One, Many, Same, Different

Book Iota (X) of Aristotle’s Metaphysics extends the discussion in book Delta (V) of things said in many ways, going into detail on what makes things one, many, the same, or different. These are extremely important matters for any sound reasoning, though somewhat technical in nature. It also contains Aristotle’s sharp critique of the saying of Protagoras, “Man is the measure of all things”.

“[T]here are four senses in which something is said to be one primarily and in its own right, rather than incidentally” (ch.1, p. 185).

As to the first, “oneness belongs to what is continuous, either simply or, especially, by nature, and not by contact or a binding cord (and of these that is more so one and is more primary of which the motion is more indivisible and simple)” (ibid).

Continuity in a material is the lowest degree of something being one in its own right. That which is materially united by contact or by any artificial means would not be one in its own right.

As to the second, “[oneness] belongs still more to what is whole and has some form and look, especially if something is of that sort by nature and not by force, as those things are that are so by means of glue or bolts or being tied with a cord, but rather has in itself that which is responsible for its being continuous. And something is of this sort if its motion is one and indivisible in place and time; and so it is clear that, if something that has a source of motion that moves it in the primary kind of the primary class of motions (by which I mean a circular type of change of place), this is one magnitude in the primary sense” (ibid).

Being a whole is a higher degree of unity than being materially continuous. The association of circular motion with a strong unity is relevant to the upcoming argument in book Lambda (XII) about the first cause.

“So some things are one in this way, insofar as they are continuous or whole, but others are one because the articulation of them is one, and of this sort are those things of which the thinking is one, and this in turn is of this sort if it is indivisible, and an act of thinking is indivisible if it is of something indivisible in form or in number” (ibid, emphasis added).

As to the third, “a particular thing is one by being indivisible in number” (ibid, emphasis added).

These would include all the independent and non-independent things that were extensively discussed in book Zeta (VII).

He continues, “but that which is one by means of intelligibility and knowledge is indivisible in form, so [fourth] what is responsible for the oneness of independent things would be one in the primary sense” (ibid, emphasis added).

I expect that this last kind will turn out to be the first cause.

“But it is necessary to notice that one must not take the sorts of things that are spoken of as one as being meant in the same way as what it is to be one, or what the articulation of it is” (p. 186).

This is analogous to the distinction between saying something about something in general, and saying what something is, also discussed in book Zeta. He illustrates this below, with the example of fire.

“The same thing would also be the case with ‘element’ and ’cause’, if one had to speak about them, distinguishing the things to which the words are applied, and giving a definition of the words. For there is a sense in which fire is an element… and a sense in which it is not; for being fire is not the same thing as being an element…. And it is that way also with ’cause’ and ‘one’ and all such things, and this is why being one is being indivisible, just exactly what it is to be a this, separate on its own in either place or form or thinking, or to be both whole and indivisible, but especially to be the primary measure of each class of things, and, in the most governing sense, of the class of things with quantity, for it has come from there to apply to other things” (ibid).

Being one in the third sense above (being a particular thing) is now said to be “just exactly what it is to be a this“. This foreshadows an extensive one-to-one mapping he will develop below, between all the ways of the saying of being he elaborates in book Delta (V), and the ways of the saying of oneness.

He goes on to speak at some length about measures, which we would call units of measurement.

The most important point is that “a measure is always the same kind of thing as what it measures, for the measure of magnitudes is a magnitude, and in particular, that of length is a length, of breadth a breadth, of spoken sounds a spoken sound, of weight a weight, and of numerical units a numerical unit” (p. 188, emphasis added).

The distinction he makes here tracks perfectly with the way that different types, dimensions, and variables are handled separately in the operations defined by modern mathematics.

“And we speak of knowledge or sense perception as a measure of things for the same reason, because we recognize something by means of them, although they are measured more than they measure” (ibid).

The simultaneously humorous and serious caveat that “they are measured more than they measure” means that knowledge and perception are constrained by reality. More precisely, they are involved in mutual dependencies with the realities of things that they at once measure and are measured by.

“And Protagoras says a human being is the measure of all things, as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception, which we say are the measures of their objects. So while saying nothing, these people appear to be saying something extraordinary” (ibid).

Aristotle, at the end of his discussion of measure (longer and more detailed than included here), refers to Protagoras’ famous saying, commonly quoted as “Man is the measure of all things”. With uncharacteristic sharpness, he calls this “saying nothing”. Why? This seems worthy of a short digression.

