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8

They are in opposition, as Quine and Kripke generally are on interpreting modal logic, and much of what is related to it. Rigid designators are defined as those picking out the same object in all possible worlds, so unsurprisingly Quine and Kripke do not see eye to eye on this issue in particular. To pick out the same object we must agree on how it is done, ...


7

The two notions (completeness and incompleteness) are not opposites but very much connected (not only by Godel's name in the name of the two theorems). Do take into account that Godel's Completeness Th of First-Order Logic is : if a sentence is true in all the models of the axioms (i.e. it is a logical consequence of the axioms) then it is also formally ...


5

Another insightful reference for the semantics of dual-intuitionistic logics is Yaroslav Shramko's paper on the "logic of scientific research" (Studia Logica 2005). Just to add a brief comment on @TMF's answer, for the benefit of the author of the original question, it is worth noting that Priest's "Da Costa Logic" was indeed proposed as a fragment of ...


4

The TL;DR version is that Kripke has misunderstood Lewis’ counterpart theory, and so his criticism is off-base. The longer version follows. To understand what is going on here, it helps to have a little background. Modal logic, with the box/diamond notation, was originally conceived by C I Lewis to express modal properties of propositions, e.g. to say of ...


4

Holism is an epistemological position, and externalism is a semantic one. Of course, some degree of interaction is to be expected, but not only is it possible to hold them together, it is not particularly challenging. The appearance of incompatibility comes from the misleading use of the word "meaning". In the holism, especially Quine's and Davidson's, "...


3

(◊ ∃x Fx) ↔ (∃x ◊ Fx) can be seen as a conjunction of (◊ ∃x Fx) → (∃x ◊ Fx) (the Barcan formula in the narrower sense) and (∃x ◊ Fx) → (◊ ∃x Fx) (the converse Barcan formula). The forward direction, (◊ ∃x Fx) → (∃x ◊ Fx), says that no new objects come into existence when going from one possible world to another: If there is an ...


3

It does make sense in a way. Kripke's thesis is that proper names have essences, properties that belong to them of necessity, not accidentally. Putnam extended this thesis to "natural kinds" of objects, whose essential properties "carve nature at the joints", in Plato's metaphor, rather than according to our cultural biases, practical needs, etc., those ...


3

You surely cannot do this in System K. Instead of focusing on symbol manipulation, it's important to understand the semantics of these sentences. System K is a normal modal logic, so we may dispense with axioms and focus on the frame conditions instead: ~◇◻P is saying that there is no accessible world W, such that every world that W can access satisfies P....


3

Shane's answer is perfectly correct as to the question as worded, but I figure we could use some added background. I think the question doesn't seem to grasp what Kripke means by rigid designator. A rigid designator by definition is a term that picks out only one thing and continues to pick out the same thing regardless of everything else. That is its ...


2

Most of the "dualized" intuitionistic logics in the literature, e.g., Priest-da Costa and anti-intuitionistic, are fragments of Cecylia Rauszer's Heyting-Brouwer logic, in which all connectives---not merely negation---are given duals. It's probably worth your time to review Rauszer's 1974 "Semi-Boolean Algebras and Their Application to Intuitionistic Logic ...


2

The paper H.P. Sankappanavar, "Heyting algebras with dual pseudocomplementation", published in Pacific journal of Mathematics 117 (1985), 405–415, I believe, provides an algebraic semantics for what Priest calls as "Da Costa Logic".


2

What you are looking for is called dynamic epistemic logic, it was developed starting in late 1980s to represent changes in knowledge. Internet Encyclopedia of Philosophy gives a nice overview with many references: "The modal knowledge operators in epistemic logic are formally interpreted by employing binary accessibility relations in multi-agent Kripke ...


2

~◇◻P → ◇◇~P Following is the proof. - ~◇◻P - ∴ ◻~◻P - ∴ ◻◇~P From ◻◇~P we can apply an axiom from Modal System D, stating that everything that is necessary is also possible, that is if P is necessarily the case then P cannot be impossible. D: ◻A → ◇A Then from ◻◇~P using Axiom D, it follows that : ◇◇~P You can find an application of System D to ...


2

The main problem with your suggestion is not philosophical but mathematical. Let's denote quus by # and plus by +. Even without any skeptical thesis, you simply cannot move from 57 # b = 5 to 57 = 5 - b. With plus, such a move is made by subtracting b from both sides. For instance, going from a+b=c to (a+b)-b=c-b to a=c-b. But such a move is valid ...


