The Temporality of Determinacy I: Philosophy of Non-Physical Sciences

Husbands, Conor

doi:10.1007/978-3-030-86530-6_3

Conor Husbands²

106 Accesses

Abstract

This chapter agglomerates evidence from the non-physical sciences in support of the temporality of determinacy. It identifies a number of fields in which the events being studied acquire determinacy, not atemporally, but in an order. It considers the work of Elena Esposito in the context of the theory of finance and economics, which provide several examples of this characteristic. It shows how the discipline of time series analysis and, in particular, recalcitrant data which display serial correlation and multicollinearity, refute strict forms of the atemporality conjecture. It locates similar conclusions in the work of Brian Massumi on the temporal logic of pre-emption. Finally, it explores the discipline of cryptography, in which the order of subject events (such as financial transactions) is the product of a dynamic consensus algorithm.

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Notes

1.
Abbott (2001), p. 37.
2.
Abbott (2001), p. 38.
3.
Abbott (2016), p. 238.
4.
Abbott (2001), p. 39.
5.
Abbott (2016), pp. xiv, 233–252.
6.
Abbott (2016), pp. 180–181.
7.
Abbott (2016), pp. ix–xi.
8.
Nietzsche (1967), p. 550.
9.
Abbott (2001), p. 38.
10.
Abbott (2001), p. 47.
11.
Abbott (2001), p. 51.
12.
Abbott (2001), pp. 56–57.
13.
Occasionally these are even mapped onto specific philosophical debates; in Abbott’s essay “The Idea of Outcome” he considers the assumptions of empirical sociology and microeconomics in terms of the philosophy of time of McTaggart, Bergson and Aristotle. See Abbott (2016), pp. 179–184.
14.
Robinson (1981), p.
15.
Robinson (1981), p. 89.
16.
Esposito (2011), p. 9.
17.
Esposito (2011), p. 6.
18.
Keynes (1936), p. 9.
19.
Keynes (1936), p. 25.
20.
Malik (2014), pp. 629–812.
21.
Soros (1987), p. 26.
22.
Esposito (2011), p. 40.
23.
Esposito (2011), p. 105.
24.
Esposito (2011), p. 54.
25.
Esposito (2011), p. 11.
26.
Esposito (2011), p. 22.
27.
Husbands (2020a), p. 117.
28.
This terminology Esposito takes over from Niklas Luhmann, particularly Luhmann (1981), pp. 126–50.
29.
Esposito (2011), p. 23.
30.
Brown (2005), p. 19.
31.
Barbour (1989).
32.
Esposito (2011), p. 23.
33.
Newton (1999).
34.
Esposito (2011), p. 22.
35.
Fama (1970).
36.
Fama (1970), p. 414.
37.
Soros (1987), p. 2.
38.
See also on this notion of reflexivity the work of Malik (2014), pp. 717–718.
39.
Soros (1987), p. 29.
40.
Esposito (2011), p. 136.
41.
Brassier et al. (2017), p. 95.
42.
Brassier et al. (2017). It should be noted that Brassier’s account addresses primarily Suhail Malik’s essay “The Ontology of Finance” in the 2014 edition of Collapse. In this respect, Brassier addresses Esposito’s argument secondarily, that is, to the extent that Malik’s research relies heavily on hers.
43.
Esposito (2011), pp. 23, 27–28.
44.
Brassier et al. (2017).
45.
Esposito (2011), p. 136.
46.
Jon Roffe establishes a similar distinction in his own research in the theory of finance Abstract Market Theory. See Roffe (2015), p. 4.
47.
Esposito (2011), p. 136.
48.
It is worth observing that whilst this case compares the expected value of the future spot price with the spot price at the reference time, a related question arises in the context of discussions which compare the former to the price of a futures contract on the same underlying asset. Futures are standardized, exchange-traded contracts which oblige two parties to exchange a good on a specified date for a specified price, though rarely involving the delivery of the reference asset and often transacted for speculative purposes. These discussions consider why the expected value of the spot price three months later should differ from the traded futures price. They attempt to account for this difference in terms of determinate and evaluable circumstantial factors: storage costs, dividends, convenience yields, interest rates, risk reduction benefits, correlation with other markets and other variables, all