1/ 33 ‘Consequentialism’? David Ripley University of Connecticut http://davewripley.rocks Arché Inferentialism November 2015 davewripley@gmail.com
2/ 33 Where’s the inference? ‘Consequentialism’? Consequence as prior Conclusion davewripley@gmail.com
Where’s the inference? Inferentialism vs representationalism 3/ 33 Where’s the inference? Inferentialism vs representationalism davewripley@gmail.com
Where’s the inference? Inferentialism vs representationalism 4/ 33 People infer. People represent. davewripley@gmail.com
Where’s the inference? Inferentialism vs representationalism 5/ 33 According to inferentialism, inference is explanatorily prior to representation. According to representationalism, representation is explanatorily prior to inference. davewripley@gmail.com
Where’s the inference? Inferring is doing 6/ 33 Where’s the inference? Inferring is doing davewripley@gmail.com
Where’s the inference? Inferring is doing 7/ 33 Inference is an action, a particular psychological process. Two kinds of inferentialism: · What’s prior is how people do infer. · What’s prior is how people should infer. davewripley@gmail.com
Where’s the inference? Inferring is doing 8/ 33 Either way, there is familiar trouble; neither notion is particularly well-behaved. Descriptive: Wason selection task Normative: options about how to proceed davewripley@gmail.com
Where’s the inference? Inferring is doing 9/ 33 Perhaps for these reasons, some people who call themselves ‘inferentialists’ don’t actually think that inference is prior to reference. Some of us think that something else is prior to both. davewripley@gmail.com
‘Consequentialism’? I know, it’s a bad name. Sorry. 10/ 33 ‘Consequentialism’? I know, it’s a bad name. Sorry. davewripley@gmail.com
‘Consequentialism’? I know, it’s a bad name. Sorry. 11/ 33 One option is to think that consequence is the prior notion. This requires understanding consequence some way that doesn’t require either inference or representation. davewripley@gmail.com
‘Consequentialism’? Positions and bounds 12/ 33 ‘Consequentialism’? Positions and bounds davewripley@gmail.com
‘Consequentialism’? Positions and bounds 13/ 33 Let a position be a set of assertions and denials. Some positions are in bounds; others are out of bounds. davewripley@gmail.com
‘Consequentialism’? Positions and bounds 14/ 33 The bounds are a social kind: which positions are in bounds depends on which positions are taken to be in bounds. davewripley@gmail.com
‘Consequentialism’? Positions and bounds 15/ 33 Let [Γ | ∆] represent the position that asserts everything in Γ and denies everything in ∆ . Γ ⊢ ∆ means that [Γ | ∆] is out of bounds. Consequence, on this picture, is the bounds. davewripley@gmail.com
‘Consequentialism’? Positions and bounds 16/ 33 This gives a notion of consequence that is nice in many ways. davewripley@gmail.com
Consequence as prior to inference 17/ 33 Consequence as prior to inference davewripley@gmail.com
Consequence as prior to inference 18/ 33 How to see this notion of consequence as prior to inference? Again, there is a choice: · Inferences we do make, or · inferences we should make? davewripley@gmail.com
Consequence as prior to inference 19/ 33 I suspect neither is achievable, for more or less the same reasons as before. Instead, I will offer an account of nonampliative inference. Consequence settles when conclusions do not go beyond the premises that lead to them. This is at most part of a story about how we do or should infer. davewripley@gmail.com
Consequence as prior to nonampliativity 20/ 33 Consequence as prior to nonampliativity davewripley@gmail.com
Consequence as prior to nonampliativity 21/ 33 Equivalence: A position [Γ | ∆] is equivalent to [Γ ′ | ∆ ′ ] iff for all Σ , Θ : Σ , Γ ′ ⊢ ∆ ′ , Θ . Σ , Γ ⊢ ∆ , Θ iff Equivalent positions leave the same options open for in-bounds expansion. davewripley@gmail.com
Consequence as prior to nonampliativity 22/ 33 Implicit assertion for sentences: A position [Γ | ∆] implicitly asserts A iff it is equivalent to [Γ , A | ∆] . That is, iff for all Σ , Θ : Σ , Γ , A ⊢ ∆ , Θ iff Σ , Γ ⊢ ∆ , Θ . davewripley@gmail.com
Consequence as prior to nonampliativity 23/ 33 Nonampliative inference: Inferring A from Π is nonampliative iff: every position that asserts Π implicitly asserts A . That is, iff for all Γ , ∆ , Σ , Θ : Σ , Γ , Π , A ⊢ ∆ , Θ iff Σ , Γ , Π ⊢ ∆ , Θ . (That is, iff for all Γ , ∆ : Γ , Π , A ⊢ ∆ iff Γ , Π ⊢ ∆ .) Once you’ve asserted the premises of a nonampliative inference, you may as well have asserted the conclusion as well. davewripley@gmail.com
Consequence as prior to nonampliativity 24/ 33 Nonampliative inference obeys: · Reflexivity, monotonicity, and finite transitivity by its nature, whatever ⊢ is like. (Implicit appeal to contraction and expansion for ⊢ here.) · Complete transitivity when ⊢ is compact. davewripley@gmail.com
Consequence as prior to nonampliativity 25/ 33 Example: Suppose ⊢ obeys weakening on the left and ∧ L. Then we have: Γ , A , B , A ∧ B ⊢ ∆ Γ , A ∧ B ⊢ ∆ Γ , A ∧ B ⊢ ∆ Γ , A , B , A ∧ B ⊢ ∆ That is, the inference from A , B to A ∧ B is nonampliative, as are the inferences from A ∧ B to A and to B . davewripley@gmail.com
Consequence as prior Undeniability and inference 26/ 33 Consequence as prior Undeniability and inference davewripley@gmail.com
Consequence as prior Undeniability and inference 27/ 33 When we infer, we conclude things; we do not merely rule out denying them. davewripley@gmail.com
Consequence as prior Undeniability and inference 28/ 33 What is the relation between consequence and nonampliative inference? davewripley@gmail.com
Consequence as prior Undeniability and inference 29/ 33 Cut: If ⊢ obeys weakening and cut, then if X ⊢ A , the inference from X to A is nonampliative. Why? By weakening, Γ , X ⊢ ∆ implies Γ , X , A ⊢ ∆ . Γ , X , A ⊢ ∆ together with X ⊢ A gives Γ , X ⊢ ∆ via cut. davewripley@gmail.com
Consequence as prior Undeniability and inference 30/ 33 Id: If ⊢ obeys weakening and identity, then if the inference from X to A is nonampliative, X ⊢ A . Why? Since X , A ⊢ A , it must be that X ⊢ A . davewripley@gmail.com
Consequence as prior Undeniability and inference 31/ 33 So if ⊢ obeys weakening, cut, and id, then nonampliative inference is shaped a lot like consequence. But whatever ⊢ is like, nonampliative inference is grounded in consequence. davewripley@gmail.com
Conclusion 32/ 33 Conclusion davewripley@gmail.com
Conclusion 33/ 33 • Inference is a thing people do. • Only some ‘inferentialists’ really ground representation in it. • Consequence can ground both representation and nonampliativity of inference. davewripley@gmail.com
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