Aristotle flourished before the great flowering of Greek mathematics that gave us Euclid, Ptolemy, Apollonius, and Aristarchus. In his day, mathematics amounted to just arithmetic and simple geometry. In spite of the famous Pythagorean theorem that the square constructed from the hypotenuse of a right triangle is equal in area to the sum of the squares constructed from the other two sides, the historic reality of the Pythagorean movement had more to do with number mysticism, other superstitions, and curious injunctions like “don’t eat beans” than it did with real mathematics.

I think Aristotle was entirely right to conclude that arithmetic and simple geometry were of little use for explaining change in the natural world. I’ve characterized his physics as grounded in a kind of semantic inquiry that Aristotle pioneered. We are not used to thinking about science this way, as fundamentally involved with a very human inquiry about the meaning of experience in life, rather than predictive calculation. For Aristotle, the gap between natural science and thoughtful reflection about ordinary experience was much smaller than it is for us.

Aristotle invented the notion of cause as a semantic tool for expressing the reasons why changes occur. Aristotle’s notion is far more abstract than the metaphor of impulse or something pushing on something else that guided early modern mechanism. Even though the notion of cause was originally developed in a text included in Aristotle’s Physics, the “semantic” grounding of Aristotelian physics places it closer to logic than to modern physical inquiries.

I think the discussion of the kinds of causes could equally well have been grouped among his “logical” works. In fact, the form in which we have Aristotle’s works today is the result of the efforts of multiple ancient editors, who sometimes stitched together separate manuscripts, so there is room for a legitimate question whether the discussion of causes was originally a separate treatise. We tend to assume that there must be something inherently “physical” about the discussion of causes, but this is ultimately due to a circular argument from the fact that the more detailed version of it came down to us as part of the Physics (there is another, briefer one that came down to us as part of the Metaphysics).

Since Hume and especially since the later 19th century, many authors have debated about the role of causes in science. Bertrand Russell argued in the early 20th century that modern science does not in fact depend on what I have called the modern notion of cause.

More recently, Robert Brandom has argued that the purpose of logic is “to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary”. I see Aristotelian causes in this light.

I want to recommend a return to a notion of causes in general as explanatory reasons rather than things that exert force. This can include all the mathematics used in modern science, as well as a broader range of reasons relevant to life. (See also Aristotelian Causes; Mechanical Metaphors; Causes: Real, Heuristic?; Effective vs “Driving”; Secondary Causes.)

Logic for Expression

In recent times, Robert Brandom has pioneered the idea that the role of logic is primarily expressive. In his 2018 essay “From Logical Expressivism to Expressivist Logic”, he says this means its purpose is “to make explicit the inferential relations that articulate the semantic contents of the concepts expressed by the use of ordinary, nonlogical vocabulary” (p. 70).

In my humble opinion, this is what logic was really supposed to be about in Aristotle, but the tradition did not follow Aristotle. Aristotle insisted that logic is a “tool” not a science, but most later authors have assumed the contrary — that logic was the “science” of correct reasoning, or perhaps the science of consequence relations. Several scholars have nonetheless rediscovered the idea that the purpose of logical demonstration in Aristotle is not to prove truths, but to express reasoned arguments as clearly as possible.

Brandom says that “the task of logic is to provide mathematical tools for articulating the structure of reasoning” (p. 71). People were reasoning in ordinary life long before logic was invented, and continue to do so. But the immensely fertile further development of logic in the late 19th and early 20th centuries was mostly geared toward the formalization of mathematics. Reasoning in most specialized disciplines — such as the empirical sciences, medicine, and law — actually resembles reasoning in ordinary life more than it does specifically mathematical reasoning.

According to Brandom, “The normative center of reasoning is the practice of assessing reasons for and against conclusions. Reasons for conclusions are normatively governed by relations of consequence or implication. Reasons against conclusions are normatively governed by relations of incompatibility. These relations of implication and incompatibility, which constrain normative assessment of giving reasons for and against claims, amount to the first significant level of structure of the practice of giving reasons for and against claims.”

“These are, in the first instance, what Sellars called ‘material’ relations of implication and incompatibility. That is, they do not depend on the presence of logical vocabulary or concepts, but only on the contents of non- or prelogical concepts. According to semantic inferentialism, these are the relations that articulate the conceptual contents expressed by the prelogical vocabulary that plays an essential role in formulating the premises and conclusions of inferences” (pp. 71-72).

