Quick Note on Proof Theory

I read Aristotelian demonstration as more a making explicit than a proof of truths. The logical expressivism of the author of Making It Explicit (Robert Brandom) does something similar with modern logic. Nonetheless it would be very wrong to conclude that proof theory has no philosophical relevance.

To begin with, proof theory is itself not concerned with proving this or that truth. It is the study of proofs, the beginning of which is to recognize that proofs and proof calculi are themselves mathematical objects. Proofs are functions from premises to conclusions. This has profound consequences.

At an utterly simple level, one small piece of a far larger result is that the notion of an implication A => B is at a certain level formally interchangeable with the notion of a mathematical function A => B. Frege very explicitly treats logical predication as a function as well.

Category theory builds all of mathematics on such morphisms, starting from a single basic operation of composition of arrows. Homotopy type theory suggests that we think of the arrows as paths through spaces. All this is an elaboration and abstraction of the utterly simple but crucial notion of “follows from”, or what Brandom calls subjunctive robustness.

Then an Aristotelian syllogism can be seen on the model of the composition of two predications or functions or morphisms or arrows or paths A => B and B => C around a common type or middle term B that is the output of one and the input of the other. This is not intended to capture a sophisticated result like a mathematical theorem, but rather to express sound reasoning in the simplest, most perspicuous, and most universal way possible.

Next in this series: Reason Relations

Averroes vs Ghazali

The Persian al-Ghazali (1055–1111 CE), known to the Latins as Algazel, is regarded as the greatest theologian of the Ash‘arite school of Sunni Islam. According to Wikipedia, the Ash‘arites are one of several schools that advocate the use of reason in expounding the Islamic revelation. In this sense they are definitely to be distinguished from the literalists. The Ash‘arites nonetheless defend a radical version of omnipotence.

Ghazali wrote a work that circulated in the Latin world, which summarized the views of the Islamic philosophers accurately enough that the Latins mistakenly regarded him as one of them. “Philosophy” in this context principally refers to the thought of al-Farabi and Ibn Sina (Avicenna). But Ghazali is best known to historians of philosophy for his sharp attack The Incoherence of the Philosophers, which treated Ibn Sina as representative. Ghazali was a very strong creationist who insisted that creation must be understood as having occurred in time. Like Duns Scotus and William of Ockham a bit later in the West, he defended a radically voluntarist theology.

In a short work called the Decisive Treatise that was never translated to Latin, Ibn Rushd (Averroes) argues as an Islamic jurist that the Koran commands those capable of doing so to study philosophy. Though his philosophy had very little influence in the Islamic world, he was the leading Maliki jurist in al-Andalus and the Maghreb in his day. He wrote the authoritative textbook of Maliki jurisprudence. I learned that Maliki law is still practiced in many Islamic countries.

Ibn Rushd wrote a refutation of Ghazali called The Incoherence of the Incoherence, which interspersedly contains the full text of Ghazali’s work. It circulated in Latin under the title Destructio Destructionum (destruction of the destruction). I’ve transcribed some small excerpts of this historically fascinating book.

The dispute is basically about Aristotle versus creationism. The particular focus of the first part I have excerpted addresses this from the angle of views about the relation between what is eternal and what is in time. The other part I’ve excerpted has to do with Aristotle versus theological voluntarism.

[Ghazali] “The philosophers say: It is impossible that the temporal should proceed from the absolutely Eternal…. When the world begins in time, a new determinant either does or does not arise…. If it does not, the world will stay in the same state of pure possibility as before; if a new determinant does arise… either we shall have an infinite regress or we shall arrive at a principle determining eternally” (Averroes’ Tahafut al-Tahafut (The Incoherence of the Incoherence), tr. Van Den Bergh (1954), p. 1).

[Averroes] “This argument is in the highest degree dialectical and does not reach the pitch of demonstrative proof. For its premises are common notions, and common notions approach the equivocal, whereas demonstrative premises are concerned with things proper to the same genus” (ibid).

Averroes retains Farabi’s exaggerated emphasis on strict demonstration in the sense of the Prior Analytics in Aristotle. Reading Aristotle partly through a Farabian lens, Averroes does not recognize the large place and positive role that Aristotle implicitly gives to dialectic in the sense of the Topics throughout his works. Averroes sees “dialectic” as an intellectually loose approach that easily falls into sophistry.

[Averroes] “For the term ‘possible’ is used in an equivocal way of the possible that happens more often than not, of the possible that happens less often than not, and of the possible with equal chances of happening, and these three types of the possible do not seem to have the same need for a new determining principle” (ibid).

“All these are multifarious and difficult questions which need, each of them, a special examination, both in themselves and in regard to the opinions the ancients held about them. To treat what is in reality a plurality of questions as one problem is one of the well-known seven sophisms, and a mistake in one of these principles becomes a great error by the end of the examination of reality” (pp. 1-2).

[Ghazali] “[The world’s] existence was not willed before and therefore did not happen… at the exact moment it began it was willed by an eternal will and therefore began” (p. 3).

[Averroes] “The act of the agent necessarily implies a change and … each change has a principle which causes it…. [T]he Eternal cannot change in any way. But all this is difficult to prove” (ibid).

“[O]ur expressions ‘eternal will’ and ‘temporal will’ are equivocal, indeed contrary…. [W]hen one says: ‘There is a Willer who wills eternally one of two contraries in Himself’, the definition of the will is abandoned” (p. 4).

[Ghazali summarizing the philosophers] “The effect only takes place when a new event, i.e. entering the house or the arrival of tomorrow, has actually happened…. A delay in the object willed is imaginable only in decision, for decision is not sufficient for the existence of the act” (p. 5). “If, however, the eternal Will is analogous to our decision, it does not suffice to produce the thing decided upon, but the act of creation must be accompanied by a new act of volition, and this brings us again to the idea of a change” (ibid). “[W]ithout the realization of any new condition, this effect comes into existence and is produced. And this is absurd” (p. 6).

[Averroes] “[Ghazali’s] example of divorce based on convention seems to strengthen the argument of the philosophers, but in reality it weakens it. For it enables the Ash’arites to say: In the same way as the actual divorce is delayed after the formula of divorce till the moment when the condition of someone’s entering the house, or any other, is fulfilled, so the realization of the world can be delayed after God’s act of creation until the condition is fulfilled on which this realization depends, i.e. the moment when God willed it. But conventional things do not behave like rational” (ibid).

