In the previous article in the C-theory series I have argued that the present is not experienced as a point in time but as a meaningful event whose phenomenal duration may vary depending on its relational properties. By existentially quantifying over a particular evental identity we invoke a window of time for that evental identity to be realised as the present, and that constitutes the characteristic duration of its phenomenal unity. In this article I formulate a C-theoretic account of change and then show how the C-structure of a world can be temporalised on two dimensions.
When we say that x has changed we imply two things: first, relative change of x with respect to not-x and, second, ontic continuity of x being unaffected by that change. In other words, the nominal identity x endures despite constitutive or contextual changes in the object identified as x: “change needs identity as well as difference.” (Mellor 1998, 89) This, we can say, is the sense of change. The above description applies to total replacement of a thing as much as to partial change in the constitution of a thing, because replacement is meaningful only if there is an enduring placeholder or functional identity that answers the question of what is being re-placed.
Nothing changes in itself unless it also changes for something else. (Axiom of Relational Ontology)
Only that which endures through change can be said to change, but, insofar as the constitutive sequence of an object has directional logic (from condition to the conditional), something new is created in addition to that which existed prior to the change: nominally, x+Δx replaces x. The content of change (Δx), the pure difference between x-condition and x-conditional, has no history prior to the change. The past of the new can be construed only by locating its genesis in the constitutive order of that which is not-new, but temporal continuity of the not-new does not of itself account for emergence of the new.
In the absence of information-content in the present instant, perception of change may be accounted for by either positing emergence of the new in the constitutive structure, as a necessary consequence of the logically prior step in the constitutive sequence, or in the consciousness of the witness. The first hypothesis entails both supervenience and super-determinism, and thus casts doubt on free-will as well as on agential causative power, making it untestable from the position of agency and therefore philosophically uninteresting. The only hypothesis worth pursuing is that of perception of change and its corollary – the primitive present – being just properties of reflexive consciousness that stands not within but above the constitutive structure and thus eliminates supervenience while preserving the possibility of free-will.
“A singularity is that with which a thought begins. But if this beginning is a mere consequence of the logical laws of a world, it merely appears in its place and begins – strictly speaking – nothing.” (Badiou 2009, 357) If thought, as proposed by Badiou, entails a singularity that may give rise to conception of a new being, then any subsequent change in that being implies its logical continuation under the same nominal identity plus another singularity: the conception of pure difference within identity (Δ). The internal difference has no history beyond the present of its own realisation, establishing thereby a fixed direction in the logical order of change where every thought constitutes a new present. “The existential now is determined by the present of preoccupation…” (Ricoeur 1984, 63)
A thought that gave rise to the conception of a new being cannot be ever un-thought but only negated by another thought, by a new thought that does not erase the primary thought but adds to it. “By negating a concept, one only manages to create another concept.” (Kojève 1980, 256) The negated thought is retained in the constitutive structure as a condition that gives meaning to its subsequent negation, maintaining thereby logical continuity and order of the ‘historical’ process that is constitutively irreversible. In other words, change does not erase being but introduces a new being that either comes under an existing identity and thus, nominally, merges with it; or is separated from the existing identity and thus becomes a different being. The negated state of being does not inexist but, having once existed, retains its place within the constitutive order of the present being. “There is no such thing as ceasing to exist (…). When we say that something has ceased to exist we only mean that it has ceased to be present; and this only means that the sum total of existence has increased.” (Broad 1923, 69)
I can now incorporate the phenomenal present (singularity) into the constitutive structure of the abcd-world by taking account of the negated state of being (⊙), change (Δ), and conditionality (↚). The following diagram shows two consecutive states in the C-structure, where t and ti signify, respectively, the condition and its immediate conditional in the constitutive order:
The next diagram shows the time-matrix for the originary object d which is in continuous, positive existence over a lifespan of four t increments in the constitutive sequence (horizontal axis), until it is negated at two t increments before the phenomenal present (‘now’). For each state in the constititive sequence, the past of d is subject to a different historical identity (vertical axis).
Apart from the relational content of the C-structure, the historical and the constitutive dimension resemble the A-series and the B-series, respectively. I am therefore in agreement with Mellor (1998, 13) that “each B-moment defines a different A-series, namely that in which it is the present moment”, but I disagree insofar as A- and B-series lack the unity of one temporal whole for a system of objects.
The fenced-off areas in the time-matrix above mark two states in the constitutive sequence (C-series). The C-series-d at t shows d as having no history at t; the C-series at ti shows d in two constitutive steps under the same historical identity di. The object d does not have a fixed historical identity but continues to change historically and is indexed accordingly. Since the C-structure has a topological-coordinative effect that precludes evental ambiguity, a compatible matrix can be constructed for any C-series without incurring the kind of temporal contradiction identified by McTaggart.
For the C-structure to be consistent it is only necessary for the principle of conditionality not to be violated. The temporal matrix, on the other hand, expresses the logic of internal difference: the differences within the object-identity. But since all difference, if it is to retain the character of relation, must belong to the same constitutive order of existence, it is further concluded that time is a systemically internal, constitutive relation, dependent on the positive ontological status and consistency of the C-series (a logical condition of being-in-a-world), and on singularity of consciousness that generates change as the present.
“The passage from the idea of a static relation to that of a dynamic operation implies an actual addition to the taxonomic model, which genuinely does chronologize it, at least in the sense that a transformation takes time.” (Ricoeur 1985, 57)
In this series of articles I have argued that time can be consistently modelled as a biaxial, homogeneous relation between multiple orders of internal difference. Every order of internal difference signifies a unique object-identity undergoing constitutive change, which is in turn topologically and qualitatively ordered with respect to other object-identities. The conditional logic of internal difference guarantees irreversibility of the order, while episodic (constitutive sequence) and configurational (historical) dimensions of time express systemic consistency of a relationally unified object-set (C-structure). Time characterised in this way is a logical property of appearing in a world. Finally, the notion of appearing presupposes a transcendental limit with respect to which different articulations of the same identity are temporally related, and the most plausible transcendental limit of appearing is consciousness.
- Badiou, Alain. Logics of Worlds: Being and Event II. London: Continuum, 2009.
- Broad, C. D. Scientific Thought. London: Kegan Paul, Trench, Trubner & Co., 1923.
- Kojève, Alexandre. Introduction to the Reading of Hegel. Ithaca and London: Cornell University Press, 1980.
- Mellor, D. H. Real Rime II. London: Routledge, 1998.
- Ricoeur, Paul. Time and Narrative (Volume 1). Chicago: The University of Chicago Press, 1984.
- Ricoeur, Paul. Time and Narrative (Volume 2). Chicago: The University of Chicago Press, 1985.