Two Epistemic Paradigms

27 December 2011

Tuesday


René Descartes lived in this house in Westermarkt 6, Amsterdam. If you wanted to rebuild it from the ground up, you would need to live in another house in the meantime.

Yesterday in The Philosophy of Fear I quoted Descartes from his Discourse on Method, from the section in which he introduces an implicit distinction between the theoretical principles he will use to guide his philosophical activities and the practical moral principles that he will employ in his life while he is going about his theoretical activity. Here is his exposition of his four theoretical principles:

The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.

The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.

The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.

And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.

Anyone who knows Descartes’ works will recognize that he has here stated, much more simply and compactly, the principles that he was working on in his unfinished manuscript Rules of the Direction of Mind. Here, by way of contrast, is a highly condensed version of Descartes’ practical and provisional moral principles:

The first was to obey the laws and customs of my country, adhering firmly to the faith in which, by the grace of God, I had been educated from my childhood and regulating my conduct in every other matter according to the most moderate opinions, and the farthest removed from extremes, which should happen to be adopted in practice with general consent of the most judicious of those among whom I might be living.

My second maxim was to be as firm and resolute in my actions as I was able, and not to adhere less steadfastly to the most doubtful opinions, when once adopted, than if they had been highly certain; imitating in this the example of travelers who, when they have lost their way in a forest, ought not to wander from side to side, far less remain in one place, but proceed constantly towards the same side in as straight a line as possible, without changing their direction for slight reasons, although perhaps it might be chance alone which at first determined the selection; for in this way, if they do not exactly reach the point they desire, they will come at least in the end to some place that will probably be preferable to the middle of a forest.

My third maxim was to endeavor always to conquer myself rather than fortune, and change my desires rather than the order of the world, and in general, accustom myself to the persuasion that, except our own thoughts, there is nothing absolutely in our power; so that when we have done our best in things external to us, all wherein we fail of success is to be held, as regards us, absolutely impossible: and this single principle seemed to me sufficient to prevent me from desiring for the future anything which I could not obtain, and thus render me contented…

Descartes wrote a lot a extremely long run-on sentences, so that one must cut radically in order to quote him (except for his theoretical principles, above, which I have quoted entire), but I have tried to include enough above to give a genuine flavor of how he expressed himself. Although Descartes did not himself make this distinction between theoretical and practical principles explicit, although the distinction is explicitly embodied in his two sets of explicitly stated principles, he does provide a justification for the distinction:

“…as it is not enough, before commencing to rebuild the house in which we live, that it be pulled down, and materials and builders provided, or that we engage in the work ourselves, according to a plan which we have beforehand carefully drawn out, but as it is likewise necessary that we be furnished with some other house in which we may live commodiously during the operations, so that I might not remain irresolute in my actions, while my reason compelled me to suspend my judgement, and that I might not be prevented from living thenceforward in the greatest possible felicity, I formed a provisory code of morals, composed of three or four maxims, with which I am desirous to make you acquainted.”

After I quoted this in The Philosophy of Fear I realized that it constitutes a perfect antithesis to the conception of the rational reconstruction of knowledge embodied in the image of Neurath’s ship, which I have quoted several times.

Rational reconstruction was an idea that fascinated early twentieth century philosophers, especially the logical positivists, whose philosophical tradition would eventually mature and transform itself into mainstream analytical philosophy. It was logical positivism that gave us an enduring image of rational reconstruction, as related by Otto Neurath:

“There is no way of taking conclusively established pure protocol sentences as the starting point of the sciences. No tabula rasa exists. We are like sailors who must rebuild their ship on the open sea, never able to dismantle it in dry-dock and to reconstruct it there out of the best materials. Only the metaphysical elements can be allowed to vanish without trace.”

Quine then used this image in his Word and Object:

“We are like sailors who on the open sea must reconstruct their ship but are never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way, by using the old beams and driftwood the ship can be shaped entirely anew, but only by gradual reconstruction.”

These two epistemic paradigms — what I will call Descartes’ house and Neurath’s ship — represent antithetical conceptions of the epistemological enterprise. Neurath’s ship is usually presented as an anti-foundationalist parable, which would suggest that Descartes’ house is a foundationalist parable. There are certain problems with this initial characterization. The logical positivists who invoked Neurath’s ship with approval were often foundationalists in the philosophy of mathematics while being anti-foundational in other areas.