[Ghazali] “[T]he party which believes in the creation of the world in time through an eternal Will includes so many persons that no country can contain them and no number enumerate them, and they certainly do not contradict the logically minded out of obstinacy, while knowing better in their hearts” (p. 7).

[Averroes] “[T]his argument is mistaken, for it is not a condition of objective truth that it should be known to all” (ibid).

[Ghazali] “[T]o suppose the Creator of the world ignorant of His own work is necessarily absurd” (ibid).

[Averroes] “This assertion belongs to the class of assertions whose contrary is equally false. For there exists no proof which refutes anything that is evidently true, and universally acknowledged. Anything that can be refuted by a demonstrative proof is only supposed to be true, not really true…. Equally, if it is absolutely true that the effect of a cause cannot be delayed after the causation and the Ash’arites claim that they can advance a proof to deny it, then we can be absolutely sure that they cannot have such a proof. If there is a controversy about questions like this, the final criterion rests with the sound understanding which does not base itself on prejudice and passion, when it probes according to the signs and rules by which truth and mere opinion are logically distinguished” (p. 8).

[Ghazaili] “[E]ternity of the world is impossible, for it implies an infinite number and an infinity of unities for the spherical revolutions, although they can be divided by six, by four, and by two” (p. 9).

[Averroes] “This too is a sophistical argument. It amounts to saying: In the same way as you are unable to refute our demonstrative argument for the creation of the world in time, that if it were eternal, its revolutions would be neither even nor uneven, so we cannot refute your theory that the effect of an agent whose conditions to act are always fulfilled cannot be delayed. This argument aims only at creating and establishing a doubt, which is one of the sophist’s objectives…. But when the existence of an eternal prime mover had been proved, whose act cannot be posterior to his being, it followed that there could as little be a beginning for his act as for his being; otherwise his act would be possible, not necessary, and he would not be a first principle…. The agent who has no beginning either for his existence or for those acts of his which he performs without an instrument, has no first instrument either to perform those acts of his without beginning which by their nature need an instrument.”

“But since the theologians mistook the accidental for the essential, they denied this eternal agent” (pp. 10-11).

“It will be clear to you that neither the arguments of the theologians for the temporal creation of the world of which Ghazali speaks, nor the arguments of the philosophers which he includes and describes in his book, suffice to reach absolute evidence or afford stringent proof” (p. 12).

Like Aquinas, Averroes holds that arguments on neither side of the debate for and against creationism reach demonstrative certainty. Averroes defends a theory of eternal “creation” that is far removed from what creationists mean by creation. It has been argued that Albert the Great also had a notion of eternal creation.

[Averroes] “No motion possesses totality or forms an aggregate, i.e. is provided with a beginning or an end, except in so far as it is in the soul, as is the case with time. And it follows from the nature of circular movement that it is neither even nor uneven except as represented in the soul” (p. 13).

“[T]he impossibility of an actual infinite is an acknowledged axiom in philosophical theory, equally valid for material and immaterial things…. Perhaps Avicenna wanted only to satisfy the masses, telling them what they were accustomed to hear about the soul. But this theory is far from satisfactory” (p. 14).

[Ghazali] “We seek to show by all this that the philosophers cannot shake the conviction of their adversaries that the eternal Will is connected with temporal creation, except by claiming its absurdity by the necessity of thought, and that therefore they are in no way different from the theologians who make the same claim against the philosophical doctrines opposed to theirs. And out of this there is no issue” (p. 15).

“[W]e say that the soul of Zaid is either identical with the soul of Amr or different from it; but their identity would mean something absurd, for everyone is conscious of his own identity and knows that he is not another” (ibid).

[Averroes] ” ‘[D]ifferent’ is an equivocal term, and ‘identity’ too is predicated of a number of things which are also called ‘different’…. The souls of Zaid and Amr are one in one sense and many in another; we might say, one in relation to their form, many in relation to their substratum” (pp. 15-16).

“When someone denies a truth of which it is absolutely certain that it is such-and-such, there exists no argument by which we can come to an understanding with him; for every argument is based on known premises about which both adversaries agree. When each point advanced is denied by the adversary, discussion with him becomes impossible, but such people stand outside the pale of humanity and have to be educated” (p. 16, emphasis added).

In emphasizing argument from agreed-upon premises, Averroes treats something like Platonic dialogue as a norm.

[Ghazali] “God before the creation of the world was able to create it, say, one year or two years before He did, and there is no limit to His power; but He seemed to have patience and did not create. Then He created” (p. 17).

[Averroes] “[W]hat has no beginning does not finish or end.” (ibid).

[Ghazali for the philosophers] “[W]e philosophers know by the necessity of thought that one thing does not distinguish itself from a similar except by a differentiating principle…. [I]f you answer that the Will of God is the differentiating principle, then one has to inquire what differentiates the Will, i.e. the reason why it has been differentiated in such or such way (p. 18).”

[Ghazali] “[W]ill is a quality which has the faculty of differentiating one thing from another, and if it had not this faculty, power in itself would suffice…. And to ask why will differentiates one of two similars is like asking why knowledge must comprehend the knowable” (ibid).

[Averroes] “As the theologians were unable to give a satisfactory answer, they took refuge in the theory that the eternal Will is a quality the nature of which is to differentiate between two similar things, without there being for God a differentiating principle which inclines Him to one of two similar acts” (p. 20).

This is the originally Stoic idea of a “freedom of indifference”. The Ash‘arites defend both predestination and theological and anthropological voluntarism.

[Ghazali] “Everyone, therefore, who studies, in the human and the divine, the real working of the act of choice, must necessarily admit a quality the nature of which is to differentiate between two similar things…. Suppose two similar dates in front of a man who has a strong desire for them, but who is unable to take them both. Surely he will take one of them through a quality in him the nature of which is to differentiate between two similar things” (p. 21).

[Averroes] “[I]t is by no means a matter of distinguishing between two similar things when, in this condition, he takes one of the two dates. It is nothing but the admission of an equivalence of two similar things. His will attaches itself therefore merely to the distinction between the fact of taking one of them and the fact of leaving them altogether” (p. 23).

