Consequentialism? David Ripley University of Connecticut - - PowerPoint PPT Presentation

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‘Consequentialism’?

David Ripley

University of Connecticut http://davewripley.rocks

Arché Inferentialism November 2015

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Where’s the inference? ‘Consequentialism’? Consequence as prior Conclusion

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Where’s the inference? Inferentialism vs representationalism 3/ 33

Where’s the inference?

Inferentialism vs representationalism

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Where’s the inference? Inferentialism vs representationalism 4/ 33

People infer. People represent.

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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.

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Where’s the inference? Inferring is doing 6/ 33

Where’s the inference?

Inferring is doing

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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.

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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

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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.

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‘Consequentialism’? I know, it’s a bad name. Sorry. 10/ 33

‘Consequentialism’?

I know, it’s a bad name. Sorry.

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‘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.

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‘Consequentialism’? Positions and bounds 12/ 33

‘Consequentialism’?

Positions and bounds

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‘Consequentialism’? Positions and bounds 13/ 33

Let a position be a set of assertions and denials. Some positions are in bounds;

• thers are out of bounds.

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‘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.

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‘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.

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‘Consequentialism’? Positions and bounds 16/ 33

This gives a notion of consequence that is nice in many ways.

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Consequence as prior to inference 17/ 33

Consequence as prior

to inference

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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?

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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.

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Consequence as prior to nonampliativity 20/ 33

Consequence as prior

to nonampliativity

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Consequence as prior to nonampliativity 21/ 33

Equivalence: A position [Γ | ∆] is equivalent to [Γ′ | ∆′] iff for all Σ, Θ: Σ, Γ ⊢ ∆, Θ iff Σ, Γ′ ⊢ ∆′, Θ. Equivalent positions leave the same options open for in-bounds expansion.

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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.

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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.

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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.

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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.

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Consequence as prior Undeniability and inference 26/ 33

Consequence as prior

Undeniability and inference

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Consequence as prior Undeniability and inference 27/ 33

When we infer, we conclude things; we do not merely rule out denying them.

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Consequence as prior Undeniability and inference 28/ 33

What is the relation between consequence and nonampliative inference?

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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.

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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.

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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.

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Conclusion 32/ 33

Conclusion

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Conclusion 33/ 33

• Inference is a thing people do.
• Only some ‘inferentialists’ really ground representation in it.
• Consequence can ground both representation and nonampliativity
• f inference.

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