An Isomorphism

“The present point is that if the claim that it is possible to identify a rational structure common to what is expressed in pragmatic and semantic metavocabularies could be made out in detail, it would cast light on issues of much wider philosophical significance. For we can look at the relations between what is expressed in normative pragmatic and representational semantic metavocabularies in another way: as articulating the relations between the activities of talking and thinking, and what is being talked or thought about. This is the intentional nexus between subjects and objects, between mind and the world, knowers and the known.” (Brandom in Hlobil and Brandom, Reasons for Logic, p. 8).

Brandom uses the term intentionality in a non-psychological sense that he elsewhere attributes to Kant. We are implicitly in what I think of as Aristotelian-Hegelian territory, where a Cartesian-style division into Subject and Object is not assumed. Brandom’s low-key summary of what to me are the rather dramatic stakes in this issue focuses on the American pragmatists, whom he discussed in the recent Pragmatism and Idealism lectures.

“The American Pragmatists inherited from the German Idealists — who in turn inherited it from Romantic critics of the Enlightenment — the idea that the Cartesian tradition failed structurally, making itself a patsy for skepticism, by attempting to define subjects and objects independently of one another, and then later on facing the problem of how to bolt together things understood as having wholly disparate natures…. The better strategy, they thought, was to start with a conception of intentionality as successful cognition (and action)…. One way to work out such a strategy begins with the thought that there is a kind of structure common to what normative pragmatic metavocabularies make it possible to say about the practices of discursive subjects using declarative sentences to manifest practical attitudes and undertake commitments, on the one hand, and what representational semantic metavocabularies make it possible to say about the modal relations among matter-of-factual states of the world those sentences come to represent by being so used, on the other” (ibid).

Here he references the classic pragmatist emphasis on “successful” thought and action. But especially since he is about to explicitly invoke an Aristotelian (and Scholastic) connection on the next page, this suggests to me that even a very elementary mainstream notion of pragmatism could be recast as evincing a kind of Aristotelian teleological concern with ends and that-for-the-sake-of-which, but in language that hides this angle and is suited to survive in the climate of uncomprehending modern antipathy to Aristotle. The main difference is that Aristotle says much more clearly that the ends that matter are those that are sought for their own sake, and not as means to other ends.

I used to think that logical and linguistic pragmatics as a field of study had nothing in particular to do with pragmatism as a view of the world. Brandom’s recent writings provocatively suggest that there is indeed a connection.

The emphasis on structure is also significant. Although Brandom does not identify with it as I did especially in my youth, French so-called structuralism and poststructuralism represent another major strand of non-Cartesian, non-subject-centered thought in the 20th century. Brandom’s usage seems closer to mathematical structuralism, and perhaps to the structural functionalism of the sociologist Talcott Parsons and the cognitive psychologist Jean Piaget that attracted Jürgen Habermas, whom Brandom has called a personal hero.

“For the worldly version of the relations that articulate the structure we are calling ‘conceptual’ are relations of necessity and impossibility whose existence owes nothing to the activities of discursive practitioners. They are objective relations, specified in the alethic modal vocabulary used to state laws of nature, and more generally to specify subjunctively robust relations” (pp. 8-9).

Brandom has consistently highlighted the significance of modality and modal logic for formulating what he likes to call subjunctive robustness. Next he invokes non-Cartesian strands within analytic philosophy.

“We take the view we develop to be a way of understanding what Frege means when he says ‘A fact is a thought that is true’. It is also one way of understanding the Tractarian [early Wittgenstein] claim that the world is the totality of facts…. John McDowell (1996) explores the same sort of conceptual realist view in Mind and World under the slogan ‘The conceptual has no outer boundary’.”

While I am highly sympathetic to the non-Cartesian ambitions here, I think that facts alone are too shallow a basis to constitute a world. I am not a Wittgenstein scholar, but I think he later moved away from this attempt to ground everything on atomic facts. But what else is needed is something like the subjunctive robustness or modal aspect of things that Brandom dwells upon. This emerges naturally as we move from world-as-totality-of-fact to the idea of a world constituted from implications and distinctions (the latter being my preferred way of thinking about what Brandom calls incompatibilities).

