Aristotelian Demonstration

Demonstration is literally a showing. For Aristotle, its main purpose is associated with learning and teaching, rather than proof. Its real objective is not Stoic or Cartesian certainty “that” something is true, but the clearest possible understanding of the substantive basis for definite conclusions, based on a grasping of reasons.

Aristotle’s main text dealing with demonstration, the Posterior Analytics, is not about epistemology or foundations of knowledge, although it touches on these topics. Rather, it is about the pragmatics of improving our informal semantic understanding by formal means.

For Aristotle, demonstration uses the same logical forms as dialectic, but unlike dialectic — which does not make assumptions ahead of time whether the hypotheses or opinions it examines are true, but focuses on explicating their inferential meaning — demonstration is about showing reasons and reasoning behind definite conclusions. Dialectic is a kind of conditional forward-looking interpretation based on consequences, while demonstration is a kind of backward-looking interpretation based on premises. Because demonstration’s practical purpose has to do with exhibiting the basis for definite conclusions, it necessarily seeks sound premises, or treats its premises as sound, whereas dialectic is indifferent to the soundness of the premises it analyzes in terms of their consequences.

We are said to know something in Aristotle’s stronger sense when we can clearly explain why it is the case, so demonstration is connected with knowledge. This connection has historically led to much misunderstanding. In the Arabic and Latin commentary traditions, demonstration was interpreted as proof. The Posterior Analytics was redeployed as an epistemological model for “science” based on formal deduction, understood as the paradigm for knowledge, while the role of dialectic and practical judgment in Aristotle was greatly downplayed. (See also Demonstrative “Science”?; Searching for a Middle Term; Plato and Aristotle Were Inferentialists; The Epistemic Modesty of Plato and Aristotle; Belief; Foundations?; Brandom on Truth.)

Normative Pragmatics

Brandom sees inferential semantics as tightly interwoven with normative pragmatics, and depending on it. Wittgenstein notwithstanding, pragmatics — concerned with linguistic usage — has historically often been neglected in favor of syntax and semantics, and most discussions of linguistic usage among analytic philosophers have focused on empirical usage rather than good usage (including good argument and good dialogue). Good usage for Brandom especially means good inferential usage, respecting material incompatibilities and material consequences. He holds that these have both an alethic modal role (having to do with truth and counterfactual robustness) on the semantic side and a deontic normative role on the pragmatic side (having to do with “oughts”). There is a natural close tie between meanings and proprieties of use. (See also Normative “Force”.)

Brandom’s interest in linguistic pragmatics also reflects his emphasis on practical doings and his broad identification with the American pragmatist tradition in philosophy. Saying something — even just meaning something — is unequivocally a kind of doing for Brandom.

I want to construe good natural language usage broadly as also involving a commitment to recognize all the ethical dimensions of communication as a social act, including both concern for others and concern for inferential proprieties.

In Spirit of Trust, Brandom actually goes further than I would in denying any real role for representational truth. He proposes that even concepts of truth-as-goal should be entirely replaced by concepts of truth-process. I think Truth as a Socratic ethical goal is an invaluable heuristic, provided we maintain Platonic/Aristotelian epistemic modesty and recognize that such a concept of Truth is materially incompatible with any claim to simple possession of it. The whole point of a goal is something to aim at. Aiming necessarily involves a defeasible element. Even if we think static Truth is unachievable, I’m sure he would agree that we should do the best we can at every moment in the larger process. After all, the natural workings of mere Understanding — if only they are taken far enough — lead beyond themselves to the recognition and resolution of error. (See also Honesty, Kindness; Definition.)