2

Kripke's argument for a casual-historical view of names is first and foremost about proper names. It is a theory to explain how proper names are used in natural languages. Kripke argues that rigid designators are central to our use of language and how we, in this world as opposed to a possible world, use language. To illustrate, from Marc Cohen: The claim ...


2

Long comment I'm puzzled also, but for a different reason... From (∃y) ((x) ◊(x ≠ y)), using a fresh term a, we have, by (∃-elim): (x) ◊(x ≠ a). Thus, using (∀-elim) with a (legitimate) we have: ◊(a ≠ a) and finally with (∃-intro): (∃y) ◊(y ≠ y). But how we can say that the premise is satisfiable, if we can derive from it: ◊(a ≠ a) ?


2

Yes. Reading Kripke's works is very different than reading a math book on set theory, principally because his interests are in "meta" issues, and his works (books), are comprised of his lecture series, in many cases. But if, you do have an understanding of Philosophy of Language and Logic that's derived from your understanding of Frege, Russell, and ...


2

Descriptivism requires that proper names have their reference fixed in virtue of a description attached to them, which singles out a unique object in the world, and which is analytic: the meaning of a proper name can be expressed by a definite description. Analytic means: in virtue of the meaning of words. It is implicit here that the meaning of words is ...


1

I shall try explicate Kripke's footnote against the backdrop of Lewis's 1968 paper "Counterpart Theory and Quantified Modal Logic" and leave it to the reader to decide how felicitous Kripke's phrasing is and how rigorous Lewis's counterpart-theoretical formalism is. Lewis defines four primitive predicates of counterpart theory: Wx: x is a ...


1

Kripke has more recently come to hold that socalled fictional entities are real entities, and more specifically Kripke holds that e.g. Scherlock Holmes is an abstract object created by the author A.C. Doyle. This strategy may solve many riddles concerning socalled empty names, and perhaps create new riddles. Kripke, Saul A. 2011. “Vacuous Names and ...


1

If a meter is the same thing in all possible worlds, we're referring to an abstract measurement, divorced from any definition that can vary. The meter has been defined as a tenth of a millionth of the distance from North Pole to equator going through Paris, or by a platinum-iridium bar with scratches on it, or as a certain number of wavelengths of a ...


1

There's really no translation to be done. Here's an outline of a proof. Assume P ⊨c Q. To show ⊨k 򪪪(P → Q), assume for contradiction that 򪪪(P → Q) is not valid. This means that there's a world which falsifies P → Q, that is, in which P is true but Q is false. But that contradicts the assumption that Q follows classically from P.


1

Kripke models can be used to prove that a formula is not valid. Reagrading your example, this means, to show that the antecedent: (p & q → (p → q)) is true in w (the "actual" world) and the consequnr □(p → q) is not, i.e. (p → q) is false in some world w' accessible from w (i.e. such that wRw'). If q is false in w (written: w ⊮ q) we have that p & ...


1

Conifold's answer seems to contain all the relevant materials, but I'll try to arrange them a bit differently. So yes, there seems to be a certain collision between semantic externalism and holism. The reason is not because holism implies internalism (as your first point suggests) but because holism disputes the very distiction between internal and external ...


1

The main criticism is that were need descriptions to "know" what we're talking about, in particular in what Kripke called baptism. The first time we encounter an exemplar of a natural kind (say, a tiger) it is not enough to say that tigerhood is the kind of this exemplar, whatever it is, because the tiger might belong to several kinds depending on what we're ...


1

In General, a behaviouristic approach to psychological entities wants to identify a specific mental event with a specific behavioural event. according to this, pain will be fully identified with the behaviour of being in pain: screaming "ouch", for example. Yet, sometimes we do not present the behaviour of pain while being in pain. To avoid this problem, ...


1

There is such an implicit assumption with Kripke. This is a central assumption operative in deriving essentialism from the possible world's apparatus, and was isolated in such a context by Nathan Salmon in his book Reference and Essence. The assumption also plays a role in the Four Worlds' Paradox.


1

I took Kripke to be saying that we can rigidly designate something, and we can rigidly designate anything precisely when we pick that thing out across all possible worlds. See http://plato.stanford.edu/entries/rigid-designators/ A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything ...


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