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Ashvin's avatar

"This does not necessarily undermine the utility of mathematics in science but suggests caution in assuming that mathematical models provide direct access to the ultimate nature of reality. They may instead offer useful approximations within the constraints of our perceptual and cognitive capacities, useful precisely because there is some degree of resonance between these capacities and the environing cosmic rhythms from out of which they have emerged."

Thanks, and very well said! Pure mathematics is the closest we can get to a 'clean' experience of the spiritual realm through intellectual thinking. In mathematical reasoning/modeling, we find thinking that supports itself and makes its own movements into its object of contemplation, independent of sensory perceptions that normally anchor our intuitive orientation to reality. The mathematical thoughts are determined entirely through their inner relations with one another, which is where we gain the most intuitive certainty about the flow of perceptual experience. This is why all science naturally gravitates toward expressing their theories/models in mathematical format.

This is a prelude to what the ego secretly yearns for but doesn't yet have the inner courage to approach - the wider spiritual world, of which mathematical thinking is only a dequalitative, rigidified, and aliased instance. Hoffman and others would make the most progress when they focus less on the meaning of their mathematical thoughts, which generally point to some 'external' material or spiritual reality, and more on the flow of their real-time mathematical activity. In that way, we can attain to inner experience of the 'network of conscious agents' that we normally can only abstractly imagine is responsible for the "interface" of ordinary perceptual experience.

Ben Snyder's avatar

To me this leaves out the most interesting and clarifying manner in which Whitehead's philosophy explains how this reciprocal relationship between mind and world occurs. All action occurs in the present tense, between the fixed past and open future. Thus in the actions of judging or asserting propositions, there is a tensed distinction at play. The past world is independent of the present mind, whereas the future world is possibly (and even plausibly, or maybe even necessarily) dependent on it. The past provides a fixed reference point to which propositions may correspond in a straightforward manner (that is, the present mind can in no way influence or affect the truth-relation between proposition and past actual world): the future, on the other hand, only offers a set of possibilities, incompatible alternatives, as perhaps conditioned by the past, in a manner the present mind may influence--thus introducing a realm of agential concepts and ethical responsibilities. In my opinion, it's only when we've made this tensed distinction that our discussion really begins to accurately discuss this issue, and provide helpful concepts. There's been rigorous work done on this in the realms of temporal logic and the logic of agency--like Nuel Belnap's stit logic as he has combined it with his branching space-times metaphysics (a development from Prior's work that in many ways agrees with Whitehead).

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