“A definite moment cannot be assigned for the creation of the world, for either time did not exist before it, or there was an infinite time” (p. 32).

“[T]he temporal proceeds from the First Eternal, not in so far as it is temporal but in so far as it is eternal, i.e. through being eternal generically, though temporal in its parts…. for its arising anew is not a new fact, but is an eternal act, i.e. an act without beginning or end. Therefore its agent must be an eternal agent, for an eternal act has an eternal agent, and a temporal act a temporal agent. Only through the eternal element in it can it be understood that movement has neither beginning nor end, and this is meant by its permanence, for movement itself is not permanent, but changing” (p. 36).

[Ghazali on the philosophers] “They assert that he who affirms that the world is posterior to God and God prior to the world cannot mean anything but that He is prior not temporally but essentially” (p. 37).

[Averroes] “[T]he posteriority of the world to the Creator, since He does not precede the world in time, can only be understood as the posteriority of effect to cause” (p. 39).

[Ghazali] “How will you refute the man who claims that creation and annihilation take place through the will of God: if God wills, He creates, and if He wills, He annihilates, and this is the meaning of His being absolutely powerful, and notwithstanding this He does not alter in Himself, but it is only His act that alters?” (p. 83). “[T]he agent must be willing, choosing, and knowing what he wills to be the agent of what he wills, but according to [the philosophers] God does not will, He has no attribute whatever, and what proceeds from Him proceeds by the compulsion of necessity” (p. 87).

[Averroes] “Ghazali’s words ‘The agent must be willing, choosing, and knowing what he wills to be the agent of what he wills’ are by no means self-evident and cannot be accepted as a definition of the maker of the world without a proof, unless one is justified in inferring from the empirical to the divine” (pp. 87-88).

“[H]e who chooses and wills lacks the things which he wills, and God cannot lack anything He wills. And he who chooses makes a choice for himself of the better of two things, but God is in no need of a better condition. Further, when the willer has reached his object, his will ceases and, generally speaking, will is a passive quality and a change, but God is exempt from passivity and change. God is still farther distant from natural action, for the act of the natural thing is a necessity in its substance, but is not a necessity in the substance of the willer and belongs to its entelechy. In addition, natural action does not proceed from knowledge: it has, however, been proved that God’s act does proceed from knowledge. The way in which God becomes an agent and a willer has not become clear in this place, since there is no counterpart to His will in the empirical world. How is it therefore possible to assert that an agent can only be understood as acting through deliberation and choice? For then this definition is indifferently applied to the empirical and the divine” (p. 88).

The argument that the One cannot lack anything is a good example of a neoplatonic argument that was widely adopted and applied to the monotheistic God in later theistic traditions. Although it is speculative in the pre-Hegelian sense, the logic seems unassailable.

Ghazali uses the Aristotelian term “deliberation”, but gives it a different sense. In Aristotle, deliberation determines choice, and there is no separate faculty of will. The idea of a faculty of will separate from reason is a later development that was designed to support the notion of a freedom of indifference. This has the disastrous effect of subordinating reason to arbitrariness.

Aristotle never says that the First cause deliberates, only that it contemplates. The idea of a freedom of indifference is Stoic and only emerged later. Aristotle would not have regarded his notion of deliberation as compatible with the alleged freedom of indifference, because deliberation is concerned with identification of differences or distinctions that have practical import.

[Ghazali] “We say: ‘Agent’ means someone from whom there proceeds an act with the will to act according to choice and with the knowledge of the object willed. But according to the philosophers the world stands in relation to God as the effect to the cause, in a necessary connexion which God cannot be imagined to sever, and which is like the connexion between the shadow and the man, light and the sun, but this is not an act at all” (p. 89).

[Averroes] “The agent is what causes some other thing to pass from potency to actuality and from nonexistence to existence; this actualization occurs sometimes from deliberation and choice, sometimes by nature, and the philosophers do not call a person who throws a shadow an agent, except metaphorically, because the shadow cannot be separated from the man” (ibid).

[Averroes] “His assertion that not every cause is called an agent is true, but his argument that the inanimate is not called an agent is false, for the denial that the inanimate exhibits acts excludes only the rational and voluntary act, not act absolutely, for we find that certain inanimate things have powers to actualize things like themselves; e.g. fire, which changes anything warm and dry into another fire like itself, through converting it from what it has in potency into actuality” (p. 92).

[Ghazali] “If the inanimate is called an agent, it is by metaphor, in the same way as it is spoken of metaphorically as tending and willing” (ibid).

[Averroes] “[W]hen by these expressions is meant that it actualizes another’s potency, it is really an agent in the full meaning of the word” (ibid).

[Ghazali] “This is wrong, because will necessarily implies knowledge, and likewise act necessarily implies will” (ibid).

[Averroes] “But in the definition of ‘act’ knowledge is not included, because actualization of another thing is possible without knowing it” (p. 93).

[Ghazali] “[T]here is as a matter of fact a contradiction when ‘natural act’ is taken in a real sense, only this contradiction is not at once evident to the understanding nor is the incompatibility of nature and act felt acutely, because this expression is employed metaphorically; for since nature is in a certain way a cause and the agent is also a cause, nature is called an agent metaphorically. The expression ‘voluntary act’ is as much redundant as the expression ‘he wills and knows what he wills’ ” (ibid).

[Averroes] “This statement is undoubtedly wrong, for what actualizes another thing, i.e. acts on it, is not called agent simply by a metaphor, but in reality, for the definition of ‘agent’ is appropriate to it. The division of ‘agent’ into ‘natural’ and ‘voluntary agent’ is not the division of an equivocal term, but the division of a genus” (ibid).

“But as a matter of fact the natural agent has an act much more stable than the voluntary agent, for the natural agent’s act is constant — which is not the case with the act of the voluntary agent” (p. 94).

[Ghazali] “[I]f a man were to throw another into a fire and kill him, it is the man who would be called his killer, not the fire…. This proves that the word ‘agent’ is used of one whose act proceeds from his will, and, behold, the philosophers do not regard God as endowed with will and choice” (p. 95).

[Averroes] “This is an answer of the wicked who heap fallacy on fallacy. Ghazali is above this, but perhaps the people of his time obliged him to write this book to safeguard himself against the suspicion of sharing the philosophers’ view. Certainly nobody attributes the act to its instrument, but only to its first mover. He who killed a man by fire is in the proper sense the agent and the fire is the instrument of the killing, but when a man is burned by a fire, without this fact’s depending on someone’s choice, nobody would say that the fire burned him metaphorically” (ibid).