“Material” relations of consequence and incompatibility have a different structure from formal ones. Formal consequence is monotonic, which means that adding new premises does not change the consequences of existing premises. Formal contradiction is “explosive”, in the sense that any contradiction whatsoever makes it possible to “prove” anything whatsoever (both true statements and their negations), thereby invalidating the very applicability of proof. But as Brandom reminds us, “outside of mathematics, almost all our actual reasoning is defeasible” (p. 72). Material consequence is nonmonotonic, which means that adding new premises could change the consequences of existing ones. Material incompatibilities can often be “fixed” by adding new, specialized premises. (As I somewhere heard Aquinas was supposed to have said, “When faced with a contradiction, introduce a distinction”.)

Brandom notes that “Ceteris paribus [“other things being equal”] clauses do not magically turn nonmonotonic implications into monotonic ones. (The proper term for a Latin phrase whose recitation can do that is ‘magic spell’.) The expressive function characteristic of ceteris paribus clauses is rather explicitly to mark and acknowledge the defeasibility, hence nonmonotonicity, of an implication codified in a conditional, not to cure it by fiat” (p. 73).

“There is no good reason to restrict the expressive ambitions with which we introduce logical vocabulary to making explicit the rare material relations of implication and incompatibility that are monotonic. Comfort with such impoverished ambition is a historical artifact of the contingent origins of modern logic in logicist and formalist programs aimed at codifying specifically mathematical reasoning. It is to be explained by appeal to historical causes, not good philosophical reasons” (ibid). On the other hand, making things explicit should be conservative in the sense of not changing existing implications.

“…[W]e should not emulate the drunk who looks for his lost keys under the lamp-post rather than where he actually dropped them, just because the light is better there. We should look to shine light where we need it most” (ibid).

For relations of material consequence, the classical principle of “explosion” should be replaced with the weaker one that “if [something] is not only materially incoherent (in the sense of explicitly containing incompatible premises) but persistently so, that is incurably, indefeasibly
incoherent, in that all of its supersets are also incoherent, then it implies everything” (p. 77).

“The logic of nonmonotonic consequence relations is itself monotonic. Yet it can express, in the logically extended object language, the nonmonotonic relations of implication and incompatibility that structure both the material, prelogical base language, and the logically compound sentences formed from them” (p. 82).

Material consequence relations themselves may or may not be monotonic. Instead of requiring monotonicity globally, it can be declared locally by means of a modal operator. “Logical expressivists want to introduce logical vocabulary that explicitly marks the difference between those implications and incompatibilities that are persistent under the addition of arbitrary auxiliary hypotheses or collateral commitments, and those that are not. Such vocabulary lets us draw explicit boundaries around the islands of monotonicity to be found surrounded by the sea of nonmonotonic material consequences and incompatibilities” (p. 83).

Ranges of subjunctive robustness can also be explicitly declared. “The underlying thought is that the most important information about a material implication is not whether or not it is monotonic — though that is something we indeed might want to know. It is rather under what circumstances it is robust and under what collateral circumstances it would be defeated” (p. 85).

“The space of material implications that articulates the contents of the nonlogical concepts those implications essentially depend upon has an intricate localized structure of subjunctive robustness and defeasibility. That is the structure we want our logical expressive tools to help us characterize. It is obscured by commitment to global structural monotonicity—however appropriate such a commitment might be for purely logical relations of implication and incompatibility” (pp. 85-86).

“Logic does not supply a canon of right reasoning, nor a standard of rationality. Rather, logic takes its place in the context of an already up-and-running rational enterprise of making claims and giving reasons for and against claims. Logic provides a distinctive organ of self-consciousness for such a rational practice. It provides expressive tools for talking and thinking, making claims, about the relations of implication and incompatibility that structure the giving of reasons for and against claims” (p. 87).

Real-World Reasoning

I think most people most of the time are more influenced by apprehended or assumed meanings than by formal logic. What makes us rational animals is first of all the simple fact that we have commitments articulated in language. The interplay of language and commitment opens us to dialogue and the possibility of mutual recognition, which simultaneously ground both values and objectivity. This opening, I’d like to suggest, is what Hegel called Spirit. (See also Interpretation.)