“These are deep waters. These pronouncements by great philosophers are mentioned to indicate that the stakes are high for the enterprise of explicating any form of conceptual realism. Here is a sketch of how we go about it. One of the key arguments we appeal to in filling in this neo-Aristotelian metalinguistic bimodal conceptual realism is a technical result…. Greg Restall and David Ripley have worked out what they call a ‘bilateral’ normative pragmatic understanding of the turnstile that marks implication relations in multisuccedent sequent calculi [which looks approximately like |~ and means that if all formulae on the left (often represented as a context capital gamma Γ) are true, then at least one formula on the right is true.]…. The Restall-Ripley bilateral normative pragmatic metavocabulary turns out to be related in surprising ways to what we take to be the most sophisticated contemporary heir of Tarskian model theory and later intensional semantics in terms of possible worlds (Lewis, out of Kripke, out of Carnap), namely Kit Fine’s truth-maker semantic framework…. The representational content of declarative sentences is then understood in terms of assignments to them of sets of states as truth-makers and falsifiers. Global structural conditions on modally partitioned state spaces (for instance requiring that all the mereological parts of possible states be possible) interact with conditions on assignments of truth-makers and falsifiers (for instance forbidding the truth-makers and falsifiers of logically atomic sentences to be overlapping sets).”

Sequent calculi are proof-theoretic notations due to Gerhard Gentzen in the 1930s. They generalize Gentzen’s system of natural deduction. In sequent calculi, every line is a conditional or sequent, rather than an unconditional assertion. In effect, the primitive terms are implications. This is a formal analogue of Brandom’s idea that the common structure of the world and of thought is at root constituted out of implications (and distinctions) rather than simple facts. Hlobil and Brandom’s book shows that it is general enough to support radically nonmonotonic and nontransitive cases.

“We show below that if one defines semantic consequence in just the right way, a powerful, fruitful, and detailed isomorphism can be constructed relating truth-maker modal semantic metavocabularies and bilateral normative pragmatic vocabularies” (pp. 9-10).

Serious logicians mainly study the properties of different logical systems, or logics, and develop new ones. Alternate logics have hugely proliferated since the first half of the 20th century. He is alluding to the fact that many differently detailed notions of logical consequence have been proposed. What is the “right” one depends in part on its conditions of use.

An isomorphism is a structure-preserving mapping that works bidirectionally. The existence of an isomorphism — like the one mentioned further below between algebra and geometry, or the one Brandom is talking about immediately below, between semantics and pragmatics — is an extremely nonrandom, rare occurrence, and therefore is often taken to be deeply significant.

“Assertion and denial line up with truth and falsity, combinations of commitments (to accept and reject) in a position line up with fusion of truth-making and falsifying states, and normative out-of-boundness (preclusion of entitlement to the commitments incurred by those assertions and denials) of a compound practical position lines up with the modal impossibility of such a fusion state.”

“When Spinoza looked back on the relations between algebraic equations and geometric shapes on which Descartes modeled mind-world relations, he saw that the key feature distinguishing that new, more abstract notion of representation from earlier atomistic resemblance-based conceptions is the existence of a global isomorphism between the algebraic and geometrical vocabularies. Spinoza’s slogan for the holistic insight that animated the representational revolution was ‘The order and connection of ideas is the same as the order and connection of things’ (Spinoza, Ethics II, Prop. vii). The isomorphism between normative pragmatic and alethic representational metavocabularies turns out to make possible in our setting a precise, tractable, and productive specification of that shared rational ‘order and connection’. We think this is a good way to rationally reconstruct some central aspects of Aristotelian (and Scholastic) intelligible forms. This isomorphism is the core of our version of bimodal (deontic/alethic) metalinguistic conceptual realism” (p. 11).

Brandom has been a consistent critic of standard versions of representationalism, but he has always been careful not to reject too much. The more affirmative reference to representation and Tarskian model theory here specifically involves not just any representation but an inferentialist semantics that undoes many conventional assumptions. Apparently there is a formal result to the effect that inferentialist semantics can be expressed not only in terms derived from Gentzen’s proof theory, but also in terms of an evolved variant of Tarski’s model theory in which the things represented are implications.

