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[The following is summary]
Gilles Deleuze's Philosophy of Time:
A Critical Introduction and Guide
Chapter 2: The first synthesis of time
Part 1: The living present
What do the synthetic processes of Deleuze's living present got to do with you?
Deleuze offers a sense of the living present that like in phenomenology regards it as a passive synthesis bringing together past and future events into the present, but unlike phenomenology, this sort of passively synthesized time does not proceed forwardly on account of a primordial flow of phenomenal time but rather the arrow of time results from the asymmetry between the particularity of the selected past events whose selections determine paths to the generalities of awaited futures.
To understand why contraction is not simply memory, we first consider Deleuze's notion of 'repetition for itself'. (22c) Deleuze observes this following paradox:
a) for something to repeat, one instance needs to be related to another instance
b) but this means each instance must have occurred independently (22-23)
Thus repetition implies that all instances are not in themselves related, so something outside them must contract them. (23a)
"This is a case of Deleuze's reliance on Leibniz's law or the principle of indiscernibility of indenticals: '... no two substances are entirely alike and differ only in number ' (Leibniz, 1998:60)" [Leibniz Philosophical Texts Oxford]
If one instance was followed by another that is exactly the same, then really there has not been the movement to another instance.
"The paradox of repetition is then that although it is defined as the repetition of something that is the same, it can only be the repetition of a difference for something that is not the repeated thing". (23bc)
So when we think we are repeating something, in fact each occurrence is distinct from the others. Secondarily our mind contracts them, and in that way, as Deleuze writes "Repetition ... changes nothing in the object, in the state of things AB. ... a change takes place in the mind that contemplates. (DRf, 96)" [qtd, with my elipses, from Williams 23d]
Deleuze's explanation for the relation of instants in time cannot
a) involve conceiving instants as implying one another, because they are independent, and it cannot
b) portray instants as being contained in a larger grouping [like divisions of a flow of time], because that means all instants share a certain property and thus there would be a connection between instants that we have already said were inherently unconnected.
"Repetition does not require a mind, it requires a contraction. Repetition does not take place in time, but rather time - or one of the syntheses of time, the first one - is a contraction: 'Properly speaking, [contraction] forms a synthesis of time' (DRf, 97)." (24d)
Contraction's 'third term' then is not necessarily a mind but is rather a process. (24d) And it is an 'originary' but not an 'original' synthesis. (25a) It is not original, because it is not the fundamental ground of time. But since it produces a sort of temporality, contractive time, we may still consider it originary. (25a.b)
The first synthesis, or living present, is a process that brings together the past and future, because past occurrences are contracted into the present one, and future occurrences that will later contract with the current and past ones are now being anticipated. (25c.d) "This leads Deleuze to make the claim that past and future are only dimensions of the living present with no existence distinct from their contraction in it." (25d) Our memory and understanding cannot conceivably perform an action that remembers every single past contracted occurrence and anticipate every sort of future one, so the contraction cannot be considered active and is thus a passive synthesis. (26b)
The first synthesis contracts particular past occurrences with the present one, yet it cannot know in advance the future ones, so it 'awaits' rather than expects generalities and not particulars in the future. (26-27) And because the quantity of particulars and generalities is too great for any act of the mind to consider all at once, this contraction is an unconscious receptivity rather than a conscious action. (27b) It does not select specific particulars and thus is not an activity.
"even in activity the present is contemplation, that is, passive absorption and transformation of retained particulars beyond the set considered in an action." (26b) "passivity and activity are distinguished as processes where passivity is a form of retention and of expectation that is not related through a process selecting particular past events and associating them with a restricted number of general outcomes. This latter process is activity, but passivity is the wider condition for any active process." (26d)
Because past contracted events are particular and future ones are general, there is an asymmetry resulting from the first synthesis and it is responsible for the forward-pointing arrow of time. (28c)
"The passage is from particular to general and not the reverse." (28c) "Asymmetry [...] refers to the essential difference between particulars and generalities, where the former are actual and retained and transformed in the present and the latter are possible and expected in the present. There is no symmetry between the two because any set of particulars determines a much wider set of generalities, yet also, any given set of generalities neither determines nor includes a set of particulars." (28-29)
We may now reject two interpretations of the living present. It is not
The subject involved in the second synthesis is not an acting human subject but is rather a subject that makes the transformation between past particulars and future generalities. (29bc)
In sum, the living present is necessary because otherwise repeated terms would have no connections. The synthesis establishes paths from the particular past events that it selects to future expected possible outcomes that are determined by that given selection. (29-30) "there is no repetition, no relation between actual events and possible events, and no relation between instants, without the living present." (30ab)
Williams, James. Gilles Deleuze's Philosophy of Time: A Critical Introduction and Guide. Edinburgh: Edinburgh University Press, 2011.