It is extremely common to see references to “predication” as if it were a central concept of Aristotelian logic. We are so used to a grammatical interpretation in terms of relations between subjects and predicates that it is hard to disengage from that. However, historically it was Aristotelian logic that influenced ancient Greek accounts of grammar, not vice versa.

Modern logicians distinguish between a neutral proposition — which might be merely mentioned, rather than asserted — and the assertion of the proposition. Grammatical predication in itself does not imply any logical assertion, only a normatively neutral syntactic relation between sentence components. But “said of” in Aristotle always refers to some kind of meaningful assertion that has a normative character, not to grammatical predication.

Aristotle talks about what we might call kinds of “sayables” (“categories”). He famously says that we can only have truth or falsity when one kind of sayable is “said of” another. Mere words or phrases by themselves don’t assert anything, and hence cannot be true or false; for that we need what modern writers have referred to as a “complete thought”.

The ordinary meaning of “to categorize” in ancient Greek was “to accuse in a court of law”. Aristotle used it to talk about assertions. It didn’t originally connote a classification. The modern connotation of classification seems to stem from the accident that independent of what “category” meant in his usage, Aristotle famously developed a classification of “categories”.

Aristotle also talks about logical “judgment” (apophansis, a different word from practical judgment or phronesis). Husserl for instance transliterated this to German, and followed the traditional association of logical judgment with “predication”. But the ordinary Greek verb apophainein just means to show or make known. Aristotle’s usage suggests a kind of definite assertion or expressive clarification related to demonstration, which makes sense, because demonstrations work by interrelating logical judgments.

All of Aristotle’s words and phrases that get translated with connotations of “predication” actually have to do with normative logical assertion, not any connecting of a grammatical subject with a grammatical predicate. Nietzsche and others have complained about the metaphysical status foisted on grammatical subjects, implicitly blaming Aristotle, but all these connotations are of later date.

The great 20th century scholar of ancient and medieval logic and semantics L. M. de Rijk in his Aristotle: Semantics and Ontology (2002) argued at length that Aristotle’s logical “is” and “is not” should be understood as not as binary operators connecting subjects and predicates, but as unary operators of assertion and negation on whole propositions formed from pairs of terms. (See also Aristotelian Propositions.)

As in similar cases, by no means do I wish to suggest that all the work done on the basis of the common translation of “predication” is valueless; far from it. But I think we can get additional clarity by carefully distinguishing the views and modes of expression of Aristotle himself from those of later commentators and logicians, and I think Aristotle’s own more unique perspectives are far fresher and more interesting than even good traditional readings would allow.

Formal and Material Interpretation

Human reasoning has two sides, that could be called formal and material. Any reasoning applicable to the real world necessarily involves the “material” side that is concerned with actual meaning “content”. It may also involve the “formal” side, which aims to express reasoning in terms of mechanically repeatable operations that are completely agnostic to the actual meanings they are used to operate on. Reasoning in some abstract contexts may rely entirely on the formal side.

Aristotle is usually credited with inventing formal logic, but he paid a lot of attention to the material side as well. In the Latin middle ages both sides were recognized, but the formal side was generally emphasized.

Formal mathematical logic underwent an immense development in the 20th century, somewhat like the earlier success story of mathematical physics. The syntactic devices of mathematical logic seemed so powerful that its rise led to a great neglect of the material, interpretive side of logic. Husserl was one of the few 20th century authors who questioned this from the start. More recently, Brandom has argued that Kant and Hegel were both fundamentally concerned with the material, interpretive side of logic, and that this is what Kant meant by “transcendental” logic (and what Hegel meant by “dialectic”).

Generally when I mention interpretation here, I have the material side in mind, but there is also such a thing as formal interpretation. Formal interpretation or “evaluation” of expressions in terms of other expressions is the most fundamental thing that interpreters and compilers for programming languages do. As with material interpretation, formal interpretation makes meanings explicit by expressing them in terms of more elementary distinctions and entailments, but it uses purely syntactic substitution and rewriting to do so.

Material interpretation can always potentially go on indefinitely, explaining real-world meanings by relating them to other meanings, and those in terms of others, and so on. In practice, we always cut it short at some point, once we achieve a relatively stable network of dependencies.

