[lit-ideas] Re: Ruth Barcan Marcus 1921-2012
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Tue, 20 Mar 2012 11:20:29 -0400 (EDT)
McEvoy was quoting from Neale's quotation in the NYT obit of Ruth
Charlotte Barcan Marcus.
This from
Menzel, Christopher, "Actualism", The Stanford Encyclopedia of Philosophy
(Fall 2011 Edition), Edward N. Zalta (ed.), URL =
<http://plato.stanford.edu/archives/fall2011/entries/actualism/>.
-- the formulae therein should relate.
‘It is possible that there is an x such that x is an Alien’
◊∃xAx.
‘Something is possibly an alien’
∃x◊Ax
Joseph Ratzinger (i.e., the Pope at the time of this writing...) could
have had a son who could have become a priest.
◊∃x(Sxp ∧ ◊Px)
The K schema, which asserts that if a conditional is necessary, then if the
antecedent is necessary, so is the consequent:
□(φ→ψ) → (□φ→□ψ)
The T schema, which asserts that a formula true in every possible world is
simply true:
□φ → φ
The 5 schema, which asserts that if a formula φ is possible, then it is
necessarily the case that it is possible:
◊φ → □◊φ
The so-called Barcan [Schema]
∀x□φ → □∀xφ
◊∃xφ → ∃x◊φ.
---
∀x□∃y(y=x)
The Converse Barcan Schema
□∀xφ → ∀x□φ
Given an explicit predicate to express existence, the actualist principle
A can be expressed formally as follows:
∀xE!x.
"But we can say more. For the actualist position isn't that it's just an
accident that there are no mere Necessarily, everything there is is actual.
□∀xE!x.
x is contingent =df ◊E!x ∧ ◊~E!x
"Actualists and possibilists alike, then, generally agree that there are
contingent beings."
∃x(◊E!x ∧ ◊~E!x)
"Actualists often simply define the existence predicate ‘E!’ in terms of
the existential quantifier thus:
E!Def: E!x =df ∃y(y=x).
∀x□E!x.
□∀x□∃y(y=x).
□∀x□E!x.
Converse Barcan Schema (revisited)
□∀xE!x → ∀x□E!x
and so on.
Refs cited in the Stanford entry, by Barcan Marcus: two:
Barcan, Ruth Charlotte, 1946, “A Functional Calculus of First Order Based
on Strict Implication,” Journal of Symbolic Logic, 11: 1–16.
Marcus, Ruth Charlotte Barcan, 1986, “Possibilia and Possible Worlds,”
Grazer Philosophische Studien, R. Haller (ed.), 25/26 (1985/1986): 107–33.
Cheers,
Speranza
---
Appendix A:
Festschrift for Barcan Marcus:
_Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus_
(http://www.amazon.com/Modality-Morality-Belief-Essays-Barcan/dp/0521440823/ref=
sr_1_3?ie=UTF8&qid=1332256526&sr=8-3) by Walter Sinnott-Armstrong, Diana
Raffman and Nicholas Asher (Hardcover - Jan 27, 1995)
Appendix B:
Ruth Barcan Marcus: essays in "Modalities" (Oxford):
_1 Modalities and Intensional Languages_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-1)
_Appendix 1A: Discussion_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-appendix-1)
_Appendix 1B: Smullyan on Modality and Description_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-appendix-2)
_2 Iterated Deontic Modalities_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-2)
_3 Essentialism in Modal Logic_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-3)
_4 Essential Attribution_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-4)
_Appendix 4A: Strict Implication, Deducibility, and the Deduction Theorem_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-97
80195096576-appendix-3)
_5 Quantification and Ontology_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-5)
_6 Classes, Collections, Assortments, and Individuals_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-
6)
_7 Does the Principle of Substitutivity Rest on a Mistake?_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-cha
pter-7)
_8 Nominalism and the Substitutional Quantifier_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-8)
_9 Moral Dilemmas and Consistency_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-9)
_10 Rationality and Believing the Impossible_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-10)
_11 Spinoza and the Ontological Proof_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-11)
_12 On Some Post‐1920s Views of Russell on Particularity, Identity, and
Individuation_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-12)
_13 Possibilia and Possible Worlds_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chapter-13)
_14 A Backward Look at Quine's Animadversions on Modalities_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-ch
apter-14)
_15 Some Revisionary Proposals About Belief and Believing_
(http://www.oxfordscholarship.com/view/10.1093/0195096576.001.0001/acprof-9780195096576-chap
ter-15)
Other related posts:
