An Argument For Necessitism*

Goodman, Jeremy

doi:10.1111/phpe.12086

Cited by 17 publications

(8 citation statements)

References 30 publications

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“…Furthermore, if we accept The Identity Identity , we can derive these principles from the following natural analogues of Booleanism for the quantifiers:

\begin{matrix} true \\ left (false(λ v_{10} \dots v_{n} . A false) \equiv false(λ v_{1} \dots v_{n} . A \land B false)) \leftrightarrow (false(λ v_{1} \dots v_{n} . \exists v_{0} (A) false) \equiv false(λ v_{1} \dots v_{n} . \exists v_{0} (A) \land B false)) \\ left (false(λ v_{10} \dots v_{n} . A false) \equiv false(λ v_{1} \dots v_{n} . A \lor B false)) \leftrightarrow (false(λ v_{1} \dots v_{n} . \forall v_{0} (A) false) \equiv false(λ v_{1} \dots v_{n} . \forall v_{0} (A) \lor B false)) \end{matrix}

(Here B is a formula in which v 0 does not occur free. See Dorr and J. Goodman for more on these “Adjunction” principles.) To get to S5, on the other hand, we would have to add something much less clearly well‐motivated, namely the

□

‐necessity of distinctness:

false(x ≢_{τ} y false) \to false((x ≢_{τ} y) \equiv ⊤ false)

For arguments that Booleans should reject this principle, see see Bacon MS and J. Goodman MS.…”

mentioning

confidence: 99%

“…(Here B is a formula in which v 0 does not occur free. See Dorr and J. Goodman for more on these “Adjunction” principles.) To get to S5, on the other hand, we would have to add something much less clearly well‐motivated, namely the

□

‐necessity of distinctness:

false(x ≢_{τ} y false) \to false((x ≢_{τ} y) \equiv ⊤ false)

For arguments that Booleans should reject this principle, see see Bacon MS and J. Goodman MS.…”

mentioning

confidence: 99%

See 1 more Smart Citation

To Be F Is To Be G

Dorr¹

2016

Philosophical Perspectives

151

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“…Furthermore, if we accept The Identity Identity , we can derive these principles from the following natural analogues of Booleanism for the quantifiers:

\begin{matrix} true \\ left (false(λ v_{10} \dots v_{n} . A false) \equiv false(λ v_{1} \dots v_{n} . A \land B false)) \leftrightarrow (false(λ v_{1} \dots v_{n} . \exists v_{0} (A) false) \equiv false(λ v_{1} \dots v_{n} . \exists v_{0} (A) \land B false)) \\ left (false(λ v_{10} \dots v_{n} . A false) \equiv false(λ v_{1} \dots v_{n} . A \lor B false)) \leftrightarrow (false(λ v_{1} \dots v_{n} . \forall v_{0} (A) false) \equiv false(λ v_{1} \dots v_{n} . \forall v_{0} (A) \lor B false)) \end{matrix}

□

‐necessity of distinctness:

false(x ≢_{τ} y false) \to false((x ≢_{τ} y) \equiv ⊤ false)

For arguments that Booleans should reject this principle, see see Bacon MS and J. Goodman MS.…”

mentioning

confidence: 99%

□

‐necessity of distinctness:

false(x ≢_{τ} y false) \to false((x ≢_{τ} y) \equiv ⊤ false)

For arguments that Booleans should reject this principle, see see Bacon MS and J. Goodman MS.…”

mentioning

confidence: 99%

To Be F Is To Be G

Dorr¹

2016

Philosophical Perspectives

151

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“…We can discern two important routes along which higher‐order modal logic is taken to lead to necessitism (for a third one, see Goodman, 2016b). Both proceed via higher‐order necessitism, the view that necessarily all higher‐order properties, relations and propositions exist necessarily (a formal instance of which is: □∀ X □∃ Y ( X ≡ Y )).…”

Section: Higher‐order Metaphysics Of Modalitymentioning

confidence: 99%

Higher‐order metaphysics

Skiba

2021

Philosophy Compass

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Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher‐order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico‐philosophical toolbox, while neither being reducible to nor fully explicable in terms of first‐order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, as well as on the metaphysics of modality.

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“…We cannot take for granted that

⌜ (λ x . φ) ⌝

can be faithfully glossed as

⌜

is an

x

such that

φ ⌝

– i.e., that it is equivalent to

⌜ (λ y . \exists x (x = y \land φ)) ⌝

. (Goodman (2016) makes a parallel point in reply to those like like Stalnaker (2012) who maintain that

(λ x . (λ y . \neg \exists z (z = y)) x) a = (λ x . \neg \exists z (z = x)) a ⃗ (λ y . \neg \exists z (z = y)) a = \neg \exists z (z = a)

is a counterexample to Reduction Congruence for

a

that only contingently exist.) This is important to keep in mind, since below we will consider the view of Bacon & Russell (2017) according to which not only does this equivalence fail, but the above argument would fail only at step (iii) were the

λ

‐terms involved replaced with their quantification‐involving counterparts.…”

mentioning

confidence: 99%

Classical Opacity*

Caie

Goodman

Lederman

2019

Philos Phenomenol Research

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It is an apparent truism that, for any things x and y, if x and y are identical, then x and y have the same properties. For if x and y are identical they are one and the same thing, and so it seems whatever properties the one has the other must have as well. In this paper we will explore views that deny this apparent truism. We begin with familiar examples like the following: Hesperus/Phosphorus: Hesperus is Phosphorus. But while the ancients knew that Hesperus was visible at night, the ancients did not know that Phosphorus was visible at night. This example presents a putative false instance of the following schematic principle: Substitution a ¼ b ! ðu $ u½b=aÞ. 1 We will call false instances of Substitution cases of opacity. Given the existence of cases of opacity, it follows, given classical quantificational logic, that there are false instances of: Quantified Substitution 8x8yðx ¼ y ! ðu $ u½y=xÞÞ.

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An Argument For Necessitism*

Cited by 17 publications

References 30 publications

To Be F Is To Be G

To Be F Is To Be G

Higher‐order metaphysics

Classical Opacity*

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