[Ghazali] “Our aim is to show that such is not the meaning of ‘act’ and ‘work’. These words can mean only that which really proceeds from the will. But you reject the real meaning of ‘act’, although you use this word, which is honoured amongst Muslims. But one’s religion is not perfect when one uses words deprived of their sense” (p. 96).

[Averroes] “This would indeed be a correct conclusion against the philosophers, if they should really say what Ghazali makes them say…. He does not unmask their imposture by his words, but he himself deceives by ascribing to them theories which they do not hold” (ibid).

[Ghazali] ” ‘Act’ applies to temporal production, but for [the philosophers] the world is eternal and is not produced in time. The meaning of ‘act’ is ‘to convert from not-being into being by producing it’ and this cannot be imagined in the eternal, as what exists already cannot be brought into existence. Therefore ‘act’ implies a temporal product, but according to them the world is eternal; how then could it be God’s act?” (ibid).

[Averroes] “If the world were by itself eternal and existent (not in so far as it is moved, for each movement is composed of parts which are produced), then, indeed, the world would not have an agent at all. But if the meaning of ‘eternal’ is that it is in everlasting production and that this production has neither beginning nor end, certainly the term ‘production’ is more truly applied to him who brings about an everlasting production than to him who procures a limited production” (pp. 96-97).

“And therefore, just as the eternal existent is more truly existent than the temporal, similarly that which is eternally in becoming is more truly coming to be than that which comes to be only during a definite time” (p. 100).

[Ghazali] “We do not say that the simultaneity of agent and act is impossible, granted that the act is temporal…. It is only an eternal act that we consider impossible, for to call an act that which does not come into being out of not-being is pure metaphor and does not conform to reality…. Our answer is that our aim in this question is to show that you philosophers use those venerable names without justification, and that God according to you is not a true agent, nor the world truly His act, and that you apply this word metaphorically — not in its real sense. This has now been shown” (p. 102).

In Aristotle there is a very important distinction between ordinary “action” as understood by everyone and his own completely original notion of “act”, which, as Gwenaëlle Aubry has very thoroughly documented, is most properly said of entelechy as a self-referential, purely internal determination, and is therefore not an “action” in the ordinary sense at all. In particular, Aristotelian act in its proper sense has nothing to do with efficient causality, especially as that latter notion was transformed by Latin writers such as Aquinas and Suárez. Efficient cause in Aristotle is the instrumental means by which some end is achieved. As such, it is the least primary of Aristotle’s four causes, not the most primary as it is for Aquinas and Suárez. This is a really big difference between them and Aristotle.

[Averroes] “In this argument he supposes that the philosophers concede to him that they only mean by God’s agency that He is the cause of the world, and nothing else, and that cause and effect are simultaneous. But this would mean that the philosophers had abandoned their original statement, for the effect follows only from its cause, in so far as it is a formal or final cause, but does not necessarily follow from its efficient cause, for the efficient cause frequently exists without the effect’s existing” (p. 103).

“[T]he term ‘eternal becoming’ is more appropriate to the world than the term ‘eternity’ ” (p. 104).

“When, however, after a close examination, it was discovered that all things tend to one end, and this end is the order which exists in the world, as it exists in an army through its leader, and as it exists in cities through their government, they came to the conclusion that the world must have one highest principle…. They believed therefore, because of the good which is present in everything, that evil occurs only in an accidental way…. [F]or the existence of much good with a little evil is preferable to the non-existence of much good because of a little evil” (p. 106). “Nowadays, however, … that out of the one all things proceed by one first emanation, is generally accepted, and with our contemporaries we need discuss only this latter statement” (p. 107).

The military metaphor does briefly appear in book Lambda of the Metaphysics. To me though, it has always seemed incongruous with Aristotle’s main idea of the First cause as a pure entelechy.

[Averroes] “But when the philosophers of our religion, like Farabi and Avicenna, had once conceded to their opponents that the agent in the divine world is like the agent in the empirical, and that from the one agent there can arise but one object (and according to all the First was an absolutely simple unity), it became difficult for them to explain how plurality could arise from it” (ibid).

This notion of the First as an absolutely simple One sounds to me more like Plotinus than Aristotle. “According to all” in this context would presumably be a reference to the neoplatonizing Farabian tradition. Of all medieval philosophers, Averroes is probably the closest to being a pure Aristotelian, but that is a relative distinction, not an absolute one. The only completely pure Aristotelian I know of is Aristotle himself. (Though I try to distinguish a genuinely historical Aristotle from the many Aristotles of the commentary tradition, I am certainly no pure Aristotelian either.)

[Averroes] “[T]hey declared that from the First, who is a simple existent, the mover of the highest sphere proceeds, and from this mover, since he is of a composite nature, as he is both conscious of himself and conscious of the First, a duality, the highest sphere, and the mover of the second sphere, the sphere under the highest can arise. This, however, is a mistake, according to philosophical teaching, for thinker and thought are one identical thing in human intellect and this is still more true in the case of the abstract intellects. This does not affect Aristotle’s theory, for the individual agent in the empirical world, from which there can only proceed one single act, can only in an equivocal way be compared to the first agent…. And thereby Aristotle proves that the agent of the human intelligibles is an intellect free from matter, since this agent thinks all things, and in the same way he proves that the passive [sic] intellect is ingenerable and incorruptible, because this intellect also thinks all things” (p. 108).

“They” in this case is clearly a reference to the Farabian tradition. The translator’s choice of “passive” intellect above for the potential intellect reflects the near total absence of specific scholarship on the texts of Averroes that still prevailed in the mid-20th century. In Averroes, the difference between the potential or “material” intellect on the one hand, and the passive “intellect” or the soul’s faculty of cogitation on the other, is huge. (See Cogitation, Intention; Imagination, Cogitation).

[Averroes] “Aristotle connects sensible existence with intelligible, saying that the world is one and proceeds from one, and that this Monad is partly the cause of unity, partly the cause of plurality. And since Aristotle was the first to find this solution, and because of its difficulty, many of the later philosophers did not understand it, as we have shown” (pp. 108-109). “But what we said of this connexion of every existent with the One is something different from what is meant by ‘agent’ and ‘object’, ‘maker’ and ‘product’ in this sublunary world” (p. 112).