of which make the temporal interval between the formation of the initial expected value and the future three months later a source of inequivalence. There is, however, a residual question as to whether these variables could ever provide a complete account of this inequivalence. To the extent that these differ in ways unaccountable by determinate factors, this is because neither the value of the asset nor the worth is not determined, but only modelled output, simulated worth, or subjective instinct, conferring a statistical or judgmental rather than an objective meaning. See e.g. Hull (2002), pp. 56–63.
49.
Even today, financial commentators on asset classes which are frequently described as bubbles refer to the questions over this description as moot until after the bubble is (or is not) burst; see for a recent example UBS Global Real Estate Bubble Index, UBS Chief Investment Office (2020).
50.
Esposito (2011), pp. 27–28.
51.
Hull (2002), p. 246.
52.
Esposito (2011), p. 139.
53.
Esposito (2011), p. 9.
54.
Esposito (2011), p. 134.
55.
Malik (2014), pp. 629–636.
56.
Esposito (2011), p. 105.
57.
A similar distinction to Esposito’s, the distinction between market pricing and value, is analysed at length in Roffe (2015), and Mackenzie (2006).
58.
These confer the right but not the obligation to purchase a security at an agreed strike price at an agreed time, or within an agreed time-window. See Hull (2002).
59.
It is interesting and surprising to observe that in spite of their almost entirely antithetical line of thinking on this matter, Lindsay and Margenau intimate the existence of a similar distinction between different temporal parameters at work in systems and their descriptions, both with their modulating criteria for the time-independence of a law, and with their limitation of the scope of their claims about the time-independence of laws to closed causal systems, paralleling the notion of endogeneity which appears in the rather different context of Esposito’s work. See Lindsay and Margenau (1963) and Margenau (1977).
60.
Russell (1918), p. 199.
61.
This notation follows that of Anderson and Zalta (2004).
62.
Esposito (2018), pp. 219–220.
63.
Esposito (2011), pp. 24–25.
64.
Johnson (2016), p. 189.
65.
Roffe (2015), p. 150.
66.
Roffe goes so far as to declare that belief in the reliability of pricing models constitutes a kind of mental sickness, and ascribes an absolute uncertainty, unknowability and unpredictability to future states. Roffe (2015), p. 14.
67.
Malik (2014), p. 715.
68.
Malik (2014), p. 718.
69.
See Ayache (2010) and Ayache (2015). The latter (p. 137) features his claim that the derivatives market could be regarded as a form of Brownian motion.
70.
See Mackenzie (2006).
71.
Hamilton (1994).
72.
Campbell, Lo and MacKinlay (1997), pp. 8–9.
73.
Brock and De Lima (1996).
74.
Hamilton (1994), p. 25.
75.
This, provided a suitable definition of the matrices, coheres with Abbott’s framing of the role of the GLM which, as recounted earlier in this chapter, can be expressed in the form X_t = X_t − 1B + U.
76.
Hamilton (1994), p. 45.
77.
Chatfield and Xing (2019), p. 17.
78.
Chatfield and Xing (2019), p. 43.
79.
Hamilton (1994) and Chatfield and Xing (2019), p. 16.
80.
Chatfield and Xing (2019), p. 41.
81.
Chatfield and Xing (2019), p. 42.
82.
Chatfield and Xing (2019), p. 9 allude to this relationship as one of partial determination of the system’s behaviour given initial (past) conditions—as well as once again disinterring the problematic relationship between determinism and predictability. Deterministic time series are those which can be predicted exactly, stochastic time series are those for which the history of the system determines its future only to a partial degree, meaning future outcomes are best described by a probability distribution.
83.
Chatfield and Xing (2019), p. 42.
84.
Chatfield and Xing (2019), p. 45.
85.
Berkovitz et al. (2006), pp. 668–671.
86.
Grimmett and Stirzaker (2001), p. 47.
87.