Protagoras was a prominent Sophist, who appears in Plato’s dialogue of the same name. He wrote a controversial treatise entitled Truth, which began with the sentence, “Of all things the measure is man: of those that are, that they are; and of those that are not, that they are not”. Plato and Aristotle both took Protagoras to be asserting a kind of individualist relativism. Reportedly, the skeptic Sextus Empiricus also read him this way. Plato took him to deny any objective reality. Aristotle in book Gamma (IV) shows rare outrage at his other reported claim that “it is not possible to contradict”. I didn’t mention him by name in my account, but Aristotle names him there as well.

Aristotle implies it is a bit more plausible to much more specifically say that knowledge and perception are measures of things, but even that only with the caveat that really “they are measured more than they measure”.

But why go on to add with such sharpness that Protagoras is “saying nothing”? I suspect the answer may lie with the other part of Aristotle’s interpretation: “as if he were saying that a knower or perceiver were the measure, and these because the one has knowledge and the other perception”.

I’m inclined to think Aristotle would regard it as outrageous to transfer what may (ambiguously) be said of specific knowledge and perception, to an unqualified saying about one who is said to possess knowledge and perception in general.

Aristotle has just given an account of what a measure is, that it must be of the same kind as the things that it measures. How could one thing (“man”) possibly be the measure of countless things that have no common measure? That does sound like nonsense. Any measure has to be of one kind or another. Modern mathematics agrees that kinds, dimensions, variables can only be collapsed together if very specific criteria are met.

What Aristotle emphasizes here about knowledge and perception — that they have a remarkable involvement with things that also measure them — seems very consistent with his general views. But the way Protagoras implicitly presents “man” as their possessor makes the possessor stand apart from the mutual involvement with things that Aristotle emphasizes, in which knowledge and perception and things measure one another. In splendid isolation from all constraints of real measure, the possessor seems to have arbitrary freedom to claim whatever she wishes.

I intuitively associate Protagoras with the attitude that what’s true for you is true for you, but what’s true for me is true for me, so don’t tell me I’m wrong, and I won’t tell you you’re wrong! Then and now, such sentiments had and have a superficial appeal, because they seem to express a live-and-let-live attitude, which seems to be a good thing. But the way it is expressed, in fact it completely undermines any possibility of meaningful dialogue, which undermines reason itself, which undermines the very thing that makes us human.

Back to the text, Aristotle turns to illustrating the one-to-one mapping I mentioned between sayings about being and sayings about oneness.

“[S]ince not even being itself is an independent thing as though it were some one thing capable of having being apart from the many beings (since it is common to them), other than solely as a thing attributed to them, it is clear that oneness is not a universal either” (ch. 2, p. 189).

For Aristotle, neither Being nor the One is an independent thing in its own right. He will nonetheless argue in book Lambda (XII) that there is a first cause for all things.

“What’s more, what is true about oneness must hold true in a similar way for all things; and being and oneness are meant in equally many ways” (ibid).

“And the same account applies also to the other classes of things, … and [if] in all instances it is the case both that the number is a number of something and that oneness is some particular one thing, and oneness itself is not the thinghood of it, then it must also be the same way with independent things” (p. 190).

“[S]o too in thinghood, one independent thing is oneness itself; and that oneness in a certain way means the same thing as being, is clear from the fact that it follows along equally through the ways being is attributed, and is not any one of them (for instance, it is not what anything is, nor of-what-sort anything is, but stands similarly toward them just as being does), and from the fact that no other thing is predicated in ‘one human being’ over and above what is predicated in ‘human being’ (just as being is not something over and above what and of-what-sort and how-much a thing is), or in ‘being one’ over and above being any particular thing” (ibid).

Saying something is one human being is the same as saying it is a human being. In book Zeta, he analogously said that “good” and “being good” are the same.

Things are often one in one respect, but many in another. The one and the many are “contraries, and not opposed as contradictories or as what are called relative terms” (ch. 3, p. 190). Next he turns to the meanings of same, other, and different.

“Since the same is meant in more than one way, in one way we sometimes speak of what is the same in number, but we say it in another sense if things are one in meaning as well as in number, as you are one with yourself in both form and material, and in another again if the articulation of the primary thinghood of things is one, for instance in the way equal straight lines are the same, … but in these equality is oneness” (p. 191).