Formal interpretation on the other hand is usually engineered to be decidable, so that it actually does reach an end at some point. The fact that it reaches an end is closely related to the fact that precise formal models are always in some sense only approximations of a determination of reality that is actually open-ended. Formal models are a sort of syntactic reification of open-ended material interpretation. We may think we have taken them as far as they can go, but in real life it is always possible that some new case will come up that requires new detail in the model.

We also use a kind of formal interpretation alongside material interpretation in our spontaneous understanding of natural language. Natural language syntax helps us understand natural language meaning. It provides cues for how different clauses are intended to relate to one another. Is what is meant in this clause an exception? A consequence? A presupposition? A fact? A recommendation? Something being criticized? (See also Formal and Informal Language.)

Logic for People

Leading programming language theorist Robert Harper refers to so-called constructive or intuitionistic logic as “logic as if people mattered”. There is a fascinating convergence of ideas here. In the early 20th century, Dutch mathematician L. E. J. Brouwer developed a philosophy of mathematics called intuitionism. He emphasized that mathematics is a human activity, and held that every proof step should involve actual evidence discernible to a human. By contrast, mathematical Platonists hold that mathematical objects exist independent of any thought; formalists hold that mathematics is a meaningless game based on following rules; and logicists argue that mathematics is reducible to formal logic.

For Brouwer, a mathematical theorem is true if and only if we have a proof of it that we can exhibit, and each step of that proof can also be exhibited. In the later 19th century, many new results about infinity — and infinities of infinities — had been proved by what came to be called “classical” means, using proof by contradiction and the law of excluded middle. But from the time of Euclid, mathematicians have always regarded reproducible constructions as a better kind of proof. The law of excluded middle is a provable theorem in any finite context. When the law of excluded middle applies, you can conclude that if something is not false it must be true, and vice versa. But it is not possible to construct any infinite object.

The only infinity we actually experience is what Aristotle called “potential” infinity. We can, say, count a star and another and another, and continue as long as you like, but no actually infinite number or magnitude or thing is ever available for inspection. Aristotle famously defended the law of excluded middle, but in practice only applied it to finite cases.

In mathematics there are conjectures that are not known to be true or false. Brouwer would say, they are neither true nor false, until they are proved or disproved in a humanly verifiable way.

The fascinating convergence is that Brouwer’s humanly verifiable proofs turn out also to exactly characterize the part of mathematics that is computable, in the sense in which computer scientists use that term. Notwithstanding lingering 20th century prejudices, intuitionistic math actually turns out to be a perfect fit for computer science. I use this in my day job.

I am especially intrigued by what is called intuitionistic type theory, developed by Swedish mathematician-philosopher Per Martin-Löf. This is offered simultaneously as a foundation for mathematics, a higher-order intuitionistic logic, and a programming language. One might say it is concerned with explaining ultimate bases for abstraction and generalization, without any presuppositions. One of its distinctive features is that it uses no axioms, only inference rules. Truth is something emergent, rather than something presupposed. Type theory has deep connections with category theory, another truly marvelous area of abstract mathematics, concerned with how different kinds of things map to one another.

What especially fascinates me about this work are its implications for what logic actually is. On the one hand, it puts math before mathematical logic– rather than after it, as in the classic early 20th century program of Russell and Whitehead — and on the other, it provides opportunities to reconnect with logic in the different and broader, less formal senses of Aristotle and Kant, as still having something to say to us today.

Homotopy type theory (HoTT) is a leading-edge development that combines intuitionistic type theory with homotopy theory, which explores higher-order paths through topological spaces. Here my ignorance is vast, but it seems tantalizingly close to a grand unification of constructive principles with Cantor’s infinities of infinities. My interest is especially in what it says about the notion of identity, basically vindicating Leibniz’ thesis that what is identical is equivalent to what is practically indistinguishable. This is reflected in mathematician Vladimir Voevodsky’s emblematic axiom of univalence, “equivalence is equivalent to equality”, which legitimizes much actual mathematical practice.

So anyway, Robert Harper is working on a variant of this that actually works computationally, and uses some kind of more specific mapping through n-dimensional cubes to make univalence into a provable theorem. At the cost of some mathematical elegance, this avoids the need for the univalence axiom, saving Martin-Löf’s goal to avoid depending on any axioms. But again — finally getting to the point of this post — in a 2018 lecture, Harper says his current interest is in a type theory that is in the first instance computational rather than formal, and semantic rather than syntactic. Most people treat intuitionistic type theory as a theory that is both formal and syntactic. Harper recommends that we avoid strictly equating constructible types with formal propositions, arguing that types are more primitive than propositions, and semantics is more primitive than syntax.