McDowell on the Space of Reasons

John McDowell’s paper “Sellars and the Space of Reasons” (2018) provides a useful discussion of this concept. Unlike Brandom, who aims to complete Sellars’ break with empiricism, McDowell ultimately wants to defend “a non-traditional empiricism, uncontaminated by the Myth of the Given” (p. 1).

McDowell begins by quoting Sellars: “in characterizing an episode or a state as that of knowing, we are not giving an empirical description of that episode or state; we are placing it in the logical space of reasons, of justifying and being able to justify what one says” (ibid; emphasis added).

For Sellars, to speak of states of knowing is to talk about “epistemic facts”. A bit later, McDowell says that Sellars’ epistemic facts also include judgments and uses of concepts that might not be considered knowledge. Not only beliefs but also desires end up as a kind of epistemic facts. McDowell uses this to argue that the space of reasons is a version of the concept of knowledge as justified true belief. I want to resist this last claim.

McDowell points out that knowledge for Sellars has a normative character. Sellars also regards the foundationalist claim that epistemic facts can be explained entirely in terms of non-epistemic facts (physiology of perception and so on) as of a piece with the naturalistic fallacy in ethics.

McDowell cites Donald Davidson’s contrast between space-of-reasons intelligibility and the kind of regularity-based intelligibility that applies to a discipline like physics, but does not want to assume there is a single model for all non-space-of-reasons intelligibility.

He notes that Sellars contrasts placing something in the space of reasons with empirical description, but wants to weaken that distinction, allowing epistemic facts to be grounded in experience, and to be themselves subject to empirical description. “Epistemic facts are facts too” (p. 5). I prefer going the other direction, and saying empirical descriptions are judgments too.

The space of reasons is only occupied by speakers. Sellars is quoted saying, “all awareness of sorts, resemblances, facts, etc., in short all awareness of abstract entities — indeed, all awareness even of particulars — is a linguistic affair” (p. 7, emphasis in original). “And when Sellars connects being appropriately positioned in the space of reasons with being able to justify what one says, that is not just a matter of singling out a particularly striking instance of having a justified belief, as if that idea could apply equally well to beings that cannot give linguistic expression to what they know” (ibid).

“‘Inner’ episodes with conceptual content are to be understood on the model of overt performances in which people, for instance, say that things are thus and so” (p. 8). “What Sellars proposes is that the concept of, for instance, perceptual awareness that things are thus and so should be understood on the model of the concept of, for instance, saying that things are thus and so” (p. 10). All good so far.

To be in the space of reasons, “the subject would need to be able to step back from the fact that it is inclined in a certain direction by the circumstance. It would need to be able to raise the question whether it should be so inclined” (pp. 10-11, emphasis in original). But McDowell says — and I agree — that this is without prejudice as to whether there is still a kind of kinship between taking reasons as reasons, on the one hand, and the purposeful behaviors of animals, on the other.

McDowell acknowledges that the idea that epistemic facts can only be justified by other epistemic facts is easy to apply to inferential knowledge, but rather harder to apply to the “observational knowledge” that he claims should also be included in the space of reasons. For McDowell, observational knowledge is subject to a kind of justification by other facts.

McDowell and Brandom both recognize something called “observational knowledge”, but Brandom thinks that it necessarily involves appeal to claimed non-epistemic facts, whereas McDowell wants to broaden the concept of epistemic facts enough to be able to say that observational knowledge can be justified by appealing only to epistemic facts. I would prefer to say, observational judgments are subject to a kind of tentative justification by other judgments.

McDowell says that acquiring knowledge noninferentially is also an exercise of conceptual capacities. This clearly implies a noninferential conception of the conceptual, and seems to me to presuppose a representationalist one instead. This has huge consequences.

He says that the space of reasons must include noninferential relations of justification, which work by appeal to additional facts rather by inference. But where did those facts come from? In light of Kant, I would say that we rational animals never have direct access to facts that just are what they are. Rather, if we are being careful, we should recognize that we can only consider claims and judgments of fact, which may be relatively well-founded or not. But appeal to claims of fact for justification is just passing the buck. Claims of any sort always require justification of their own.

As an example, McDowell discusses claims to know that something is green in color. As non-inferential justification in this context, he says one might say that “This is a good light for telling the colours of things by looking” (p. 18). That is fine as a criterion for relatively well-founded belief, but that is all it is.

A bit later, he adds, “I can tell a green thing when I see one, at least in a good light, viewed head-on, and so forth. A serviceable gloss on that remark is to say that if I claim, in suitable circumstances, that something is green, then it is” (p. 19).

This is to explicitly endorse self-certification of one’s authority. It is therefore ultimately to allow the claim, it’s true because I said so. I think it was a rejection on principle of this kind of self-certification that led Plato to sharply distinguish knowledge from belief.

As Aristotle pointed out in discussing the relation between what he respectively called “demonstration” and “dialectic”, we can apply the same kinds of inference both to things we take as true and to things we are examining hypothetically. We can make only hypothetical inferences (if A, then B) from claims or judgments of A; we can only legitimately make categorical inferences (A, therefore B) from full-fledged knowledge of A — which, to be such, must at minimum not beg the question or pass the buck of justification.

The great majority of our real-world reasoning is ultimately hypothetical rather than categorical, even though we routinely act as if it were categorical. One of Kant’s great contributions was to point out that — contrary to scholastic and early modern tradition — hypothetical judgement is a much better model of judgment in general than categorical judgment is. The general form of judgment is conditional, and not absolute.

I think it’s fine to include beliefs, opinions, and judgments in the space of reasons as McDowell wants to do, provided we recognize their ultimately hypothetical and tentative character. But once we recognize the hypothetical and tentative character of beliefs, I think it follows that all relations within the space of reasons can be construed as inferential.

I don’t think contemporary science has much to do with so-called observational knowledge of the “it is green” variety, either. Rather, it has to do partly with applications of mathematics, and partly with well-controlled experiments, in which the detailed conditions of the controls are far more decisive than the observational component. The prejudice that simple categorical judgments like “it is green” have anything to do with science is a holdover from old foundationalist theories of sense data.