In Fregean terms, things are what Aristotle calls one in number when they have the same reference. They are what Aristotle calls one in meaning when they have the same sense. Frege illustrates how they differ by saying that the morning star and the evening star have the same reference, but different sense.

“Things are alike if, not being simply the same, nor without difference in their composite thinghood, they are the same in form, just as a larger square is like a smaller one…. Other things are alike if they have the same form, and have it in them to be more and less, but are neither more nor less than one another. Other things, if they are the same attribute, and one in form, say white, more and less intensely, people say are alike because their form is one. Other things are alike if they have more things the same than different, either simply or superficially, as tin is like silver insofar as it is white, and gold is like fire insofar as it is yellow and fiery-red” (ibid).

“So it is clear also that other and unlike are meant in more than one way” (ibid).

“[B]ut difference is something other than otherness…. [W]hat is different from something is different in some particular respect, so it must necessarily be the same in some respect as that with which it differs” (p. 192).

For Aristotle, calling two things different presupposes that they can be meaningfully compared in the first place. This is not the case for things that are just “other” than one another. Black is different from white; they are both colors. But an apostrophe is just other than an aardvark.

This is followed by a ten-page discussion of technical details of contrariety, which I will mostly skip. Contrariety supports a definitive ruling out of some things based on other things. This has great importance for reasoning.

Incidentally, Aristotle explains why there is no essential difference between human beings with different colorings.

“And since one sort of thing is articulation while another is material, those contrarieties that are in the articulation make a difference in species, but those that are in what is conceived together with the material do not make such a difference. This is the reason that whiteness of a human being, and blackness, do not make such a difference…. For there is a difference between a white human being and a black horse, but that is not insofar as the one is white and the other is black” (ch. 9, pp. 201-202).

Finally, he argues that destructibility and indestructibility inhere in things by necessity. Whether a thing is destructible or not depends strictly on what genus of things its species belongs to.

“[A] destructible thing and an indestructible thing must be different in genus…. Therefore it is necessary that destructibility either be the thinghood or be present in the thinghood of each destructible thing; and the same argument also concerns the indestructible, since both are among things present by necessity” (ch. 10, p. 202).

Next in this series: Toward a First Cause

Parmenides

The late 6th or early 5th century BCE poet Parmenides of Elea was commonly regarded in the Greek tradition as a philosopher. Apparently his only work was a poem of 800 or so verses in epic hexameter form, of which about 160 are known from quotations in later authors, principally the commentary by the neoplatonist Simplicius on Aristotle’s Physics.

Parmenides may have been the first person to make strong claims purportedly grounded in nothing but pure reason. At the same time, he drew a sharp distinction between appearance and reality. He achieved notoriety among his fellow Greeks because his claims contradicted all experience. His disciple Zeno used Parmenidean principles to “prove” that arrows cannot fly, and that the speedy Achilles could never overtake a tortoise that had a head start.

According to Parmenides, we can “neither know, or attain to, or express, non-being”. He concluded from this that all distinction, becoming, and motion were mere appearances of “the way of error in which the ignorant and double-minded mortals wander. Perplexity of mind sways the erring sense. Those who believe Being and non-being to be the same, and then again not the same, are like deaf and blind men surprised, like hordes confusedly driven”.

“But the truth is only the ‘is’; this is neither begotten of anything else, nor transient, entire, alone in its class, unmoved and without end; it neither was, nor will be, but is at once the all. For what birth wouldst thou seek for it? How and whence should it be augmented? That it should be from that which is not, I shall allow thee neither to say nor to think, for neither can it be said or thought that the ‘is’ is not. What necessity had either later or earlier made it begin from the nothing? Thus must it throughout only be or not be; nor will any force of conviction ever make something else arise out of that which is not. Thus origination has disappeared, and decease is incredible. Being is not separable, for it is entirely like itself; it is nowhere more, else would it not hold together, nor is it less, for everything is full of Being. The all is one coherent whole, for Being flows into unison with Being: it is unchangeable and rests securely in itself; the force of necessity holds it within the bounds of limitation. It cannot hence be said that it is imperfect; for it is without defect, while non-existence is wanting in all” (quoted in Hegel, History of Philosophy vol. 1, Haldane trans., pp. 252-253).