Harper disavows any deep philosophy, but I find this idea of starting from a type theory and then treating it as first of all informal and semantic rather than formal and syntactic to be highly provocative. In real life, we experience types as accessibly evidenced semantic distinctions before they become posited syntactic ones. Types are first of all implicit specifications of real behavior, in terms of distinctions and entailments between things that are more primitive than identities of things.

Things Themselves

Husserl continues his Logical Investigations with a long critical discussion of the then-current tendency to reduce logic to psychological “laws” of mental operations, which are in turn supposed to be reducible to empirically discoverable facts. He then begins to discuss what a pure logic ought to be. “We are rather interested in what makes science science, which is certainly not its psychology, nor any real context into which acts of thought are fitted, but a certain objective or ideal interconnection which gives these acts a unitary relevance, and, in such unitary relevance, an ideal validity” (p. 225).

To do this, we need to look at both things and truths from the point of view of their interconnections. In his famous phrase, we need to go “to the things themselves”. As Aristotle emphasized before, we need to look carefully at distinctions of meaning.

Expressive meanings are not the same thing as indicative signs. Meaning for Husserl is not reducible to what it refers to; it originates in a kind of act, though it is not to be identified with the act, either. Verbal expressions have an “intimating” function. “To understand an intimation is not to have conceptual knowledge of it… it consists simply in the fact that the hearer intuitively takes the speaker to be a person who is expressing this or that” (p. 277). “Mutual understanding demands a certain correlation among the acts mutually unfolded in intimation…, but not at all in their exact resemblance” (p. 278). “In virtue of such acts, the expression is more than a sounded word. It means something, and insofar as it means something, it relates to what is objective” (p. 280). “The function of a word… is to awaken a sense-conferring act in ourselves” (p. 282).

“Our interest, our intention, our thought — mere synonyms if taken in sufficiently wide senses — point exclusively to the thing meant in the sense-giving act” (p. 283). “[A]ll objects and relations among objects only are what they are for us, through acts of thought essentially different from them, in which they become present to us, in which they stand before us as unitary items that we mean” (ibid).

“Each expression not merely says something, but says it of something: it not only has a meaning, but refers to certain objects” (p. 287). “Two names can differ in meaning but can name the same object” (ibid). “It can happen, conversely, that two expressions have the same meaning but a different objective reference” (p. 288). “[A]n expression only refers to an objective correlate because it means something, it can rightly be said to signify or name the object through its meaning” (p. 289). “[T]he essence of an expression lies solely in its meaning” (ibid).

“Expressions and their meaning-intentions do not take their measure, in contexts of thought and knowledge, from mere intuition — I mean phenomena of external or internal sensibility — but from the varying intellectual forms through which intuited objects first become intelligibly determined, mutually related objects” (ibid). Meanings do not have to do with mental images.

“It should be quite clear that over most of the range both of ordinary, relaxed thought and the strict thought of science, illustrative imagery plays a small part or no part at all…. Signs are in fact not objects of our thought at all, even surrogatively; we rather live entirely in the consciousness of meaning, of understanding, which does not lapse when accompanying imagery does so” (p. 304). “[A]ny grasp is in a sense an understanding and an interpretation” (p. 309).

“Pure logic, wherever it deals with concepts, judgments, and syllogisms, is exclusively concerned with the ideal unities that we here call ‘meanings'” (p. 322). “[L]ogic is the science of meanings as such, of their essential sorts and differences, as also of the ideal laws which rest purely on the latter” (p. 323). “Propositions are not constructed out of mental acts of presentation or belief: when not constructed out of other propositions, they ultimately point back to concepts…. The relation of necessary consequence in which the form of an inference consists, is not an empirical-psychological connection among judgements as experiences, but an ideal relation among possible statement-meanings” (p. 324).

“Though the scientific investigator may have no reason to draw express distinctions between words and symbols, on the one hand, and meaningful thought-objects, on the other, he well knows that expressions are contingent, and that the thought, the ideally selfsame meaning, is what is essential. He knows, too, that he does not make the objective validity of thoughts and thought-connections, … but that he sees them, discovers them” (p. 325).

