Abstract
What is possible, according to the empiricist conception, is what our evidence positively allows; and what is necessary is what it compels. These notions, along with logical possibility, are the only defensible notions of possibility and necessity. In so far as nomic and metaphysical possibilities are defensible, they fall within empirical possibility. These empirical conceptions are incompatible with traditional possible world semantics. Empirically necessary propositions cannot be defined as those true in all possible worlds. There can be empirical possibilities without empirical necessities. The duality of possibility and necessity can be degenerate and can even be falsified.
My thanks to Yemima Ben-Menahem, Jeremy Butterfield, Patrick Dürr, Carl Hoefer, Edouard Machery, Brian McLoone, James Norton, Matt Parker, Bryan Roberts, Margot Strohminger and Jim Woodward for helpful discussion. They bear no responsibility for the content of this paper other than for failing to talk me out of it.
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Notes
- 1.
A “small-e” empiricist holds that we can only learn contingent truths of the world from experiences of the world. A “big-E” Empiricist holds the stronger view that these experiences are all we can learn.
- 2.
The two arguments are the “cosmological” and the “ontological” arguments for god’s existence. Van Inwagen (2009, Ch. 6 and 7) provides a contemporary formulation and discussion. He coincedes (p. 141) that all versions of ontological argument depends on some logical error or unsupported premise.
- 3.
Kripke (1980), pp. 123–25.
- 4.
The standard philosopher’s understanding of experience as that which we sense directly is wholly inadequate to explicate how evidence from the world is used in science. Boyd (2018) provides a serviceable, updated account.
- 5.
A contingent proposition is here taken to be one that may be either true or false according to the state of the world. That is, its truth or falsity is not compelled by the meaning of the terms in the proposition.
- 6.
This option concerning a sufficient level of inductive support will be elaborated below.
- 7.
In Norton (2021) and earlier papers cited there.
- 8.
The restriction to contingent propositions is needed since it is usually held that any body of evidence deductively entails a tautology. Without the restriction, we could then find that, on the evidence of a coin toss, it is empirically necessary that either dinosaurs once lived or dinosaurs once did not live. This awkward result would arise in a set of propositions concerning coin tosses and dinosaurs, but where the evidence consists only of propositions about coin tosses.
- 9.
Kment (2014, p. 2) is a welcome exception in the literature that allows for degrees of possibility.
- 10.
The probability of no heads in ten tosses is (1/2)10 = 0.0009766 and of at least one head in ten such tosses is 1 – (1/2)10 = 0.9990234.
- 11.
Roca-Royes (2017) develops an empiricist epistemology of de re possibility (but not necessity). Her project differs from that of this paper in that it is epistemic. It concerns how we come to know some possibilities inductively. Here those possibilities are reduced to the inductive relations themselves.
- 12.
“To say that a world w is a complete way things might have been is to say that for each proposition in the sphere of discourse under discussion, w either verifies or falsifies that proposition;…” From the entry “Possible Worlds,” in Kim (2009, p. 502, emphasis in original).
- 13.
For one account of this episode, see Norton (2021, Ch. 9, Sect. 7).
- 14.
This is not a typographical error. For justification, see Norton (2010).
- 15.
An interval (x, y) is non-empty just if y > x.
- 16.
The probability of no heads in nine tosses is (1/2)9 = 0.001953; and the probability of at least one head in nine tosses is 1 − (1/2)9 = 0.998047.
- 17.
The atomic propositions specify a specific sequence of nine coin toss outcomes, each with (1/2)9 = 0.001953. So the most probable proposition not entailed by the evidence is just a negation of a single atom, which has probability 1 − (1/2)9 = 0.998047.
- 18.
For a brief survey of decline of steady-state cosmology, see Norton (2021, Ch. 9, Sect. 8). It has also proved difficult to find a general formulation in general relativity that expresses the conservation of energy, understood as a conserved quantity extended over space. For a comprehensive survey of these problems, see Duerr (ms).
- 19.
