David Corfield Robert Brandom

Articulating Reason

Chap 1

Representationalism blocks Hume on induction. Like the truth table argument against induction when each instance is an atom.

Brandom close to Goodman. Logic to codify existing deductive and inductive practices.

Non-representationalism accords better with intuitionism? No finite truth tables there. Why does Brandom put so much weight on negation and incompatibility? If A and B implies $\bot$, then A implies $\neg B$. Need he rely on excluded middle?

Invariance under substitution, keeping “designated vocabulary” fixed. HoTT expands the range: $A set, B set, card(A) = m, card(B) = n$, then $card(A +B) = card(A) + card(B)$. True under substitution of types.

Statistics hopes to provide steps in reasoning under uncertainty. To what extent can introduction and elimination rules be specified? Naivete of

Data justifies $n \sigma$ claim justifies action. RCT justifies $2 \sigma$ claim justifies use of drug.

Look at particle physics – much more subtle.

Chap 2

Judgment as unit of meaning, rather than term and predicate (p.80). Does this favour ‘$\vdash a: A$’ over ‘$A(a)$ is true’?

From Empiricism to Expressivism, HUP, 2015

Another opposition to Rorty’s left/right Sellarsians (grounding normativity naturalistically/socially) is attitude towards Sellars on categories/Sellars on noumenon-phenomenon, science as measure of what there is.

…when we appreciate the modal commitments implicit in the use of all empirical descriptive vocabulary, we see that strongly cross-sortal identity claims–those that link items falling under different sortal predicates with different criteria of identity and individuation–are never true. (FETE, p. 27)

Due to modal, subjunctive difference tied to type membership. No type is insulated from modal commitments.

p. 118 on maths

P, seems P, seems to seem P

A red apple, an apple that seems red, something that seems to be a red apple.

Levels of endorsement - graded modality?

“The Kant-Sellars thesis about modality”

“…in being able to use nonmodal, empirical descriptive vocabulary, one already know how to do everything one needs to know how to do in order to deploy modal vocabulary, which according can be understood as making explicit structural features that are always already implicit in what one does in describing.” (p. 143)

These include endorsing claims as to what would be the case if things were different. Under variance. See modality.

“This confluence of traditional empiricist with logicist difficulties concerning the content expressed by modal vocabulary had the result that for roughly the first two-thirds of the twentieth century, Anglophone philosophy regarded alethic modal vocabulary with extreme suspicion, if not outright hostility.” (p. 146)

Perspectives on pragmaticism, HUP, 2011.

pp. 186 and onward on assertion/inference and vocabularies sufficient for the practice of using ordinary vocabs, this seems very close to the passage from a deductive graph to its free cartesian closure, p. 55 of Lambek and Scott.

There are various maps from X to free cartesian category – set, category, signature.

What for free cartesian closure on X?

Toposes as 2-monadic over categories.

Then once there toposes, we have slices and adjoints, so modalities relative to types.

Reason, Genealogy, and the Hermeneutics of Magnanimity

Kant correctly saw judging and acting intentionally as exercises of authority that come with correlative responsibilities: commitments to having reasons for and acknowledging consequences of those undertakings. He understood concepts as functions of judgment, in the sense of rules that determine what would count as a reason for applying those concepts in judgment, and what the further consequences of doing so are. In a strict sense, all Kantian rational creatures can do is apply concepts, in judging and acting.

Concepts = types!