“All theoretical science consists, in its objective content, of one homogeneous stuff: it is an ideal fabric of meanings” (ibid). “[M]eaning, rather than the act of meaning, concept and proposition, rather than idea and judgement, are what is essential and germane in science” (ibid). “The essence of meaning is seen by us, not in the meaning-conferring experience, but in its ‘content'” (p. 327).

Husserl on Normativity

Translator J. N. Findlay ranks Husserl (1859-1938) with Plato, Aristotle, Kant, and Hegel, and calls Husserl’s Logical Investigations (1899-1901) his greatest work. My previous acquaintance with Husserl has been limited to his later, explicitly “phenomenological” period.

In the first two chapters, Husserl surveys and criticizes the then-dominant views of Utilitarian John Stuart Mill and his followers on the nature of logic, objecting that they reduced it to a “technology dependent on psychology” (p. 56). Frege had already introduced mathematical logic, but the great flowering of the latter had not occurred yet. Husserl in these chapters is particularly concerned with the objectivity of knowledge, and with principles of validation.

I was initially confused by his polemic against the claim that logic is a “normative discipline”. To me, “normative” means “axiological”, i.e., concerned with value judgments. I take the Aristotelian view that judgment refers first of all to a process of evaluation, rather than a conclusion. In this sense, judgment and normativity inherently involve a Socratic dimension of genuinely open inquiry about what is good.

All versions of normativity involve a “should”. But it turns out that the view Husserl is polemicizing against treated a “normative discipline” as one that takes some particular and predetermined end for granted, and is only concerned with what we “should” do to realize that predetermined end. On this view, “normativity” is only concerned with necessary and/or sufficient conditions for achieving predetermined ends. Thus Husserl associates it with a sort of technology, rather than with something ultimately ethical. So, what he is doing here is rejecting a merely technological view of normativity.

There is also a theoretical-versus-practical axis to Husserl’s argument. Aristotle had contrasted the ability to successfully perform an operation with the ability to explain the principles governing it. One does not necessarily imply the other. Husserl notes how many activities in life are merely oriented toward operational success, and says that most of the practice of modern sciences — including mathematics — has a mainly operational character.

Elsewhere I have contrasted “tool-like” reason with what I like to call ethical reason, but I don’t think they are mutually exclusive, and my notion of “tool-like” reason has potentially rather more positive connotations than that toward which Husserl seems to be leading. I don’t take the fact that engineering tends to drive science to be inherently bad. I think engineering can drive science in a good way, involving an integral consideration of ends; a concern with good design guided by those ends and the best practices we can come up with; and a recognition that the real world doesn’t always cooperate with our intentions.

On the other hand, I also find that the best engineering relies more on fundamental theoretical insight and well-rounded judgment than on sheer technology. This is a perspective that is simultaneously “practical” and concerned with first principles. When Husserl argues for the priority of theoretical disciplines over practical ones, he is mainly arguing for the importance of a concern for first principles. While I generally prefer the Kantian/Brandomian primacy of practical reason, I find common ground with Husserl in the concern for principles.

Logic as Ethics

Since the groundbreaking work of Boole, De Morgan, Pierce, and Frege in the later 19th century, logic has been treated as either the foundation of mathematics — as Russell argued — or as a branch of mathematics, as suggested by contemporary type theory and category theory. This all builds on the “formal” view of logic that has been dominant in the West since the later middle ages.

In fact, the place of formalism in the practice of mathematics is debated by mathematicians. A century after Hilbert and Bourbaki, the complete systematic formalization of mathematics remains an unrealized ideal, although new work in homotopy type theory seems the most promising development yet for this (see New Approaches to Modality).

Plato and Aristotle never thought that reasoning should be “value free”. On the contrary, they treated it as an essential part of ethical life. Aristotle pioneered formal reasoning by composition, but justified the principle of non-contradiction in unmistakably ethical terms. Plato and Aristotle reasoned mainly by examining meanings, whereas in the formal view of logic, all that matters are formal rules for mechanical manipulation of arbitrary symbols. (See also Formal and Informal Language.)

Taking up Kant’s thesis of the primacy of practical (ethical) reason, Hegel took what he called “logic” in a very different direction from that of the modern formalists, focusing like Plato and Aristotle on the development of concrete meanings rather than rules for formal, meaning-agnostic operators.

