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If a frame is based on a symmetric accessibility relation, then the Barcan formula will be valid in the frame if, and only if, the converse Barcan formula is valid in the frame. It states that domains cannot shrink as one moves to accessible worlds, i.e. that individuals cannot cease to exist. The
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The Barcan formula has generated some controversy because—in terms of possible world semantics—it implies that all objects which exist in any possible world (accessible to the actual world) exist in the actual world, i.e. that domains cannot grow when one moves to accessible worlds. This thesis is
39:(more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas were introduced as axioms by
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seems plausible since it is at least theoretically possible that such a machine could exist. However, it is not obvious that this implies that there exists a machine that possibly could tap the energy of the
Atlantic.
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is a machine that can tap all the energy locked in the waves of the
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possible individuals. There is some debate as to the informal interpretation of the Barcan formula and its converse.
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converse Barcan formula is taken to be more plausible than the Barcan formula.
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Journal of
Symbolic Logic (1946),11 and (1947), 12 under Ruth C. Barcan
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343:{\displaystyle \exists x\Diamond Fx\to \Diamond \exists xFx}
286:{\displaystyle \Box \forall xFx\rightarrow \forall x\Box Fx}
165:{\displaystyle \Diamond \exists xFx\to \exists x\Diamond Fx}
104:{\displaystyle \forall x\Box Fx\rightarrow \Box \forall xFx}
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224:{\displaystyle \Diamond \exists xFx}
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37:converse Barcan formula
18:Converse Barcan formula
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365:Commutative property
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54:The Barcan formula
41:Ruth Barcan Marcus
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492:Modal logic
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29:modal logic
481:Categories
371:References
198:antecedent
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269:∀
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179:actualism
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402:Archived
359:See also
35:and the
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183:merely
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