized applications such as inventories and tax records. Later, new applications would require larger vocabularies, but by then scribes would increasingly have found it easier to add new rules to their writing system rather than new pictograms. For example, in some systems, if a word sounded like two or more other words in sequence, it could be represented by the pictograms for those words. If English were written in pictograms, that would allow us to write the word ‘treason’ as ‘’. This would not represent the sound of the word precisely (nor does its actual spelling, for that matter), but it would approximate it well enough for any reader who spoke the language and was aware of the rule.
Following that innovation, there would have been less incentive to coin new pictograms – say ‘’ for ‘treason’. Coining one would always have been tedious, not so much because designing memorable pictograms is hard – though it is – but because, before one could use it, one would somehow have to inform all intended readers of its meaning. That is hard to do: if it had been easy, there would have been much less need for writing in the first place. In cases where the rule could be applied instead, it was more efficient: any scribe could write ‘’ and be understood even by a reader who had never seen the word written before.
However, the rule could not be applied in all cases: it could not represent any new single-syllable words, nor many other words. It seems clumsy and inadequate compared to modern writing systems. Yet there was already something significant about it which no purely pictographic system could achieve: it brought words into the writing system that no one had explicitly added. That means that it had reach. And reach always has an explanation. Just as in science a simple formula may summarize a mass of facts, so a simple, easily remembered rule can bring many additional words into a writing system, but only if it reflects an underlying regularity. The regularity in this case is that all the words in any given language are built out of only a few dozen ‘elementary sounds’, with each language using a different set chosen from the enormous range of sounds that