CONCRETE IMPOSSIBLE WORLDS Martin Vacek Institute of Philosophy Slovak Academy of Sciences Oklahoma Graduate Conference, Norman, 30/03/2013

Plan  Exposition of modal realism  Applications of the theory  Why to bother with Impossibilia?  An Argument against Impossible Worlds  Proposals

Modal Realism What there is? Concrete actual individuals Concrete nonactual individuals Concrete possible worlds Sets Principle of unrestricted mereological summation Recombination principle There are no IMPOSSIBILIA.

Modal Realism Modal Realism An individual x is a world iff any parts of x are spatiotemporally related to Each other, and anything spatiotemporally related to any part of x is itself a part of x

Possible Worlds: Why We Need Them? Analysis of modality Properties and Propositions Counterfactuals Beliefs Knowledge

Problems – several pre- theoretical opinions Impossible properties Impossible propositions Counterfactuals with impossible antecedents Impossible beliefs

IMPOSSIBILIA TO THE RESCUE(?)

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P). 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P). 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P). 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P) 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P) 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

An Argument against Concrete Impossible Worlds 1. There exists an impossible world at which (P and ~P). 2. At w ~P iff ~(at w, P) 3. At w (P and ~P) iff at w P and ~(at w P) 4. To tell the alleged truth about the contradictory things is not different from contradicting yourself. 5. There is no subject matter about which you can tell the truth by contradicting yourself. Therefore Impossible worlds do not exist.

Proposal(s) If there is subject matter about which you can tell the truth by contradicting yourself

Proposal(s) If there is subject matter about which you can tell the truth by contradicting yourself Paraconsictent Approach

(A, ¬A) ⊨ B

Paraconsictent Approach (A, ¬A) ⊨ B

Paraconsictent Approach (A, ¬A) ⊨ B (A ∧ ¬A)

Proposal(s) is it a justified and legitimate pre- theoretical opinion that classical logic holds unrestrictedly?

Proposal(s) is it a justified and legitimate pre- theoretical opinion that classical logic holds unrestrictedly? localising the applicability of the overall logic

Proposal(s) is it a justified and legitimate pre- theoretical opinion that classical logic holds unrestrictedly? localising the applicability of the overall logic we barely have an idea of what it means for a world to obey one logic rather than another

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