How can this be? Very briefly, given the paucity of evidence, we do not know if the correct representation of the parameter is h or 1/h. The conditions 0 < h < 1 corresponds to 1 < 1/h<∞; and 0 < 1/h < 1 corresponds to 1 < h<∞.
- 20.
Of course, theorists of epistemic possibility know this, but that does not ameliorate the failures.
- 21.
In physics, where we might hope to find universal truths, we know of none. General relativity is our best account of space, time and gravitation, but it fails in the very small. Quantum theory is our best account of matter in the very small, but it fails where general relativity thrives, in domains of very strong gravity.
- 22.
This holds of a case examined in more detail by Ismael (2017, p. 116): theories based on physical chances, formulated in terms of probabilities. For they just tell us that the evidence of the antecedent supports various consequents according to the inductive strengths of the associated probabilities.
- 23.
Their footnote: “In contemporary discussions, at any rate.”
- 24.
Fine’s footnote: “It seems to be something like this that [Kripke (1980, p. 99)] has in mind when he talks of necessity ‘in the highest degree.’”
- 25.
An electron in a bimodal well can be present equally in both, even if the wells are separated by great distances. This impossibility required no god to break it, but merely Erwin Schroedinger.
- 26.
Kripke (1980, p. 127) “According to the view I advocate, then, terms for natural kinds are much closer to proper names than is ordinarily supposed.”
- 27.
A growing body of empirical evidence, such as in Machery et al. (2004), shows that there is nothing fixed and thus nothing necessary about these conventions. They vary with the culture of the language users.
- 28.
Putnam is also celebrated for the claim that “water” rigidly refers to H2O. He, however, seems to defer to Kripke for the claim that there is a metaphysical necessity to the rigidity. See Putnam (1975, p. 151).
- 29.
Kripke (1980, pp. 35–36) identifies the sense of necessity explicated as metaphysical: “The second concept which is in question is that of necessity…. what I am concerned with here is a notion which is not a notion of epistemology but of metaphysics, in some (I hope) nonpejorative sense.”
- 30.
The admission is explicit for a neighboring science: Kripke (1980, p. 117) writes “… I don’t know too much chemistry.”
- 31.
Van Inwagen and Sullivan (2020)’s first sentence is: “It is not easy to say what metaphysics is.”; and the first section begins: “The word ‘metaphysics’ is notoriously hard to define.”
- 32.
For the complaint that these distinctions lack empirical manifestations, see Norton (2015).
- 33.
Editor’s notes, p. xxxv in Hume (1777).
- 34.
For a more equivocal appraisal of the two approaches, see Guay and Pradeu (2020).
- 35.
Ney (2014, p. xiii) gives a similar characterization: “Unlike the natural and social sciences that seek to describe some special class of entities and what they are like—the physical things or the living things, particular civilizations or cultures—metaphysicians ask the most general questions about how things are, what our universe is like.”
- 36.
These continuing corrections to causal metaphysics are unlike the continuing corrections within science. For the corrections in science derive from the science itself through the epistemic power of its empirical methods. Causal metaphysics has no corresponding power and no means for finding its own errors. The corrections are imposed from the outside.
- 37.
For a sketch of the debate, see Bliss and Trogdon (2016, Sect. 1).
- 38.
For a further critique, see Clarke-Doane (2019) who argues that metaphysical possibility lacks the absoluteness routinely claimed for it.
- 39.
In his demonstration of the completeness of the modal logic S5*=, Kripke (1959, p. 2) defines a subformula B as necessary if it is assigned T by every member of some set of interpretive assignments K. Crucially, if B contains free individual variables x 1, …, x n, each must be assigned the same individual in the domain D by every assignment of K. Williamson (2013, p. 120) describes this as “treating variables as rigid designators.”
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Norton, J.D. (2022). How to Make Possibility Safe for Empiricists. In: Ben-Menahem, Y. (eds) Rethinking the Concept of Law of Nature . Jerusalem Studies in Philosophy and History of Science. Springer, Cham. https://doi.org/10.1007/978-3-030-96775-8_5
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