Deontic Modality

I just realized that linguists have been using a concept of deontic modality to express various degrees of “ought”, “may”, “can”, and the like. This is interesting in a couple of ways.

Brandom often talks about a pair consisting of deontic normative and alethic modal things, while sometimes suggesting that truth is actually subordinate to normativity. “Alethic modality” is the phrase used by the linguists to express modalities of truth. I’m not sure why Brandom chose not to similarly adopt the linguists’ exact phrase for the deontic one (perhaps to save “modal” for its standard, hyperstrong logical sense), but it is certainly interesting to note that the linguists see the deontic one as also modal.

It is also very interesting to see that the linguists apparently see deontic modality as expressed in terms of degrees, which seems eminently reasonable. I tend to see deontological ethics as promoting untenably unconditional ground-level requirements, so this is a welcome relief. (See also Necessity in Normativity; Binding; Evaluation of Actions; Modality.)

Propositions, Terms

Brandom puts significant emphasis on Kant and Frege’s focus on whole judgments — contrasted with simple first-order terms, corresponding to natural-language words or subsentential phrases — as the appropriate units of logical analysis. The important part of this is that a judgment is the minimal unit that can be given inferential meaning.

All this looks quite different from a higher-order perspective. Mid-20th century logical orthodoxy was severely biased toward first-order logic, due to foundationalist worries about completeness. In a first-order context, logical terms are expected to correspond to subsentential elements that cannot be given inferential meaning by themselves. But in a higher-order context, this is not the case. One of the most important ideas in contemporary computer science is the correspondence between propositions and types. Generalized terms are interpretable as types, and thus also as propositions. This means that (higher-order) terms can represent instances of arbitrarily complex propositions. Higher-order terms can be thus be given inferential meaning, just like sentential variables. This is all in a formal context rather than a natural-language one, but so was Frege’s work; and for what it’s worth, some linguists have also been using typed lambda calculus in the analysis of natural language semantics.

Suitably typed terms compose, just like functions or category-theoretic morphisms and functors. I understand the syllogistic principle on which Aristotle based a kind of simultaneously formal and material term inference (see Aristotelian Propositions) to be just a form of composition of things that can be thought of as functions or typed terms. Proof theory, category theory, and many other technical developments explicitly work with composition as a basic form of abstract inference. Aristotle developed the original compositional logic, and it was not Aristotle but mid-20th century logical orthodoxy that insisted on the centrality of the first-order case. Higher-order, compositionally oriented logics can interpret classic syllogistic inference, first-order logic, and much else, while supporting more inferentially oriented semantics on the formal side, with types potentially taking pieces of developed material-inferential content into the formal context. We can also use natural-language words to refer to higher-order terms and their inferential significance, just as we can capture a whole complex argument in an appropriately framed definition. Accordingly, there should be no stigma associated with reasoning about terms, or even just about words.

In computer-assisted theorem-proving, there is an important distinction between results that can be proved directly by something like algebraic substitution for individual variables, and those that require a more global rewriting of the context in terms of some previously proven equivalence(s). At a high enough level of simultaneous abstraction and detail, such rewriting could perhaps constructively model the revision of commitments and concepts from one well-defined context to another.

The potential issue would be that global rewriting still works in a higher-order context that is expected to itself be statically consistent, whereas revision of commitments and concepts taken simply implies a change of higher-level context. I think this just means a careful distinction of levels would be needed. After all, any new, revised genealogical recollection of our best thoughts will be in principle representable as a new static higher-order structure, and that structure will include something that can be read as an explanation of the transition. It may itself be subject to future revision, but in the static context that does not matter.

The limitation of such an approach is that it requires all the details of the transition to be set up statically, which can be a lot of work, and it would also be far more brittle than Brandom’s informal material inference. (See also Categorical “Evil”; Definition.)

I am fascinated by the fact that typed terms can begin to capture material as well as purely formal significance. How complete or adequate this is would depend on the implementation.

Meta-Ethics as First Philosophy

I want to say that philosophy can be divided into just ethics and meta-ethics, which would comprise everything else (semantics/hermeneutics, epistemology, logic, philosophical psychology, historiography, politics, aesthetics, what was traditionally called ontology, philosophy of science, and so on). Of course, this is nonstandard. The point is that all of these things have at least indirect meta-ethical relevance in one way or another, and meta-ethics can be regarded as what Aristotle would call first philosophy.