I would also contend that all putative non-space-of-reasons intelligibility ultimately depends on space-of-reasons intelligibility. (See also What We Saw.)

Demonstration in Spinoza

Kant and Hegel both objected to Spinoza’s unusual presentation of his Ethics in something resembling the style of Euclid’s geometry. I think of philosophy mainly as interpretation rather than simple declaration, so I am broadly sympathetic to this point. On the other hand, I think Pierre Macherey is profoundly right when he emphasizes the non-foundationalist character of Spinoza’s thought.

The unique meaning Spinoza gives to “Substance” (not to be confused with its Aristotelian, Scholastic, Cartesian, or general early modern senses) is that of a complex relational whole that encompasses everything, rather than a separate starting point for deduction of the details of the world. Because of this, the apparent linearity of his development is just that — a mere appearance.

Hegel does not seem to recognize that Spinoza’s Substance resembles the relational whole of Force that Hegel himself developed in the Phenomenology. This is inseparable from an implicit notion of process in which relations of force are exhibited.

Macherey says Spinoza sees the world in terms of an infinite process, i.e., one without beginning or end or teleological structure (Hegel or Spinoza, p. 75).

(I would argue that neither Aristotle nor Hegel actually endows the world with teleological structure, though they each give ends a significance that Spinoza would deny. For Aristotle, it is particular beings in themselves that have ends. For Hegel, teleological development is a retrospectively meaningful interpretation, not an explanatory theory that could yield truth in advance. But for Spinoza, ends are either merely subjective, or involve an external providence that he explicitly rejects.)

It seems to me that the “point of view of eternity” that Spinoza associates with truth is actually intended to be appropriate to this infinite process. Spinoza points out that eternity does not properly mean a persistence in time that lasts forever, but rather a manner of subsistence that is entirely outside of — or independent of — the linear progression and falling away that characterizes time.

(Kant’s famous assertion of the “ideality of space and time”, which means that space and time are only necessary features of our empirical experience, is not inconsistent with Spinoza’s commendation of the point of view of eternity. Though it has other features Spinoza would be unlikely to accept, Kant’s “transcendental” as distinct from the empirical is thus to be viewed from a perspective not unlike Spinoza’s “point of view of eternity”.)

Spinoza wants to maintain that the order of causes and the order of reasons are the same. Whereas Aristotle deconstructs “cause” into a rich variety of kinds of “reasons why” (none of which resembles the early modern model of an impulse between billiard balls), Spinoza narrows the scope of “cause” to “efficient causes” in a sense that seems close to that of Suárez with inflections from Galilean physics, and suggests that true reasons are causes in this narrower sense. It seems to me that Spinoza’s “order of causes” resembles the infinite field of purely relational “force” that Hegel discusses in the Force and Understanding chapter.

Spinoza wants us to focus on efficient causes of things, but to do so mainly from the “point of view of eternity”. This takes us away from the event-oriented perspective of linear time, toward a consideration of general patterns of the interrelation of different kinds of means by which things end up as they concretely tend to do. In speaking of means rather than forces, I am tacitly substituting what I think is a properly Aristotelian notion of “efficient” cause for the meaning it historically seems to have had for Spinoza.

In pursuit of this, he takes up a stance toward demonstration that is actually like the one I see in Aristotle, in that it is more about improvement of our understanding through its practical exercise in inference than about proof of some truth assumed to be already understood (see also Demonstrative “Science”?). As Macherey puts it, for Spinoza “knowledge is not simply the unfolding of some established truth but the effective genesis of an understanding that nowhere precedes its realization” (p. 50). (Unlike Macherey, though, I think this is true for Aristotle and Hegel as well.)

Demonstration in both Aristotle’s and Spinoza’s sense is intended to improve our normative understanding of concepts by “showing” their inferential uses and points of application. It is only through their inferential use in the demonstrations that Spinoza’s nominal definitions and axioms acquire a meaning Spinoza would call “adequate”.

Place of a Preface

The preface to Hegel’s Phenomenology famously maintains that the conventional notion of a preface (e.g., “say what you are going to say”) is inapplicable to serious work in philosophy. There is an air of paradox about this, because in some sense he goes on to do what he just said was impossible. Hegel’s preface does summarize key conclusions of the book, but Hegel wants to make it clear that any such summary can at best be what Kant would call a dogmatic anticipation of real philosophical work yet to be done (in Brandom’s phrase, a “promissory note”).

I would note that this also reflects Hegel’s deep Aristotelianism. The way ideas are developed counts for much more than the way in which they are introduced. Aristotle did not follow the “say what you are going to say” model. Instead, he would begin with broad orienting remarks, a preliminary demarcation of subject matter, and a survey of common or leading views on the subject. Beginnings are the least certain part of a work; real substance emerges — if at all — from extensive development.

Of course it is possible to refer to an extensive development without producing or reproducing it in-line, but the relative soundness of such references depends on the soundness of the development and its applicability.

Simplicity is a pedagogical virtue that helps us on the uptake, but ultimately it cannot be the criterion of clarity. Real clarity comes from manifest interlinkages in a development that can be assessed independent of asserted conclusions (see Aristotelian Demonstration).

In his commentary, Harris says “The most important part here is Hegel’s insistence that the results of a science — whether it be philosophical or empirical — cannot be separated from the process (the Ausführung, or ‘execution’) by which they are reached” (Hegel’s Ladder I, p. 36). One of Hegel’s minor headings in the preface reads: “The principle is not the conclusion — against Formalism” (quoted on p. 48).

“We have a paradox here. The philosophical truth is absolute; but we have to hear it from one who is like ourselves. In this sphere, all particular situations are equally contingent. The philosopher, addressing her peers, will begin with this problem of how someone who accepts the finite human status can claim to say what is absolutely true — because that was precisely the problem that philosophy faced when the Phenomenology of Spirit was conceived. The philosopher and her peers, however, are not ‘in the midst of things’ in the way that the rest of us are. When she writes a book, she must take account of how we, the literate audience, are in medias res [in the midst of things]. Yet neither her situation nor ours is of any concern to philosophy as a systematic Science. For philosophy itself it is only the pure structure of ‘being in the midst of things’ that can be a possible starting point” (pp. 33-34).

