Are Disposition Ascriptions Analyzable via Relevant Implications?

Are disposition ascriptions analysable viarelevant implications?

Florian Fischer

University of Bonn

Disposition Ascriptions

Conditional analysis

Counterfactual conditional analyses

Relevance logic

1 Disposition Ascriptions

Lingusitic LevelP(a)

Ontic levelE(o1)

D(ϕ)

dynM(ϕ)

D(ϕ)

dynM(ϕ)

dynM.C(ϕ)

(dyn(M.C))(x)

(A.B)(x) is true, iff A(x) and B(x) are true.

dynM.C(ϕ)

(dyn(M.C))(x)


dynM.C(ϕ)

(dyn(M.C))(x)


[Prior 1985]

„What is commonly accepted by all those who discussdispositions is that there exists a conceptual connectionbetween a statement attributing a disposition to an item and aparticular conditional. The acceptance of the existence of thisconceptual connection is a pre-theoretic common ground.“

2 Conditional analysis

Simple conditional analysis (SCA)

(A1) ∀x[dynM.C(x)↔ (S(x)→M(x))]

(Z1) ∀x[dynDi.Su(x)↔ (Su(x)→ Di(x))]

(Zucki1) dynDi.Su(z)↔ (Su(z)→ Di(z))


(A1) ∀x[dynM.C(x)↔ (S(x)→M(x))]




(A1) ∀x[dynM.C(x)↔ (S(x)→M(x))]



φ ψ φ→ ψT T TT F FF T TF F T

(Z2) ∀x[¬dynDi.Su(x)↔ (Su(x)→ ¬Di(x))]

(Zucki2) ¬dynDi.Su(z)↔ (Su(z)→ ¬Di(z))

(Z2) ∀x[¬dynDi.Su(x)↔ (Su(x)→ ¬Di(x))]

(Zucki2) ¬dynDi.Su(z)↔ (Su(z)→ ¬Di(z))

1 ¬Su(z)

2 dynDi.Su(z)↔ (Su(z)→ Di(z)) (Zucki1)

3 ¬dynDi.Su(z)↔ (Su(z)→ ¬Di(z) (Zucki2)

4 Su(z)

5 ⊥ ⊥ Intro 1,4

6 Di(z) ⊥ Elim 5

7 Su(z)→ Di(z) → Intro 4-6

8 dynDi.Su(z) ↔ Elim 2,7

9 Su(z)

10 ⊥ ⊥ Intro 1,9

11 ¬Di(z) ⊥ Elim 10

12 Su(z)→ ¬Di(z) → Intro 9-11

13 ¬dynDi.Su(z) ↔ Elim 3,12

14 ⊥ ⊥ Intro 8,13

The problem of too many dispositions

Carnap’s reduction sentences

(Z3) ∀x[Su(x)→ (dynDi.Su(x)↔ Di(x))]

(Zucki3) Su(z)→ (dynDi.Su(z)↔ Di(z))

Carnap’s reduction sentences

(Z3) ∀x[Su(x)→ (dynDi.Su(x)↔ Di(x))]

(Zucki3) Su(z)→ (dynDi.Su(z)↔ Di(z))

3 Counterfactual conditionalanalyses

[Cross 2012]

„[T]o say that dispositions and conditionals are linked bynecessary biconditionals is not yet to endorse a reduction ineither direction.“

Simple counterfactual conditional analysis (SCCA)

(A1) ∀x[dynM.C(x)↔ (S(x)�M(x))]

(Z1) ∀x[dynDi.Su(x)↔ (Su(x)� Di(x))]

(Zucki1) dynDi.Su(z)↔ (Su(z)� Di(z))


(A1) ∀x[dynM.C(x)↔ (S(x)�M(x))]




(A1) ∀x[dynM.C(x)↔ (S(x)�M(x))]



C.B. Martin

(Fink)The conditions for gaining (or loosing) a disposition are thesame as the stimulus condition C for that specific disposition.

[Lewis 1997]

„Something x is disposed at time t to give response r tostimulus s iff, for some intrinsic property B that x has at t, forsome time t’ after t, if x were to undergo stimulus s at time t andretain property B until t’, s and x’s having B would jointly be anx-complete cause of x’s giving response r.“

Marc Johnston & Alexander Bird

(Mask / Antidote)The manifestation of can be prevented although the stimulusand the disposition are present.

[Schrenk 2010]

dynM.C(ϕ) iff (S(ϕ)�M(ϕ))

dynM.C(ϕ) iff �(S(ϕ)→M(ϕ))

[Schrenk 2010]

dynM.C(ϕ) iff (S(ϕ)�M(ϕ))

dynM.C(ϕ) iff �(S(ϕ)→M(ϕ))

[Schrenk 2010]

„“[I]f this counterexample [antidote] works then it shows enpassant that metaphysical necessity can hardly be the drivingforce behind dispositional powers.” “

The problem of the frustrated manifestation

Malzkorn’s adequacy conditions

1. The basic disposition concepts are time dependent.

2. The analysans of an disposition must not imply that C or M areactually realized at the time of the ascription of dynM.C.

3. The analysans of an disposition must not imply that an objectcan not have dynM.C, if it shows the according manifestation.

4. The analysans of an disposition must not imply that themanifestation can not show itself for other reasons.

5. Dispositions are causal properties.

6. Dispositions are first order properties.





























Malzkorn’s disposition ascriptions

(1) If C(x, t) were the case, then M(x, t+ δ) would be the case.

TC 1

C(x, t)�M(x, t + δ)

TC 2

(C(x, t)�M(x, t + δ)

)∧

(¬C(x, t)� ¬M(x, t + δ)

)

TC 3

(C(x, t)�M(x, t + δ)

)∧

((C(x, t) ∧M(x, t + δ)

)→

(¬C(x, t)�

¬M(x, t + δ)))

TC 4

(C(x, t)�M(x, t + δ)

)∧

(¬M(x, t + δ)� ¬C(x, t)

)

TC 5

dynM.C(x, t) iff CON(x, t, t + δ)�((

C(x, t)�

M(x, t + δ))∧

(¬M(x, t + δ)� ¬C(x, t)

))

4 Relevance logic

Paradoxes of material implication

M1 A→ (B→ A)M2 ¬A→ (A→ B)M3 (A→ B) ∨ (B→ A)M4 (A→ B) ∨ (B→ C)

Paradoxes of strict implication

S1 A J (B J B)S2 A J (B ∨ ¬B)S3 (A ∧ ¬A) J B

1. A1 hyp2. B2 hyp3. A1 reit 14. B→ A1 → Intro 2 - 35. A→ (B→ A)∅ → Intro 1 - 4

(NEC)The proposition p follows from p ∧ q.

(CON)A violation of New Zealand law follows from not paying incometax on honoraria given for presenting seminars at otheruniversities.

[Mares 2004]

Situated inference„[A]n implication, A B, is true in a part of the world if there isinformation in that situation that tells us that if A is true in somepart of the world, then B is also true in some part of the world.These parts of the world are situations.“

SituationsI No principle of bivalence.I Need not be consisten.

A → B is true at a situations if and only if for all situations xand y if Rsxy and A is true at x, then B is true at y.

Dispostion Situation BehaviordynM.C S1 M1dynM.C S2 M2dynM.C S3 M3dynM.C S4 M1

I Situations comunicate partial information.I Antidotes only partially determined.

Thank you!

Are Disposition Ascriptions Analyzable via Relevant Implications?

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