Next in this series: Quick Note on Proof Theory

Intention and Intuition

Husserl continues his passive synthesis lectures with more discussion of intuition as a confirmation of the concordance of intentions. It now seems pretty clear that intuition for Husserl is all about the “presentness” of presentations, and unlike the common usage does not involve any leaps. He distinguishes between intuitions that are “self-giving” (principally, external perceptions), and those that are not self-giving, but instead involve a “presentification”, like memories and expectations. He discusses at some length the question whether it is possible in advance to know which of our general intentions and presentations can potentially be confirmed in intuition.

He speaks of intentions “wanting” and “striving” to be fulfilled in present intuition, but contrasts this with a wish or will. Instead, it seems to be a more elemental directedness toward filling in the metaphorical hole in what he calls the “empty” intentions that are not correlated to a present object in intuition from external perception. Preconscious beliefs about an external object are subject to a kind of preconscious corroboration by comparison to direct impressions from sense perception.

I like the quasi-personification of intentions and intuitions here, as “wanting” or “giving themselves” (see Ideas Are Not Inert). Plato in the Republic compared the soul to a city or community of thoughts, feelings, and perceptions, thus suggesting that the kind of unity the soul has is comparable to the kind of unity a concrete community has. All our thoughts, feelings, and perceptions thus need not be attributed monolithically to a single, central agent; rather, our agency as individuals is the combined effect of numerous specialized, more or less cooperating but somewhat decentralized agencies.

All our intentions “want” to coalesce into the unity of a world.

“That we have a consciousness of our own life as a life endlessly streaming along; that we continually have an experiencing consciousness in this life, but in connection to this in the widest parameters, an emptily presenting consciousness of an environing-world — this is the accomplishment of unity out of manifold, multifariously changing intentions, intuitive and non-intuitive intentions that are nonetheless concordant with one another: intentions that in their particularity coalesce to form concrete syntheses again and again. But these complex syntheses cannot remain isolated. All particular syntheses, through which things in perception, in memory, etc., are given, are surrounded by a general milieu of empty intentions being ever newly awakened; and they do not float there in an isolated manner, but rather, are themselves synthetically intertwined with one another. For us the universal synthesis of harmonizing intentional syntheses corresponds to ‘the’ world, and belonging to it is a universal belief-certainty.”

“Yet as we already mentioned, there are breaks here and there, discordances; many a partial belief is crossed out and becomes a disbelief, many a doubt arises and remains unsolved for a time, and so forth. But ultimately, proper to every disbelief is a positive belief of a new materially relevant sense, to every doubt a materially relevant solution; and now if the world gets an altered sense through many particular changes, there is a unity of synthesis in spite of such alterations running through the successive sequence of universal intendings of a world — it is one and the same world, an enduring world, only, as we say, corrected in its particular details, which is to say, freed from ‘false apprehensions’; it is in itself the same world. All of this seems very simple, and yet it is full of marvelous enigmas and gives rise to profound considerations” (Analyses Concerning Passive and Active Synthesis, pp. 145-146).

Generalizing About the World

When I speak of things like “the goodness of the actual world”, this refers to life in general. It is not, for example, intended as an endorsement of the details of the social status quo.

Similarly, when I talk about finitude, I don’t have in mind some specific existing configuration of things, but rather the general principle that existing things are definite, while we are neither omniscient nor omnipotent.

Pure Negativity?

Hegel often characterizes the “Concept” that overcomes the opposition of subject and object in terms of what he calls “pure negativity”. This is very far removed from what contemporary logicians call classical negation (see Contradiction vs Polarity). Hegelian pure negativity is just a name for pure difference or relation with no pre-given, contentful positive terms, where the meaning of every “thing” depends on the meaning of other things, and nothing is absolutely first. This is why he can legitimately call it “absolute”. Such a perspective needs to be taken together with Hegel’s dictum that strictly speaking, there is truth only in the whole development.