Plato treats Parmenides with considerable respect, but fundamentally rejects his blunt teaching about being and non-being, replacing it with far subtler views, e.g., in The Sophist.

Aristotle says that Plato (and the atomist Democritus, whose writings are lost) were the first practitioners of extended philosophical argument, and I consider that the true beginning of philosophy; it seems to me Parmenides only made assertions and claimed they were grounded in pure reason. In his poem, the key claims are presented as revelations from a goddess. Much later, Kant would argue that nothing follows from pure reason alone.

According to Hegel’s History of Philosophy lectures, “This beginning is certainly still dim and indefinite, and we cannot say much of what it involves; but to take up this position certainly is to develop Philosophy proper, which has not hitherto existed”. Hegel says Spinoza tells us correctly that all determination is based on negation, but “Parmenides says, whatever form the negation may take, it does not exist at all” (p. 254). Spinoza scholars have criticized the claim about Spinoza, but in this context that is a side issue.

Hegel’s association of Parmenides with the beginning of philosophy needs to be understood in terms of his insistence on the inherent defectiveness of beginnings and the positive, provocative role of failures of thought. In differing degrees, Hegel also actually recognizes two other beginnings of philosophy as well — in the figurative thought of the world’s various religious traditions before Parmenides (who appears only halfway through volume 1 of Hegel’s History), and in the dialogues of Plato, with whom Hegel’s second volume begins. For Hegel, Parmenides’ bare thought of Being and denial of the basis of all determination represent an absolute failure of thought and an impossibility, but he nonetheless credits that failure and impossibility as having defined a problem that provoked all later development.

I consider it quite possible that Aristotle’s brief remarks about “being qua being” in two books of the Metaphysics were a kind of response to the Parmenidean problem. Traditionally, this has been claimed to be the subject matter of the Metaphysics, but both times Aristotle raises the problem explicitly, his discussion is limited to arguing for the moral necessity of the principle of noncontradiction, against the Sophists. In effect, he says that serious people must by definition take their commitments seriously, and therefore they do not contradict their own commitments.

Noncontradiction has a great importance for integrity in ethics, which was to be taken up anew by Kant and Hegel, with their emphasis on unity of apperception. But as Hegel points out explicitly in the Logic, pure being by itself is logically empty and sterile. In first philosophy, nothing follows from being qua being. (See also Hegel on Being.)

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.

Distinction

So, I want to say that distinction is something good, not a defect we ought to remedy. It is a fundamental symptom of life. Stoics, Buddhists and others remind us that it is best not to be too attached to particular forms. This is a wise counsel, but not the whole truth. I am tempted to say there is no compassion without some passion. Caring about anything inevitably involves distinction. It is better to care than not to care.

Everything flows, Heraclitus said. But in order to make distinctions, it has to be possible to compare things. Things must have a character, even if they do not quite ever stay still within their frames. Having a character is being this way and not that. Real being is always being some way or other. Its diversity is something to celebrate.

It is not immoral to prefer one thing to another. We can’t be who we are without definite commitments. Perfect apathy would lead to many sins of omission. It is better to have lived fully. We are not apart from the world, but inhabit the oceans of difference, and sometimes must take a side.

Nondualism?

As far as I know, the explicit term “nondualism” was first used in certain strands of Mahayana Buddhism. I believe it later was adopted by the Vedanta school of Hindu scholastic philosophy. I was fascinated with these as a young man, and was for a time much absorbed in developing a sort of Alan Watts style interpretation of Plotinus’ emphasis on the One as a similar kind of radical nondualism.

Radical nondualism goes beyond the rejection of sharply dualist views like those of Descartes on mind and world, and the different religious dualisms like those of Augustine, the Zoroastrians, the Gnostics, the Manichaeans, or the Samkhya school of Hinduism. Each of these latter has important differences from the others, but what unites them is the strong assertion of some fundamental duality at the heart of things. Radical nondualism aims to consistently reject not only these but any vestige of duality in the basic account of things.

The point of view I would take now is that many useful or arguably necessary distinctions are often formulated in naive, overly blunt ways. We should strive to overcome our naivete and our excessive bluntness, but that does not in any way mean we should try to overcome distinction per se. There can be no meaning — even of the most spiritual sort — without some sort of distinction between things. “All is One” is at best only a half-truth, even if it is a profoundly spiritual one.

