Quantisation of intellectual light

[David Bibby]

Dear Lonergan list,

I have been reading Verbum, and am particularly intrigued by what Aquinas says on intellectual light.  The counterposition that we know by looking amounts to a denial of the existence of intellectual light.  Without physical light, we cannot see, and without intellectual light, we cannot understand.  The same object may be seen with and without the presence of intellectual light.  In the first case, there is potential understanding, while in the second case, there is none.  If knowing were by looking, then there would be no objective difference between these two cases, and if intellectual light makes no difference, it is as good as if it did not exist.

We know that physical light is quantised, coming on different energy levels, given by E=hv, where E=energy, h=Planck's constant, and v=frequency.  But intellectual light may be quantised too.  These are not energy levels, because energy is physical, but levels of consciousness, and we can use maths to define what this means.  Specifically, let us consider the set theoretic definition of natural numbers.  The first few numbers are defined this way:

0 = Ø (the empty set)
1 = { Ø } (the set containing the empty set)
2 = { Ø, { Ø } } (a set of two sets - the empty set, and the set containing the empty set)
…
And in general, n+1 is constructed by the union of n with the set containing n, that is to say. n+1 = n ∪ { n } = { n, n - 1, n - 2, ..., Ø }.  We are used to applying numbers to physical objects, but we can also apply them to levels of consciousness: 0 = perception, 1 = intellect/ understanding, 2 = judgement/ reflection, 3 = decision.  Since perception does not involve any cognitional operations, it is represented by the empty set Ø.  But perception supplies the materials on which intellect operates when we try to understand the world, so the next level is { Ø }, as we think about it.  As we become conscious of our own thinking, we also raise the question of whether our thoughts correspond to reality, and on this level, we reflect both on our thoughts, and our perceptions, viz. { Ø, { Ø } }.

I wonder if this could be a way of presenting Lonergan in a way that does not take for granted the presence of intellectual light.  Unless intellectual light is present, Lonergan will not be understood.  Since intellectual light is not continually present, Lonergan will not be understood on a level that allows its spontaneous integration in the present culture.  But once intellectual light is presented as one of the necessary conditions of understanding, we can understand the reason we do not understand.  Human understanding is imperfect, limited, and we have to reason from the things that we know to the things we are yet ignorant about.

Best wishes,

David

[jaraymaker]

David,

 

you give us an interesting allusion to set theoretic numbers and to Planck's constant. That set me scrambling on google and found e.g.

 

1) In set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell.

 

2) As to set theoretic numbers, I found 

 

The set N of natural numbers is defined in this system as the smallest set containing 0 and closed under the successor function S defined by S(n) = n ∪ {n}

 

In 1) above some famous, important names come up. In 2) I come up with an immediate question, how is this or could be related to what you propose below? For me this is a learning experience.  John

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[David Bibby]

Dear John,

Thank you for your question.

It’s not easy to explain, but it can be considered in the light of what Lonergan says of mathematical judgements:

“Finally, the actual element lies in the conjunction of the material and formal elements.” (Insight, chapter 10, section 8, 2008 p336)

Think of the material element as consciousness, the formal element as the set theoretic definition of numbers, and the actual element as putting them together.

Mathematical physics uses maths applied to physical and geometrical objects. If we apply maths to consciousness, we could call it mathematical psychology, another branch of applied mathematics.

Kind regards,

David

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