Within the tradition of modern analytic philosophy, Wilfrid Sellars and Robert Brandom have revived interest in non-formal approaches to logic that are closer to the reasoning we employ in everyday life. Brandom has also written extensively on the ethical content of Hegel’s work and its connections to Hegelian logic. He has always acknowledged that his earlier work on inferential semantics is deeply indebted to Hegel. Brandom’s “inferentialism” puts reason and the interpretation of meaning in relations of reciprocal dependence, in this respect recovering what I think is the perspective of Plato and Aristotle as well as Hegel.

The suggestion here — also supported, I believe, by Harris’ commentary on the Phenomenology — is that “logic” is most fundamentally concerned with what we ought to conclude from what, within the open philosophical perspective of what Hegel somewhat confusingly called “pure negativity”, where our view of the world is “inferential all the way down”. At the level of practical application with real-world meanings that I want to say is most important, logical “laws” are neither tautologies nor some strange kind of abstract facts, but rather a kind of best practices that themselves require interpretation to be applied.

Time and Eternity in Hegel

H. S. Harris in Hegel’s Ladder I points out that Hegel took an unprecedented view of the relation between time and eternity in the Phenomenology. He argues that Hegel’s later advertisement of his logic as characterizing “the mind of God before creation” is extremely misleading with respect to Hegel’s actual views. According to Harris, detailed examination of texts suggests Hegel retained the novel view of time and eternity expressed in the Phenomenology.

Harris notes that from around 1801, Hegel came to agree with Reinhold and Bardili that logic should be “objective” in the sense of being neutral with respect to subject-object distinctions, even though he sharply rejected their formalism.  Logic for Hegel should not be subjective in the sense of Fichte’s Wissenschaftslehre or Schelling’s work before his break with Fichte.

“Hegel was able to make history subordinate in his speculative Logic precisely because he allowed it to be predominant in the lengthy formation of subjective consciousness for truly logical ‘objectivity’, which is the theme of the Phenomenology….  ‘The experience of consciousness’ is necessarily a psychological experience of the singular subject, since only singular subjects are ‘conscious’, but the ‘phenomenology of Spirit’ is the biography of God, the metaphysical substance who becomes ‘as much subject as substance’ when He is comprehended as ‘Spirit’.  The ‘experience of consciousness’ must happen in a single lifetime; the ‘phenomenology of Spirit’ cannot happen so.”

“We might remark that neither can become ‘Science’ except through the recollection in a singular consciousness of a historical process that is necessarily not confined (or confinable) within a single lifetime.  This is a way of saying that God cannot be ‘spirit’ without man being ‘spirit’ likewise — which is, of course, quite correct…. [N]ot the comprehension of ‘self’ but the comprehension of the whole social history of selfhood [is the topic of the Phenomenology]” (p. 11). 

Harris says the Phenomenology was Hegel’s “decisive divergence” (p. 13) from the whole tradition of intellectual intuition and cognitive immediacy.

“The implication is that ‘the eternal essence of God’ is not ‘outside of time’ in the way that God’s thought and action have traditionally been supposed to be.”

“We cannot mediate the problem of how logic is in time, unless we shift our attention from the ‘real philosophy’ that comes after logic (in every sense) to the ‘real philosophy’ that goes before ‘logic’, as a comprehension of the time in which it was shown finally that logic itself is as much in time as out of it and that it must come to be self-consciously ‘in’ time in order to be properly ‘out’ of it….  [F]rom Heraclitus and Parmenides to Kant and Fichte, no one has managed to formulate a consistent theory of human experience as a rational whole on any intuitive basis.  Instead of simply taking it for granted that eternity comprehends time, just as ‘possibility’ comprehends ‘actuality’, we must start from the other end and ask how time comprehends eternity.”

“There is no intuitive answer to this question” (p. 14).  The project of the Phenomenology “involves a total inversion of the intuitive assumption of all the ‘philosophers of experience’ before Hegel….  But the history of religion is more important to the argument than is the history of philosophy, in any case, because it is in religion that the natural assumption is inverted for the natural consciousness itself.  It is Hegel’s predominant concern with the actual experience of the natural (i.e., nonspeculative) consciousness that makes it hard for us to see and understand what happens to Descartes, and to the ‘philosophers of experience’ proper, in Hegel’s argument” (pp. 15-16).