I also think that logic in particular has a directly normative character. Things like tautologies, logical rules, and modalities express strongly deontically binding higher-order norms relative to particular logics, not some strange kind of facts. This was apparently Frege’s view as well.

Epistemic Conscientiousness

I see something like epistemic conscientiousness as almost the highest value, only potentially surpassable by what I will broadly call concern for others. This principally involves a commitment to understanding, which means always seeking deeper and better and more nuanced understanding (see Objectivity of Objects). But equally, it involves taking strong personal responsibility for our acceptance of claims. (See also Assumptions; Error.)

If I have accepted a claim — especially if I have acted on the basis of that acceptance, or encouraged others to accept it — and then encounter reason to question that claim, I have a responsibility to resolve the matter in some appropriate and reasonable way. If I accept a claim, I have a responsibility to also accept its consequences. I have a responsibility not to accept materially incompatible claims.

An epistemically conscientious person will also naturally care about the acceptance of claims by others. Particular concern for particular others will naturally tend to accentuate this. We also want to treat those others with respect and kindness, and combining this with questioning claims they have accepted can be delicate. (See also Things Said; Honesty, Kindness; Intellectual Virtue, Love.)

Brandom on Truth

One of the essays reprinted in Brandom’s Reason in Philosophy (2009) was “Why Truth Is Not Important in Philosophy”. Epistemic conscientiousness and the honesty that I largely equate with it are still important; it is the explanatory and justifying role of truth that he wants to question. For Brandom, well rounded inferential goodness with regard to meaning explains and justifies claims of truth, rather than the other way around. Saying an assertion is true is a lot like just repeating the assertion; it adds no content. (See also Interpretation; Foundations?)

Brandom argues that Frege understood propositional contentfulness in terms of being able to play the functional role of a premise or conclusion in an inference, and suggests going beyond Frege to say that truth just is what is preserved by good material inference. Brandom wants to say that inference is constitutive and truth is constituted. We seek not just knowledge but understanding, and not just truth but reasonableness.

All this seems entirely right to me. Though unlike Brandom in Spirit of Trust I do still see a positive role for truth-as-goal, I take this in a Socratic ethical sense that belongs entirely on the side of epistemic conscientiousness, so the difference is not large. (See also Inferential Semantics; Normative Pragmatics.)

(Working with a notion of inference that was simultaneously formal and material, Aristotle made inferential goodness the main criterion of episteme, so I think he would also be sympathetic to the thrust here. See also Aristotelian Propositions; Aristotelian Demonstration.)

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.)

Syntax, Semantics, Ethics

How we understand one another in our social interactions is of paramount importance for ethics. Pointing, gestures, and similar cues can get us started, but we cannot get very far without considering linguistic meaning, and we cannot get very far with natural language meaning without considering implicit and explicit inferences.

In concrete utterances, syntax still plays a large role in specifying the overall shape of the inferences a speaker is implicitly asking us to endorse with respect to some content in question. Here we are concerned not with formal definition of syntactic features, but with specific, concrete usage that we implicitly, defeasibly take as specifying definite higher-level inferential connections by virtue of the grammar employed.

By understanding the structure of a speaker’s overall argument from syntactic as well as semantic cues, we get all sorts of nuances like intended qualifications and specifications of scope that can be all-important in assessing the reasonableness of what is being said. How well we do this depends at least partly on us as well as what was said, and also on our familiarity with the speaker’s particular speech patterns, which may vary from what is common or usual. We can also silently compare the speaker’s speech patterns to what is common or usual, and wonder if what they seemed to say was what they actually meant; or kindly point out to them that what they actually said could be misunderstood. (See also Inferential Semantics; Honesty, Kindness.)

Inferential Semantics

Going back at least to Making It Explicit (1994), Brandom has championed a nonstandard approach to semantics, in accordance with his thesis that inference is prior to representation in the order of explanation.

More conventional approaches to semantics standardly invoke model theory, which employs universal algebra and mathematical relations to study mathematical structures that can be regarded as interpretations of the formal theories studied by proof theory. This is already interesting, insofar as it invokes relations, structures, universal algebra, proof theory, and a (formal) kind of interpretation; but to begin with, this approach is natively designed to work with formal theories, and there are nontrivial issues with its application to natural language. Then also, its principal concern is with formal models as representations.