There is a sense in which it is fair to call Descartes’ house a foundationalist parable: Descartes is suggesting a radical approach to the foundations of knowledge — utterly tearing down our knowledge in order to construct entirely anew on the same ground — and he attempted to put this into practice in his own philosophical work. He doubted everything that he could until he arrived at the fact that he could not doubt his own existence, and then on the basis of the certainty of his own existence he attempted to reconstruct the entire edifice of knowledge. The result was not radical, but actually rather conventional, but the method certainly was radical. It was also total.

Whether or not Neurath’s ship is anti-foundational, it is certainly incrementalist. If we were to attempt to rebuild a ship while at sea, we would need to proceed bit by bit, and very carefully. Nothing radical would be attempted, for to attempt anything radical would be to sink the ship. There is a sense in which we could identify this effort as essentially constructivist in spirit, though not exclusively constructivist: constructivism is certainly not the only motivation for Neurath’s ship, and many who invoked it employed non-constructive modes of reasoning.

Are Descartes’ house and Neurath’s ship mutually exclusive? Not necessarily. We do remodel houses while living in them, although when we do we need to keep some basic functions available during our residency. And we can demolish certain parts of a ship at sea; as long as the hull remains intact, we can engage in a radical reconstruction (as opposed to a rational reconstruction) of the masts and the rigging.

One ought not to push an image too far, for fear of verging on the ludicrous, but it can be observed that, while living in a house, we can tear down half of it to the ground and rebuild that half from scratch while living in the other half, and then repeat this process in the half we have been living in. In fact, I know people who have done this. There will, of course, be certain compromises that will have to be made in wedding the two halves together, so that the seam between the two has the incrementalist character of Neurath’s ship, while each half has the radical and total character of Descartes’ house.

It is difficult to imagine a parallel for the above scenario when it comes to Neurath’s ship. The hull of the ship can only be rebuilt incrementally, although almost everything else can be radically reconstructed. And it may well be that some parts of epistemology must be approached incrementally while other parts of epistemology may be radically reconstructed almost with impunity. This seems like an eminently reasonable conclusion. But it is no conclusion — at least not yet — because there is more to say.

What underlies the image of Descartes’ house and Neurath’s ship is in each case a distinct metaphor, and that metaphor is for Descartes the earth, the solid ground upon which we stand, while for Neurath it is the sea, to which we must go down in ships, and where we cannot stand but must swim or be carried. So, we have two epistemic metaphors — of what are they metaphors? Existence? Being? Human experience? Knowledge? If the house or the ship is knowledge, then the ground or the sea must be that upon which knowledge rests (or floats). This once again suggests a foundationalist approach, but points to very different foundations: a house stands on dirt and stones; a ship floats on water.

Does knowledge ultimately rest upon the things themselves — the world, existence, or being, as you prefer — or upon human experience of the world? Or is not knowledge a consequence of the tension between human experience and the world, so that both the world and human experience are necessary to knowledge?

Intuitively, and without initially putting much thought into this (although I will continue to think about this because it is an interesting idea), I would suggest that the metaphor of the earth implies that knowledge ultimately is founded on the things themselves, while the metaphor of the sea implies that knowledge ultimately is founded on the ever-changing tides of human experience.

Therefore, if knowledge requires both the world and human experience, either the metaphor of Descartes’ house or Neurath’s ship alone, in isolation from the other, is inadequate. We need something more, or something different, to illustrate our relation to knowledge and how it changes.

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If you want to rebuild a ship at sea, you'd better be careful about how you go about it.

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Friday


Given the astonishing yet demonstrable consequence of the Banach-Tarski paradox, it is the sort of thing that one’s mind returns to on a regular basis in order to savor the intellectual satisfaction of it. The unnamed author of the Layman’s Guide to the Banach-Tarski Paradox explains the paradox thus:

The paradox states that it is possible to take a solid sphere (a “ball”), cut it up into a finite number of pieces, rearrange them using only rotations and translations, and re-assemble them into two identical copies of the original sphere. In other words, you’ve doubled the volume of the original sphere.

The whole of the entry at Wolfram Mathworld runs as follows:

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of the same size as the original. The number of pieces was subsequently reduced to five by Robinson (1947), although the pieces are extremely complicated. (Five pieces are minimal, although four pieces are sufficient as long as the single point at the center is neglected.) A generalization of this theorem is that any two bodies in R3 that do not extend to infinity and each containing a ball of arbitrary size can be dissected into each other (i.e., they are equidecomposable).

The above-mentioned Layman’s Guide to the Banach-Tarski Paradox attempts to provide an intuitive gloss on this surprising result of set theory (making use of the axiom of choice, or some equivalent assumption), and concludes with this revealing comment:

In fact, if you think about it, this is not any stranger than how we managed to duplicate the set of all integers, by splitting it up into two halves, and renaming the members in each half so they each become identical to the original set again. It is only logical that we can continually extract more volume out of an infinitely dense, mathematical sphere S.