Next in this series: Indistinct Cows, Pistol Shot

Searching for a Middle Term

“But nothing, I think, prevents one from in a sense understanding and in a sense being ignorant of what one is learning” (Aristotle, Posterior Analytics; Complete Works revised Oxford edition vol. 1, p. 115). The kind of understanding spoken of here involves awareness “both that the explanation because of which the object is is its explanation, and that it is not possible for this to be otherwise” (ibid). To speak of the “explanation because of which” something is suggests that the concern is with states of affairs being some way, and the “not… otherwise” language further confirms this.

Following this is the famous criterion that demonstrative understanding depends on “things that are true and primitive and immediate and more familiar than and prior to and explanatory of the conclusion…. [T]here will be deduction even without these conditions, but there will not be demonstration, for it will not produce understanding” (ibid). The “more familiar than” part has sometimes been mistranslated as “better known than”, confusing what Aristotle carefully distinguishes as gnosis (personal acquaintance) and episteme (knowledge in a strong sense). I think this phrase is the key to the whole larger clause, giving it a pragmatic rather than foundationalist meaning. (Foundationalist claims only emerged later, with the Stoics and Descartes.) The pedagogical aim of demonstration is to use things that are more familiar to us — which for practical purposes we take to be true and primitive and immediate and prior and explanatory — to showcase reasons for things that are slightly less obvious.

Independent of these criteria for demonstration, the whole point of the syllogistic form is that the conclusion very “obviously” and necessarily follows, by a simple operation of composition on the premises (A => B and B => C, so A=> C). Once we have accepted both premises of a syllogism, the conclusion is already implicit, and that in an especially clear way. We will not reach any novel or unexpected conclusions by syllogism. It is a kind of canonical minimal inferential step, intended not to be profound but to be as simple and clear as possible.

(Contemporary category theory grounds all of mathematics on the notion of composable abstract dependencies, expressing complex dependencies as compositions of simpler ones. Its power depends on the fact that under a few carefully specified conditions expressing the properties of good composition, the composition of higher-order functions with internal conditional logic — and other even more general constructions — works in exactly the same way as composition of simple predications like “A is B“.)

Since a syllogism is designed to be a minimal inferential step, there is never a question of “searching” for the right conclusion. Rather, Aristotle speaks of searching for a “middle term” before an appropriate pair of premises is identified for syllogistic use. A middle term like B in the example above is the key ingredient in a syllogism, appearing both in the syntactically dependent position in one premise, and in the syntactically depended-upon position in the other premise, thus allowing the two to be composed together. This is a very simple example of mediation. Existence of a middle term B is what makes composition of the premises possible, and is therefore what makes pairings of premises appropriate for syllogistic use.

In many contexts, searching for a middle term can be understood as inventing an appropriate intermediate abstraction from available materials. If an existing abstraction is too broad to fit the case, we can add specifications until it does, and then optionally give the result a new name. All Aristotelian terms essentially are implied specifications; the names are just for convenience. Aristotle sometimes uses pure specifications as “nameless terms”.

Named abstractions function as shorthand for the potential inferences that they embody, enabling simple common-sense reasoning in ordinary language. We can become more clear about our thinking by using dialectic to unpack the implications of the abstractions embodied in our use of words. (See also Free Play; Practical Judgment.)

Demonstrative “Science”?

The “historiographical” notes on the history of philosophy I offer here from time to time are a sort of compromise. For much of my life, I’ve been very concerned with the fine grain of such history, and with casting a broad net encompassing many historical figures. Here, I made a strategic decision to focus instead on a mere handful of philosophers I consider most important.

Discussion of actualization in Hegel led to actualization in Aristotle, which led me to indulge my fascination with the Aristotelian commentary tradition. To the extent that it is possible to generalize about the historic readings discussed in the Greek, Arabic, Hebrew, and Latin commentaries, my own view of Aristotle is quite different on a number of key points, having more in common with some modern readings. Nonetheless, I am enormously impressed by the levels of sophistication shown by very many writers in this tradition.

I just mentioned al-Farabi again. As previously noted, al-Farabi (10th century CE) played a great historic role in the formulation of Arabic (and consequently, Hebrew and Latin) views of Aristotle. The Syrian Christians who did the majority of the translating of Aristotle to Arabic from Syriac had access to most of Aristotle’s works, but publicly only taught from the logical treatises. It was al-Farabi who initiated public teaching of the full range of Aristotelian philosophy in the Islamic world. He flourished during the so-called Islamic golden age, a time of tremendous interest in ancient learning not only by aristocrats but by many literate skilled crafts people. The political climate of the Islamic world at the time was much more embracing of secular learning than it came to be between the 13th and 19th centuries CE.

One unfortunate aspect of al-Farabi’s reading was a very strong privileging of a notion of demonstrative “science” over Aristotle’s own predominant use of dialectic in philosophical development. This was based on a reading of Aristotle’s Posterior Analytics as propounding a model of “science” as a deductive enterprise expected to result in certain knowledge, which is still dominant today, but which I (following a number of modern interpreters) think involves a misreading of the basic aims of Aristotelian demonstration.

The idea that Aristotle was fundamentally concerned to develop “sciences” yielding certain knowledge gave a more dogmatic cast to his whole work, which has been a contributing factor in common negative stereotypes of Aristotle. Many modern commentators who still accept this reading of Posterior Analytics have been puzzled by the huge gap between this and Aristotle’s actual practice throughout his works, which in fact is mainly dialectical. I think a careful reading of the Topics (on dialectic) and Posterior Analytics (on demonstration) with consultation of the Greek text on the originals of some key phrases yields a view that is far more consistent with Aristotle’s actual practice.

Demonstration is a pedagogical way of showing very clear reasons for certain kinds of conclusions. It works by assuming some premises are true, whereas dialectic makes no such assumption. Thus the only necessity that results from demonstration is the “hypothetical” one that if the premises are true, then the conclusion is also true. But the more important point in regard to the classic syllogistic form is that the common “middle term” that allows the major and minor premises to be both formally and materially composed together illuminates why we ought to consider it appropriate to assume the conclusion is true if we believe the premises are true.

Dialectic, as I have said, is cumulative, exploratory discursive reasoning about meanings in the absence of initial certainty. This is how Aristotle mainly approaches things. Dialectic implicitly relies on the same logical form of syllogistic argument explicitly used in demonstration, but Aristotle distinguishes dialectic and demonstration by whether premises are treated as hypotheses to be evaluated, or as hypothetically assumed “truths” to be interpreted.