More formally, Grimmett and Stirzaker state that the probability mass function associated with random variable X is defined as f : R → [0, 1] where f(x) = P(X = x). See Grimmett and Stirzaker (2001), p. 46.
88.
Russell (1918), p. 199.
89.
Hamilton (1994), p. 45.
90.
Lindsay and Margenau (1963), p. 522.
91.
Massumi (2010), p. 1.
92.
Massumi (2015), p. 5.
93.
Massumi (2015), p. 191.
94.
Massumi (2015), pp. 42, 107, 137.
95.
Massumi (2015), p. 194.
96.
Massumi (2015), p. 203.
97.
Massumi (2015), p. 13.
98.
Avanessian and Malik (n.d.).
99.
Massumi (2015), p. 13.
100.
An iterated modality traps a modal operator within the scope of another, so that two or more such modal operators occur in the relevant formula.
101.
Massumi (2015), p. 3.
102.
Schmitt and Stevenson (2004).
103.
Massumi (2015), p. 191.
104.
Massumi (2015), p. 191.
105.
Massumi (2015), p. 190.
106.
Trzęsicki (2015), p. 140.
107.
Trzęsicki (2015), p. 141.
108.
Trzęsicki (2015), p. 141.
109.
Trzęsicki (2015), p. 143.
110.
It should be noted that addition of this branching structure is not uncontroversial in discussions of temporal logic. See e.g. Goranko and Rumberg (2020).
111.
Trzęsicki (2015), p. 143. More fully, Trzęsicki claims that in branching temporal logic he sets out, the statement that a proposition will be true is determined if, and only if, for all branches, it will be true at some future moment. ‘it will be φ ’ is determined iff on each branch at some moment in the future it will be φ.
112.
Trzęsicki (2015), pp. 143–144.
113.
Trzęsicki (2015), p. 144.
114.
Massumi uses terminology similar to the images of branching to describe the modality of future moments, referring to future moments cutting into the present, co-presences of moments with other moments, and spatialized modes of time, conceived as convergent and divergent series of paths. See Massumi (2015), p. 117.
115.
Trzęsicki (2015), p. 144.
116.
Goranko and Rumberg (2020).
117.
Formally, T = {1, 2}, I = {a, b}, 1 < 2, p ∈ V_a(1), p ∈ V_b(1), (2, a) ⊲ (2, b), but it is false that (1, a) ⊲ (1, b). Trzęsicki (2015), p. 157.
118.
More fully,we have that 〈T, < , ⊲ , V_i〉, t ⊨ □ φ iff for any j : if (t, i) ⊲ (t, j), then 〈T, < , ⊲ , V_j〉, t ⊨ φ. Take i = a, t = 1. Since (1, a) ⊲ (1, b) fails, 〈T, < , ⊲ , V_a〉, 1 ⊨ □ φ. However, the definition of P requires that 〈T, < , ⊲ , V_i〉, t ⊨ Pφ iff there is t₁ ∈ T, t₁ < t such that: for any j ∈ I: if (t, j) ⊲ (t, i), then 〈T, < , ⊲ , V_j〉, t₁ ⊨ φ. For i = a, t = 1, there is no such t₁. <t, so whilst 〈T, < , ⊲ , V_i〉, t ⊨ □ φ holds 〈T, < , ⊲ , V_i〉, t ⊨ GPφ does not. Thus □φ → GPφ fails.
119.
Kant (1933), A426/B454.
120.
Everettian quantum mechanics offers a deterministic account of the world’s evolution, which takes place in accordance with the Schrödinger equation, as a superposition of basis states, each of which is taken to correspond to an independent world. The universe’s evolution thus takes on a branching structure. See e.g. Wallace (2012).
121.
Massumi (2015), p. 191.
122.
Massumi (2015), p. 3.
123.
Schmitt and Stevenson (2004).
124.
Massumi (2015), p. 191.
125.
Massumi (2015), p. 190.
126.
Trzęsicki (2015), p. 141.
127.
Massumi (2015), p. 194.
128.
Massumi (2015), p. 137.
129.
Massumi (2015), p. 117.
130.
Deleuze (2004), pp. 89–93.
131.
Coinmarketcap.com.
132.
https://ledgerjournal.org/ojs/ledger.
133.
Nakomoto (2008b).
134.
Land (2018), p. 1356.
135.
In particular, the claim is that protocols employed by blockchain-instantiating cryptocurrencies provide an “absolute” basis for assigning temporal coordinates to events.
136.
Lanksy (2018), p. 19 defines incorporation of distributed consensus as one of six marks of cryptocurrencies.
137.
Eyal and Sirer (2013), p. 1.
138.
Narayanan et al. (2015), p. 14.
139.
Narayanan et al. (2015), pp. 25–26.
140.
Back (2002).
141.
Narayanan et al. (2015), p. 39.
142.
Narayanan et al. (2015). p. 39.
143.
Nakomoto (2008a), p. 2.
144.