Before I read this today, I’d never come across such a clear and concise exposition of the Banach-Tarski paradox, and in provides food for thought. Can we pursue this extraction of volume in something like a process of transfinite recursion, arriving at some geometrical equivalent of ε0? This is an interesting question, but it isn’t the question that I started out thinking about as suitable for the philosophically inclined mathematician.

When I was thinking about the Banach-Tarski paradox today, I began wondering if a sufficiently generalized formulation of the paradox could be applied to ontology on the whole, so that we might demonstrate (perhaps not with the rigor of mathematics, but as best as anything can be demonstrated in ontology) that the world entire might be decomposed into a finite number of pieces and then reassembled into two or more identical worlds.

With the intuitive gloss quoted above, we can say that this is a possibility in so far as the world is ontologically infinitely dense. What might this mean? What would it be for the world to be ontologically dense in the way that infinite sets are infinitely dense? Well, this kind of question goes far beyond intuition, and therefore lands us in the open-texture of language that can accommodate novel uses but which has no “natural” meaning one way or the other. The open-texture of even our formal languages makes it like a quicksand: if you don’t have some kind of solid connection to solid ground, you are likely to flail away until you go under. It is precisely for this reason that Kant sought a critique of reason, so that reason would not go beyond its proper bounds, which are (as Strawson put it) the bounds of sense.

But as wary as we should be of unprecedented usages, we should also welcome them as opportunities to transcend intuitions ultimately rooted in the very soil from which we sprang. I have on many occasions in this forum argued that our ideas are ultimately derived from the landscape in which we live, by way of the way of life that is imposed upon us by the landscape. But we are not limited to that which our origins bequeathed to us. We have the power to transcend our mundane origins, and if it comes at the cost of occasional confusion and disorientation, so be it.

So I suggest that while there is no “right” answer to whether the world can be considered ontologically infinitely dense, we can give an answer to the question, and we can in fact make a rational and coherent case for our answer if only we will force ourselves to make the effort of thinking unfamiliar thoughts — always a salutary intellectual exercise.

Is the world, then, ontologically infinitely dense? Is the world everywhere continuous, so that it is truly describable by a classical theory like general relativity? Or is the world ultimately grainy, so that it must be described by a non-classical theory like quantum mechanics? At an even more abstract level, can the beings of the world be said to have any density if we do not restrict beings to spatio-temporal beings, so that our ontology is sufficiently general to embrace both the spatio-temporal and the non-spatio-temporal? This is again, as discussed above, a matter of establishing a rationally defensible convention.

I have no answer to this question at present. One ought not to expect ontological mysteries to yield themselves to a few minutes of casual thought. I will return to this, and think about it again. Someday — not likely someday soon, but someday nonetheless — I may hit upon a way of thinking about the problem that does justice to the question of the infinite density of beings in the world.

I do not think that this is quite as outlandish as it sounds. Two of the most common idioms one finds in contemporary analytical philosophy, when such philosophers choose not to speak in a technical idiom, are those of, “the furniture of the universe,” and of, “carving nature at its joints.” These are both wonderfully expressive phrases, and moreover they seem to point to a conception of the world as essentially discrete. In other words, they suggest an ultimate ontological discontinuity. If this could be followed up rigorously, we could answer the above question in the negative, but the very fact that we might possibly answer the question in the negative says two important things:

1) that the question can, at least in some ways, be meaningful, and therefore as being philosophically significant and worthy of our attention, and…

2) if a question can possibly be answered the negative, it is likely that a reasonably coherent case could also be made for answering the question in the affirmative.

The Banach-Tarski paradox is paradoxical at least in part because it does not seem to, “carve nature at the joints.” This violation of our geometrical intuition comes about as a result of the development of other intuitions, and it is ultimately the clash of intuitions that is paradoxical. Kant famously maintained that there can be no conflict among moral duties; parallel to this, it might be taken as a postulate of natural reason that there can be no conflict among intellectual intuitions. While this principle has not be explicitly formulated to my knowledge, it is an assumption pervasively present in our reasoning (that is to say, it is an intuition about our intiutions). Paradoxes as telling as the Banach-Tarski paradox (or, for that matter, most of the results of set theory) remind us of the limitations of our intuitions in addition to reminding us of the limitations of our geometrical intuition.