Pure Difference?

A common theme here is the conceptual priority of difference over identity. I think that identity is a derived concept, and not a primitive one (see also Aristotelian Identity).

The French philosopher Gilles Deleuze (1925-1995) in Difference and Repetition and other works argued that a pure notion of difference is by itself sufficient for a general account of things. In information theory, information is explained as expressing difference. In Saussurean structural linguistics, we are said to recognize spoken words by recognizing elementary differences between sounds. In both cases, the idea is that we get to meaning by distinguishing and relating.

Deleuze initially cites both of these notions of difference, but goes on to develop arguments grounded largely in Nietzsche and Kierkegaard, whom he uses to argue against Plato and Hegel. His very interesting early work Nietzsche and Philosophy was marred by a rather extreme polemic against Hegel, and in Difference and Repetition he announces a program of “anti-Platonism” that reproduces Nietzsche’s intemperate hostility to Plato. Nietzsche blamed Plato for what I regard as later developments. Neither Plato nor Aristotle made the kind of overly strong assertions about identity that became common later on.

In The Sophist and elsewhere, Plato had his characters speak of Same, Other, and the mixing of the two as equally primordial. Hegel took great pains to elaborate the notion of a “difference that makes a difference”. But Deleuze wants to argue that Plato and Hegel both illegitimately subordinate difference to identity. His alternative is to argue that what is truly fundamental is a primitive notion of difference that does not necessarily “make a difference”, and that come before any “making a difference”. (I prefer the thesis of Leibniz that indiscernibility of any difference is just what identity consists in.)

This is related to Deleuze’s very questionable use of Duns Scotus’ notion of the univocity of being, both in general and more particularly in his interpretation of Spinoza. For Deleuze, pure difference interprets Scotist univocal being.

I frankly have no idea what led to Deleuze’s valorization of Scotus. Deleuze is quite extreme in his opposition to any kind of representationalism, while Scotus made representability the defining criterion of his newly invented univocal being. It is hard to imagine views that are further apart. I can only speculate that Deleuze too hastily picked out Scotus because he wanted to provocatively oppose the 20th century neo-Thomism that had considerable prominence in France, and Scotus is a leading medieval figure standing outside the Thomist tradition.

For Deleuze, univocal being is pure difference without any identity. Difference that doesn’t make a difference seems to take over the functional role that identity has in theories that treat it as something underlying that exceeds any discernibility based on criteria. I don’t see why we need either of these.

I think Deleuze’s bête noir Hegel actually did a better job of articulating the priority of difference over identity. Hegel did this not by appealing to a putative monism of difference and nothing else, but by developing correlative notions of “difference that makes a difference”, and a kind of logical consequence or entailment that we attribute to real things as we interpret them, independent of and prior to any elaboration of logic in a formal sense.

In Hegel’s analysis as explicated by Brandom, any difference that makes a difference expresses a kind of “material” incompatibility of meaning that rules out some possible assertions. This is just what “making a difference” means. Meanwhile, all positive assertions can be more specifically analyzed as assertions of some consequence or entailment or other at the level of meaning (see Material Consequence). Every predication is analyzable as an assertion of consequence or entailment between subject and predicate, as Leibniz might remind us. It is always valid to interpret, e.g., “a cat is a mammal” as an inference rule for generating conclusions like if Garfield is a cat, then Garfield is a mammal.

What is missing from Deleuze’s account is anything like entailment, the idea of something following from something else. This notion of “following”, I am convinced, is prior to any notion of identity applicable to real things. Without presupposing any pre-existing identities of things, we can build up an account of the world based on the combination of differences that make a difference, on the one hand, and real-world entailments, on the other. Identity is then a result rather than an assumption. Meanings (and anything like identity) emerge from the interplay of practical real-world entailments and distinctions. It is their interplay that gives them definition in terms of one another.

Deleuze was a sort of ontological anarchist, who wanted being to be free of any pre-existing principles. While I agree that we can’t legitimately just assume such principles, I think this is very far from meaning that principles are irrelevant, or actually harmful. On the contrary, as Kant might remind us, principles are all-important. They aren’t just “given”. We have to do actual work to develop them. But if we have no principles — if nothing truly follows from anything else, or is ruled out by anything else — then we cannot meaningfully say anything at all.