It is also important to note that in the Latin scholastic tradition, the dogmatic trend resulting from wide acceptance of claims about demonstrative science was significantly mitigated by a strong counter-trend of evenhandedly analyzing arguments pro and con, which effectively revived a form of dialectic. (See also Foundations?; Fortunes of Aristotle; Scholastic Dialectic.)

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.)

Kantian Discipline

The Discipline of Pure Reason chapter in Kant’s Critique of Pure Reason makes a number of important points, using the relation between reason and intuition introduced in the Transcendental Analytic. It ends up effectively advocating a form of discursive reasoning as essential to a Critical approach.

If we take a simple empirical concept like gold, no amount of analysis will tell us anything new about it, but he says we can take the matter of the corresponding perceptual intuition and initiate new perceptions of it that may tell us something new.

If we take a mathematical concept like a triangle, we can use it to rigorously construct an object in pure intuition, so that the object is nothing but our construction, with no other aspect.

However, he says, if we take a “transcendental” concept of a reality, substance, force, etc., it refers neither to an empirical nor to a pure intuition, but rather to a synthesis of empirical intuitions that is not itself an empirical intuition, and cannot be used to generate a pure intuition. This is related to Kant’s rejection of “intellectual” intuition. We are constantly tempted to act as if our preconscious syntheses of such abstractions referred to objects in the way that empirical and mathematical concepts do, each in their own way, but according to Kant’s analysis, they do not, because they are neither perceptual nor rigorously constructive.

All questions of what are in effect higher-order expressive classifications of syntheses of empirical intuitions belong to “rational cognition from concepts, which is called philosophical” (Cambridge edition, p.636, emphasis in original). This is again related to his rejection of the apparent simplicity and actual arbitrariness of intellectual intuition and its analogues like supposedly self-evident truth. It opens into the territory I have been calling semantic, and associating with a work of open-ended interpretation. (See also Discursive; Copernican; Dogmatism and Strife; Things In Themselves.)

I am more optimistic than Kant that something valuable — indeed priceless — can come from this sort of open-ended work of interpretation. Its open-endedness means no achieved result is ever beyond question, but I think we implicitly engage in this sort of “philosophical” interpretation every day of our lives, and have no choice in the matter. I also think serious ethical deliberation necessarily makes use of such interpretation, and again we have no choice in the matter. So, pragmatically speaking, defeasible interpretation is indispensable.

Kant goes on to polemicize against attempts to import a mathematical style of reasoning into philosophy, like Spinoza tried to do. Spinoza’s large-scale experiment with this in the Ethics I find fascinating, but ultimately artificial. It does make the inferential structure of his argument more explicit, and Pierre Macherey used this to great advantage in his five-volume French commentary on the Ethics. But there is a big difference between a pure mathematical construction — which can be interpreted without remainder by something like formal structural-operational semantics in the theory of programming languages, and so requires no defeasible interpretation of the sort mentioned above, on the one hand — and work involving concepts that can only be fully explicated by that sort of interpretation, on the other. Big parts of life — and all philosophy — are of the latter sort. So it seems Kant is ultimately right on this.

Kant points out that definition only has precise meaning in mathematics, and prefers to use a different word in other contexts. I make similar well-intentioned but admittedly opinionated recommendations about vocabulary, but what is most important is the conceptual difference. As long as we are clear about that, we can use the same word in more than one sense. As Aristotle would remind us, multiple senses of words are an inescapable feature of natural language.

Kant says that unlike the case of mathematics, in philosophy we should not put definitions first, except perhaps as a mere experiment. Again, he probably has Spinoza in mind, and again — personal fondness for Spinoza notwithstanding — I have to agree. (Macherey in his reading of Spinoza actually often goes in the reverse direction, interpreting the meaning of each part in terms of what it is used to “prove”, but the order of Spinoza’s own presentation most obviously suggests the kind of thing to which Kant is properly objecting.) More than anything else, meanings are what we seek in philosophical inquiry, so they cannot be just given at the start. We can certainly discuss or dialectically analyze stipulated meanings, but that is strictly secondary and subordinate to a larger interpretive work.

Following conventional practice, Kant allows for axioms in mathematics, but says they have no place in philosophy. He has in mind the older notion of axioms as supposedly self-evident truths. Contemporary mathematics has vastly multiplied alternative systems, and effectively treats axioms like stipulative definitions instead. If we have in mind axioms as self-evident truths, Kant’s point holds. If we have in mind axioms as stipulative definitions, then his point about stipulative definitions in philosophy applies to axioms as well.

A similar pattern holds for demonstration or proof. Mathematics for Kant always has to do with strict constructions, which do not apply in philosophy, where there is always matter for interpretation. (From the later 19th century, mathematicians began increasingly to invent theories that seemed to require nonconstructive assumptions — transfinite numbers, standard set theories, and so on. This is currently in flux again. Contrary to what was thought at an earlier time, it now appears that all valid “classical” mathematics, including transfinite numbers, can be expressed in a higher-order constructive formalism. Arguments are still raging about which style is better, but I am sympathetic to the constructive side.) Philosophical arguments are informally reasoned interpretations, not proofs.

Kant says that speculative thought in general, because it does not abide by these guidelines, unfortunately ends up full of what he does not hesitate to call dishonesty and hypocrisy. (When I occasionally ascribe honesty or dishonesty to a philosopher, it is with similar criteria in mind — especially the presence or absence of frank identification of speculation as such when it occurs. See also Likely Stories.)

The kind of philosophy I am recommending is concerned with explication of meanings, not a supposed generation of truths, so it is not speculative in Kant’s sense. What may not be obvious is just how large and vital the field of this sort of interpretation really is in life. The most common and compact form by which such interpretations are expressed in the small looks syntactically like ordinary assertion, and in ordinary social interaction, mistaking one for the other has little effect on communication. When the focus is not on practical communication but on improving our understanding, we have to step back and look at the larger context, in order to tell what is a speculative assertion and what is an interpretation expressed in the form of assertion. (See also Pure Reason, Metaphysics?; Three Logical Moments.)

(In the present endeavor, the great majority of what look like simple assertions are actually compact expressions of interpretations!)