Harris speaks of an “explicitly Fichtean self…. But his self makes no Fichtean assumptions, and has no absolute ‘intuitions’.  It merely observes; and what it learns, in the end, is precisely what the standpoint of philosophical ‘observation’ is and means. This observing consciousness leaves Fichte behind decisively when it leaves moral judgment to the valets and aligns itself with the Weltgeist [world Spirit] in its evaluation of all the experience it recollects.”

“This all-accepting and all-forgiving alignment with the Weltgeist is the logical standpoint, the eternal standpoint concretely established in time and now, at last, comprehensively understood” (p. 17).  What is shown is “Spirit’s eternity in time” (p. 18), but “The ‘hero’ is the finite consciousness — Jacob wrestling with the angel” (ibid).

Harris is here using the word “consciousness” in an equivocal way to refer to something that is far beyond what Hegel described as the standpoint of Consciousness.  It is already Spirit.  The standpoint of Consciousness is inseparable from assumptions of immediacy and of what philosophers from Locke to Schelling have called “intuition”, as some sort of immediate grasping.  Emphasizing some underlying continuity where something underwent a transformation is a common way of speaking, but I would rather identify the continuity with “us” rather than an abstracted property like consciousness.

Harris properly distinguishes between “natural consciousness” and “the philosophers of experience” who purport to speak on its behalf.  Hegel sharply rejects the philosophers of experience as propounding a bad notion of experience focused on immediacy, but he wants to entice common sense to become philosophical. 

The Fichtean self is already a difficult topic.  Fichte, in his better known early writings at least, propounded a very extreme “subject-centered” point of view, but he was a brilliant writer and serious philosopher who cannot be simply reduced to that.  His “self” is certainly not an empirical matter of fact, and seems constitutionally incompatible with petty egocentrism or self-seeking (certainly a far cry from the acute vulgarization of Max Stirner in The Ego and His Own), even though it seems like he had some bad ideas about German cultural superiority.  I think the Fichtean self not so much “has” intuitions as Harris suggests, but rather is itself an “absolute intuition” (the only one) for Fichte.  But Fichte also in his later writings formulated a notion of ethical mutual recognition.

Harris alludes to Hegel at a certain early point turning back from Schelling’s mystical intuitionism toward Fichtes’s practical philosophy.  Although I think this is historically accurate, if taken out of context or connected with stereotypes of Fichte, it could lead to serious misunderstanding. 

Harris himself does not make this mistake.  He clearly indicates that Hegel cannot be reduced to Fichtean subjectivism, as the young Marx and some others have done or precipitously claimed others had done. He goes on to discuss the fundamental role of “otherness” in Hegel’s thought, particularly in regard to constitution of self.  This is as far from an “absolute intuition” of self as could be.  But Fichte’s practical-ethical orientation and sharp mind tower above not only the woolly-minded forgotten Schellingian epigones who so irritated Hegel, but also the superficial dazzle of Schelling himself.  I would also note that to ground the social in concrete relations rather than abstract collectivity is in no way to reduce the social to actions of individuals.

Fichte was accused of atheism and drummed out of Jena for identifying God with the moral order. Now I can’t find the passage, but I think Harris somewhere says Hegel put God as the moral order historically in between God as law and God as love.

The explicit idea that the eternal is constituted in time that Harris highlights is, I think, original to Hegel. Others had denied the eternal, but I don’t recall anyone arguing that a genuine eternal originates in time. Harris relates this novel aspect of Hegel’s thought to his inversion of the Kantian priority of possibility over actuality. Aristotle of course also maintained that actuality comes first, but never explicitly suggested a temporal origin of the eternal.

I think a temporal constitution of the eternal — especially when connected with logic, as Harris suggests it was for Hegel — actually makes a lot of sense. After a temporal process of experience and learning that may involve reversals and twists and turns, it is possible to construct a static logical theory (not logical in Hegel’s sense, but in the formal sense) of all the lessons learned, but not before. What Hegel calls logic is a lot closer to the twists and turns of experience. Formal logic obviously has no temporal element, but the “logic” of experience and learning does. Formal logic comes “after” Hegelian logic. Hegelian logic can be read as an account of the constitution of formal logic, through the constitution of meaning.