This said, an actor able to command a significant amount of the computing power on the network could succeed in defrauding others, by ignoring newly mined blocks which contains transactions they wish to reverse (such as them remitting currency to another party) and begin mining from the latest block which does not include such a transaction. The probability of successfully mining enough blocks without being beaten to the punch by another miner scales with the available computing power. Some species of these attacks, sometimes deemed block-withholding attacks involve the party successfully mining a block and deliberately failing to broadcast it, with the hope of discovering several consecutive blocks, independent of the rest of the chain. If successful in mining these blocks quicker than the communicative nodes, the saboteur could then declare them all at once, departing from an earlier block in the chain, overtaking and thus superceding the chain with which other miners are preoccupied, “orphaning” any blocks mined by them in the interim. Narayanan et al. (2015), p. 73.
145.
Nakomoto (2008a), p. 3.
146.
Nakomoto (2008b).
147.
Nakomoto (2008a), p. 1.
148.
Nakomoto (2008a).
149.
Indeed, going back further still, problems of synchronisation were fundamental long before the advent of modern computing and the development of systems theory. Peter Galison’s text Einstein’s Clocks, Poincaré’s Maps: Empires of Time presents a comparative history of the two physicists’ careers, and attempts to locate their innovations in electrodynamics in the socio-political context of nineteenth and twentieth Century Europe, together with the practical rather than theoretical engineering challenges which beset both of them in their extra-academic lives. See Galison (2004).
150.
Kangasharju (2013), p. 8.
151.
See e.g. Turner (2007), Lamport (1998, 2001, 2005).
152.
Lamport (2001), p. 2.
153.
Turner (2007), pp. 3–4.
154.
Lamport (2005), p. 1.
155.
Turner (2007), p. 16.
156.
More fully, Narayanan et al. identify “four checks” performed by nodes as necessary but not sufficient conditions for acceptance of a broadcast transaction. See Narayanan et al. (2015), p. 72.
157.
Wood (2018), p. 2.
158.
Bonneau et al. (2015), p. 10.
159.
Lamport indulges a broader metaphysical hypothesis, going so far as to claim that time is derivative from event-ordering. Lamport (1978), p. 558.
160.
Narayanan et al. (2015), p. 72.
161.
Of course, this assumes that the credit line available to the participants is a parsimonious one.
162.
Strictly speaking, it is mistaken to equate events, transactions and the formation of blocks. There cannot be a one-for-one correspondence of the latter to the former, since blocks embed a large number of transactions, taking a significant amount of time to mine. At the beginning of 2020, this time averaged out at around ten minutes: see e.g. Narayanan et al. (2015), p. 45, or https://data.bitcoinity.org/bitcoin/block_time/.
163.
For a mathematical illustration of this see Nakomoto (2008a), pp. 6–8.
164.
Narayanan et al. (2015), p. 144.
165.
Nakamoto (2008a), p. 5.
166.
Brassier et al., (2017).
167.
Poincaré (1913), p. 234.
168.
Brown (2005), p. 19.
169.
This principle has been referred to as the correspondence principle and is occasionally (controversially) attributed to the work of Niels Bohr. See e.g. Bokulich and Bokulich (2020).
170.
Albert (1992), pp. 43–44.
171.
Hesse (1962), p. 152.
172.
Russell’s concern, for example, is with whether “there is a functional relation of the form” specified. Russell (1918), p. 199.
173.
Peirce (1891).
174.
Peirce (1982–1993), p. 293.
175.
Smolin (2013), p. 123.
176.
Smolin (2013), p. 97.
177.
Smolin (1997), p. 106.

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Husbands, C. (2022). The Temporality of Determinacy I: Philosophy of Non-Physical Sciences. In: The Temporality of Determinacy. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-86530-6_3

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DOI: https://doi.org/10.1007/978-3-030-86530-6_3
Published: 17 June 2022
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-030-86529-0
Online ISBN: 978-3-030-86530-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)

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