Causal determinism, the idea that the present state of the world is fully determined by its antecedent states, is generally considered incompatible with causa sui thought, the idea that thought is not fully determined by the antecedent states of the world and can non-trivially affect the subsequent states of the world. A strong metaphysical challenge to causal determinism, henceforth determinism, can be constructed on the basis of Russell’s Paradox.

If sets that do not include themselves are labelled ‘normal’, and sets that do include themselves are ‘abnormal’, then the set of all normal sets cannot be determined (or be consistently defined) because in attempting to do so we would have to include that set in itself, making it abnormal, and abnormal sets are excluded by definition, therefore paradox. It follows that the ‘unversal’ set of all sets (normal and abnormal) cannot be consistently defined because at least one of its members, the set of all normal sets, cannot be consistently defined. While it may be tempting to argue that the Paradox does not arise if all real sets are in fact abnormal, such sets are themselves indeterminate. According to Whitehead & Russell (1910, 37), “given any set of objects such that, if we suppose the set to have a total, it will contain members which presuppose this total, then such a set cannot have a total.” The underlying principle is more clearly explained in relation to functions: “no function can have among its values anything which presupposes the function, for if it had, we could not regard the objects ambiguously denoted by the function as definite until the function was definite, while conversely, … the function cannot be definite until its values are definite.” (Ibid. 39)

‌This result is relevant to the question of ‘free’ (causa sui) thought – a necessary and possibly sufficient condition of free will. Every thought insofar as it has definite content is something necessarily in excess of its content; if it were included as its own content then it would not be definite as to its content and therefore not a definite thought. The circularity (and the associated infinite regress) of self-inclusion is analogous to the circularity of thought trying to perpetually, but always incompletely, grasp itself. Reflexive thought is always at the meta-level of being, always one step removed from its content irrespective of the object of thought. This can be visualised as indefinite construction of containers to fit ‘everything’ (or ‘anything’ in a new way) that subsequently become the content of another, more encompassing conceptual container.

To avoid the circularity of self-inclusion, Whitehead & Russell’s have developed the theory of logical types as a way to structurally differentiate the function from its argument in case the argument is identical to the function. In the logical structure f(f(x)), where the function f(x) takes f(x) as an argument, the outer and inner copies of f, despite being nominally the same, are relationally different: inside-to-outside is a different relation than outside-to-inside. Another way, the outer f takes as its argument a first-order function of x, while the inner function takes just individual x. (Wittgenstein 1933, Par 3.333) We can therefore say that the logical structure is directional or irreflexive. Thought about the world, or a thought about another though, is a different logical type to what the thought is about. The logical consequence of eliminating infinite regress and regaining consistency of thought is to render thought essentially incomplete, therefore non-deterministic. Russell’s paradox arising in case of direct self-reference can only be resolved in two ways: a) hierarchically, f(f(x)), but a hierarchy is Not a reflexive relation that conscousness consists in, b) socially, where individual x relates to itself by relating to a different individual y that relates to itself by relating to x, in terms of properties common to them both (but this is a separate argument).

Could incompleteness of reflexive thought still be just an effect of deterministic physical processes? If only that which is physically determinate (even if only probabilistically: adequate determinism) can be in a definite causal relation with anything else, and anything that is not in a definite causal relation either does not exist or is inconsequential to all other existents in the same world, then everything real and consequential must be a determinate part of a multiple. Another way, an indeterminate x neither satisfies nor violates the law of identity – that x is identical only to itself – therefore does not exist. The multiple must then also be determinate for anything to count as a determinate part of that multiple, but the existence of parts already presupposes the existence of the whole, an internally consistent relational totality: a world. The world includes itself as a constitutive condition of every determinate object that constitutes the world. We have thus reproduced the logical circularity of Russell’s Paradox at the physical object-level. If the physical world is complete then it is physically inconsistent and therefore unreal; if the world is consistent then it is essentially incomplete: objects cannot exist just on account of the object-world.

The sets of properties and relations that constitute the world ‘as we know it’ can only be defined at the meta-level with respect to the physical world: by thought. The world ‘as we know it’ is therefore only quasi-deterministic, presumed to be deterministic for purposes of practical rationality but essentially incomplete in regard to possibilities of description in terms of properties and relations.

While practical rationality relates to the world as quasi-deterministic, the present thought-act of determining or experiencing is essentially indeterministic: as shown above, thought is essentially incomplete. The present thought-act is subsequently objectified in the relational structure of the world as an object for another thought-act to relate to. To better illustrate the problem I will appropriate the ancient dictum of Sankara: “Brahman is real; the Universe is unreal; Brahman is the Universe”. In the context of the present argument this could be reconstructed as follows: Thought is indeterministic; the Universe is deterministic; Thought is the Universe. This paradoxical formula can be suitably interpreted along the lines followed by Hindu scholars in relation to Sankara’s dictum (Venkataramiah 1955, 290): the Universe is deterministic only in virtue of Thought that determines. Another way, indeterminism of thought is a constitutive condition of the deterministic Universe.

A committed proponent of determinism may object that just because the structure of thought is infinitely regressive does not entail that this property is not an immutable, nomological feature of reality. This idea strikes me as logically inconsistent. If reality is infinitely regressive then it is not definite, therefore not nomologically determinate as the hypothetical proponent of determinism suggests, therefore contradiction. I nonetheless accept that the hypothesis may be worth further consideration. Perhaps infinitely regressive reflexivity as a nomological (meta-level) feature of reality can be logically integrated with identity on the object level, but for now I do not see how this could work.

A sceptic might argue that rejection of determinism eliminates the problem of circularity but gives rise to another logical problem: it commits us to creation ex nihilo. Proponents of indeterministic thought must then explain how could thoughts arise without being fully determined by antecedent thoughts. I can think of two distinct ways of possibly satisfying this explanatory challenge. Appearance of thought ex nihilo could be explained by positing randomness as a fundamental property of thought. Suppose that every thought, despite being largely deterministic, possesses a random component, let us call it the capacity for ambiguity and error. Every thought could then be reasonably fitting for the occasion but containing something new, unconditioned by the past. This is still not a complete explanation as it simply posits randomness as a ‘mysterious’ feature of reality without showing how the random content could arise out of nothing. There is another, more robust possibility of accommodating creation ex nihilo. If time were itself a thought-construct, a logical rather than onto-logical property of reality, then thought would be essentially timeless, merging with our sense of time rather than emerging within it (I have shown here that emergence in time is impossible). This explanation faces a similar problem to simple randomness: it now posits timeless thought as a ‘mysterious’ property of reality. I do not know how to proceed beyond this explanatory limit.

Venkataramiah, Munagala. Talks with Sri Ramana Maharshi . Sri Ramanasramam, 1955.

. Sri Ramanasramam, 1955. Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica (Volume I) . Cambridge University Press, 1910.

. Cambridge University Press, 1910. Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Routledge & Kegan Paul, 1933.

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