Any representation involving contentful positive terms can always be superseded, as Hegel thinks it inevitably will be. But without preconceived contentful positive terms, there is nothing to supersede. Pure difference or relation thus has a kind of finality to it, precisely because it preserves the substantial content and truth we care about within a sort of ideal open-endedness.

Further and crucially, the attitude Hegel is describing is “open” not only in the epistemological sense that it avoids prejudice and may gain new insights, but also in the practical ethical sense that it is “forgiving”.

Harris in his commentary says “The concept (of self-conscious Absolute Knowing) fulfilled itself as ‘forgiveness’ in the ‘self-certain spirit’ that had no content except an ideal community; and it fulfilled itself as a real community in the historical evolution of Religion. But that real community depends for its unity on a projected image (Vorstellung) of its eternal destiny. The self-certainty of the broken-hearted Beautiful Soul must take the place of this Vorstellung…. In this final confrontation it is the singular self who acts and the community that judges. The crucial moment of ‘forgiveness’ belongs therefore to the community; but the absolute knowing belongs to the absolved individual, who thinks and knows at once for herself and for the reconciled community. It is the moral agent who steps out of the reconciled community in action; and it is she who has the knowledge of return and forgiveness. Everyone must recognize the reconciliation; but that communal recognition only preserves the community — it is not a knowing that is capable of further development.”

“In contrast, the ‘absolute knowing’ towards which we are now moving is capable of development. It is the experience precisely of the philosopher.”

“Hegel regards the self-assertion of conscientious action as identical with the advent of ‘pure thought’ — the thinking that can do Hegelian logic” (Hegel’s Ladder II, p. 723).

This last reflects a vitally important insight about Hegel’s perspective as a whole, little recognized until recently. It is one manifestation of the Hegelian version of the primacy of practical (ethical) reason. Harris has already made the better-recognized point that Hegel regarded the standpoint reached at the end of the Phenomenology as identical with that presupposed at the beginning of his Logic. Patiently following out the twists and turns of the Phenomenology with Harris, it seems to me we have come to the inescapable conclusion that — contrary to the way it has been presented by most earlier commentators — the Phenomenology is above all a book of ethics. But this conclusion then has profound implications for what Hegel will mean by “logic”, which is again very different from the way it has been characterized by most commentators. I will have more to say about this in the future.

“Pure knowing is neither judging, nor acting; it involves the letting go (Ablassen) of both ‘determinacies’ of the Concept (the active subjectivity of the agent, and the substantial Objectivity of the community). Thus pure knowing is a kind of return to the paradisal state of ‘innocence’. But we can speedily disabuse ourselves of the idea that there is anything particularly remarkable about it, by reflecting that we ourselves achieved it fairly easily and without much conscious strain, in adopting the posture of speculative observers of consciousness. The Absolute has been with us from the start, in the form of our knowledge of what our own proper position is, and what our behavior as observers should be” (p. 724).

“The Beautiful Soul is the hero of this last movement of Spirit, because its moral act is the withdrawal into Self as a pure observer. It is the antithesis of the self-actualizing Begriff [Concept], because it does not act, and is not actual. It participates in the antithesis; and in so far as it is independent knowledge of the Concept as pure essence, it is self-assertive and ‘evil’. But, in that it has become the simple knowing (observing) of the essence, the knowing that has received forgiveness, and gives it back freely to everything that it observes, it remains ‘good’. It lets the Concept go through the very same motion as Substance, or as the absolute essence. The doubling that occurs in this state of free release lets the Concept be ‘in and for itself’. In this pure knowing, the one-sidedness of self-assertion and the one-sidedness of simple being are both renounced” (ibid).

“The point is that the Spirit is what it makes itself to be, and ‘absolute Spirit’ is the unity of the knowing self with its world…. The movement is the same as in forgiveness, but we should not call it that, because it is more radical. The sides die for each other, exactly as Man and God ‘die’ for each other in the religious Vorstellung” (pp. 724-725).

“This philosophical consciousness that the knowledge-seeking Self is the world’s own necessary process of self-interpretation is the last Gestalt of Consciousness in the Science of its ‘experience'” (p. 726).

As ethical beings we are the agents of the world’s self-interpretation.