Brandom is more interested in the ethical and epistemic uses of natural language than in formal theories. Haskell Curry already spoke in the 1950s of natural language as the “use” language implicitly presupposed as a metalanguage in all formal developments. (Natural language is said to contain an indefinite regress of metalanguages.)

Brandom adopts Wittgenstein’s dictum that meaning is use. He understands this as referring principally not to instances of use but to norms governing proprieties of use, and the norms in question not as descriptions of empirical fact about what is said to be right, but about what actually ought to be, understood as a genuine question that ought to have an objective answer, even if the objectivity of any particular putative answer can never be assumed, but has to be shown through reasoning.

The intuition behind inferential semantics is that meaning in real life is primarily constituted through processes of valid implicit informal reasoning in natural language that can be made explicit in terms of material inference and material incompatibility. Unlike the model-theoretic approach, this means it’s semantics all the way down. We have to find our way to what is honestly good usage in terms of immanent criteria in an emergent process, without the convenience of a postulated syntax as an artificially tidy starting point. After all, real life is much messier than that. (See also Conceptual, Representational; Aristotelian Dialectic; Syntax, Semantics, Ethics.)

Any given explicitation of meaning through material inference and material incompatibility can always be converted to an appropriately defined static structure, which can then be nominalized for convenient reference. In contradistinction to the structure involved in attempts to apply model-theoretic semantics to natural language, however, this sort is implicitly constructed in the process of developing our explicitation, not purportedly found in empirical data.

Constructive formal logics seem to me to also naturally push semantics in an inferential direction, but this is not the path Brandom takes. Apart from some discussion of paraconsistency related to belief revision, he prefers to remain noncommittal on preferred formalisms. (See also Categorical Evil.)

Brandom actually puts normative pragmatics before any semantics, and sees the two as very closely related. He sees representational truth as derivative from rational justification.

In passing, I would note that contemporary structural operational semantics used in programming language research also seems to have a broadly inferential flavor, but is concerned with formal rather than material inference.

(I have previously used the term “semantics” in a very general way, barely distinguishable from the way I have used “hermeneutics”. When I speak, e.g., of Aristotelian semantics, all I mean is a serious and extended inquiry into meaning. When I speak of “hermeneutics”, I just mean some kind of methodologically self-aware approach to interpretation.)

Material Consequence

Interest in material consequence was revived in modern times by Wilfrid Sellars, and it became a fundamental tool for Brandom. Not to be confused with material implication, material inference is semantic rather than syntactic. That is to say, it is based on meaning. It covers constructions such as “Blood is red, so it is colored” and “It is raining, so the street will be wet”. In conjunction with material incompatibility (“The sky is gray, so it is not blue” or “The sky is gray, so the sun is not shining”), it forms the basis of Hegelian mediation, which is therefore also based on semantics not syntax.

Mediation

Mediation is any kind of dependency of things on other things. With such dependencies in mind, Euclid the geometer is famously reported to have said that there is no royal road to science, but the point also applies more broadly to all kinds of meanings. Paul Ricoeur called mediation the “long detour” essential to understanding.

Mediation makes things intelligible. We understand things in terms of other things. Mediation involves a complicity of different kinds of meant realities with one another, which gives metaphorical “thickness” to the temporal present we experience. It initially appears as a kind of quasi-recursive accumulation of “layers” of partial determination that is retrospectively elicitable, and is subject to a kind of further accumulation of layers. (See also Aristotelian Matter; Potentiality, Actuality; Efficient Cause, Again; Kantian Synthesis; Transcendental Field.)

Mediation is the substance of Hegel’s Geist and the soul of Hegelian dialectic. Hegelian mediation exhibits or just “is” a kind of form or structure discernible in the Aristotelian semantic “materiality” of concrete things, made explicit by articulating intermediate relations of material incompatibility (Hegel’s “determinate negation”) and material consequence. It is what Hegel calls the determinate rather than the indeterminate, “infinite”, or classical negation of immediacy. (See also remarks on mediation at end of Ricoeur on Justice.)

While mediation broadly corresponds to Aristotelian materiality, Hegel tilts the balance in the complex hylomorphic relation between form and matter, so that whereas for Aristotle, form — as the way of being of a thing, or its effectively operative orientation to ends — has a kind of conceptual priority over materiality, Hegel wants to emphasize that our very discernment of Aristotelian form depends on mediation. Hegel is also influenced by Kant’s talk about form and content, which pushes over to the side of content much of what Aristotle treated as form. (See Mutation of Meaning.)