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Fractals and Geometrical Intuition

1. Benoît Mandelbrot, R.I.P.

2. A Question for Philosophically Inclined Mathematicians

3. Fractals and the Banach-Tarski Paradox

4. A visceral feeling for epsilon zero

5. Adventures in Geometrical Intuition

6. A Note on Fractals and Banach-Tarski Extraction

7. Geometrical Intuition and Epistemic Space

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Tuesday


Aristotle as portrayed by Raphael

Aristotle claimed that mathematics has no ethos (Metaphysics, Book III, Chap. 2, 996a). Aristotle, of course, was more interested in the empirical sciences than his master Plato, whose Academy presumed and demanded familiarity with geometry — and we must understand that for the ancients, long before the emergence of analytical geometry in the work of Descartes (allowing us to formulate geometry algebraically, hence arithmetically), that geometry was always axiomatic thought, rigorously conceived in terms of demonstration. For the Greeks, this was the model and exemplar of all rigorous thought, and for Aristotle this was a mode of thought that lacked an ethos.

Euclid provided the model of formal thought with his axiomatization of geometry. Legend has it that there was a sign over the door of Plato's Academy stating, 'Let no one enter here who has not studied geometry.'

In this, I think, Aristotle was wrong, and I think that Plato would have agree on this point. But the intuition behind Aristotle’s denial of a mathematical ethos is, I think, a common one. And indeed it has even become a rhetorical trope to appeal to rigorous mathematics as an objective standard free from axiological accretions.

In his famous story within a story about the Grand Inquisitor, Dostoyevsky has the Grand Inquisitor explain how “miracles, mystery, and authority” are used to addle the wits of others.

In his famous story within a story about the Grand Inquisitor, Dostoyevsky has the Grand Inquisitor explain how “miracles, mystery, and authority” are used to addle the wits of others.

Our human, all-too-human faculties conspire to confuse us, to addle our wits, when we begin talking about morality, so that the purity and rigor of mathematical and logical thought seem to be called into question if we acknowledge that there is an ethos of formal thought. We easily confuse ourselves with religious, mystical, and ethical ideas, and since the great monument of mathematical thought has been mostly free of this particular species of confusion, to deny an ethos of formal thought can be understood as a strategy to protect and defend of the honor of mathematics and logic by preserving it from the morass that envelops most human attempts to think clearly, however heroically undertaken.

Kant famously said that he had to limit knowledge to make room for faith.

Kant famously stated in the Critique of Pure Reason that, “I have found it necessary to deny knowledge in order to make room for faith.” I should rather limit faith to make room for rigorous reasoning. Indeed, I would squeeze out faith altogether, and find myself among the most rigorous of the intuitionists, one of whom has said: “The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof…”

Western asceticism can be portrayed as demonic torment or as divine illumination; the same diversity of interpretation can be given to ascetic forms of reason.

Though here again, with intuitionism (and various species of constructivism generally), we have rigor, denial, asceticism — intuitionistic logic is no joyful wisdom. (An ethos of formal thought need not be an inspiring and edifying ethos.) It is logic with a frown, disapproving, censorious — a bitter medicine justified only because it offers hope of curing the disease of contradiction, contracted when mathematics was shown to be reducible to set theory, and the latter shown to be infected with paradox (as if the infinite hubris of set theory were not alone enough for its condemnation). Is the intuitionist’s hope justified? In so far as it is hope — i.e., hope and not proof, the expectation that things will go better for the intuitionistic program than for logicism — it is not justified.

Dummett has said that intuitionistic logic and mathematics are to wear their justification on their face:

“From an intuitionistic standpoint, mathematics, when correctly carried on, would not need any justification from without, a buttress from the side or a foundation from below: it would wear its own justification on its face.”

Dummett, Michael, Elements of Intuitionism, Oxford University Press, 1977, p. 2

The hope that contradiction will not arise from intuitionistic methods clearly is no such evident justification. As a matter of fact, empirically and historically verifiable, we know that intuitionism has resulted in no contradictions, but this could change tomorrow. Intuitionism stands in need of a consistency proof even more than formalism. There is, in its approach, a faith invested in the assumption that infinite totalities caused the paradoxes, and once we have disallowed reference to them all will go well. This is a perfectly reasonable assumption, but one, in so far as it is an article of faith, which is at variance with the aims and methods of intuitionism.

And what is a feasible proof, which our ultra-intuitionist would allow? Have we not with “feasible proof” abandoned proof altogether in favor of probability? Again, we will allow them their inconsistencies and meet them on their own ground. But we shall note that the critics of the logicist paradigm fix their gaze only upon consistency, and in so doing reveal again their stingy, miserly conception of the whole enterprise.

“The Ultra-Intuitionistic Criticism and the Antitraditional program for the foundations of Mathematics” by A. S. Yessenin-Volpin (who was arguing for intellectual freedom in the Soviet Union at the same time that he was arguing for a censorious conception of reason), in Intuitionism and Proof Theory, quoted briefly above, is worth quoting more fully:

The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof, in spite of the traditional incompleteness theorem, which deals only with a very narrow kinds [sic] of proofs (which I call ‘formal proofs’). I define proof as any fair way of making a sentence incontestable. Of course this explication is related to ethics — the notion fair means ‘free from any coercion or fraud’ — and to the theory of disputes, indicating the cases in which a sentence is to be considered as incontestable. Of course the methods of traditional mathematical logic are not sufficient for this program: and I have to enlarge the domain of means explicitly studied in logic. I shall work in a domain wherein are to be found only special notions of proof satisfying the mentioned explication. In this domain I shall allow as a means of proof only the strict following of definitions and other rules or principles of using signs.

Intuitionism and proof theory: Proceedings of the summer conference at Buffalo, N.Y., 1968, p. 3

What is coercion or fraud in argumentation? We find something of an illustration of this in Gregory Vlastos’ portrait of Socrates: “Plato’s Socrates is not persuasive at all. He wins every argument, but never manages to win over an opponent. He has to fight every inch of the way for any assent he gets, and gets it, so to speak, at the point of a dagger.” (The Philosophy of Socrates, Ed. by Gregory Vlastos, page 2)

According to Gregory Vlastos, Socrates used the kind of 'coercive' argumentation that the intuitionists abhor.

What appeal to logic does not invoke logical compulsion? Is logical compulsion unique to non-constructive mathematical thought? Is there not an element of logical compulsion present also in constructivism? Might it not indeed be the more coercive form of compulsion that is recognized alike by constructivists and non-constructivists?

The breadth of the conception outlined by Yessenin-Volpin is impressive, but the essay goes on to stipulate the harshest measures of finitude and constructivism. One can imagine these Goldwaterite logicians proclaiming: “Extremism in the defense of intuition is no vice, and moderation in the pursuit of constructivist rigor is no virtue.” Brouwer, the spiritual father of intuitionism, even appeals to the Law-and-Order mentality, saying that a criminal who has not been caught is still a criminal. Logic and mathematics, it seems, must be brought into line. They verge on criminality, deviancy, perversion.

Quine was no intuitionist by a long shot, but as a logician he brought a quasi-disciplinary attitude to reason and adopted a tone of disapproval not unlike Brouwer.

The same righteous, narrow, anathamatizing attitude is at work among the defenders of what is sometimes called the “first-order thesis” in logic. Quine sees a similar deviancy in modal logic (which can be shown to be equivalent to intuitionistic logic), which he says was “conceived in sin” — the sin of confusing use and mention. These accusations do little to help us understand logic. We would do well to adopt Foucault’s attitude on these matters: “leave it to our bureaucrats and our police to see that our papers are in order. At least spare us their morality when we write.” (The Archaeology of Knowledge, p. 17)

Foucault had little patience for the kind of philosophical reason that seemed to be asking if our papers are in order, a function he thought best left to the police.

The philosophical legacy of intuitionism has been profound yet mixed; its influence has been deeply ambiguous. (Far from the intuitive certainty, immediacy, clarity, and evident justification that it would like to propagate.) There is in inuitionism much in harmony with contemporary philosophy of mathematics and its emphasis on practices, the demand for finite constructivity, its anti-philosophical tenor, its opposition to platonism. The Father of Intuitionism, Brouwer, was, like many philosophers, anti-philosophical even while propounding a philosophy. No doubt his quasi-Kantianism put his conscience at rest in the Kantian tradition of decrying metaphysics while practicing it, and his mysticism gave a comforting halo (which softens and obscures the hard edges of intuitionist rigor in proof theory) to mathematics which some have found in the excesses of platonism.

L. E. J. Brouwer: philosopher of mathematics, mystic, and pessimistic social theorist

In any case, few followers of Brouwer followed him in his Kantianism and mysticism. The constructivist tradition which grew from intuitionism has proved to be philosophically rich, begetting a variety of constructive techniques and as many justifications for them. Even if few mathematicians actually do intuitionistic mathematics, controversies over the significance of constructivism have a great deal of currency in philosophy. And Dummett is explicit about the place of philosophy in intuitionistic logic and mathematics.

The light of reason serves as an inspiration to us as it shines down from above, and it remains an inspiration even when we are not equal to all that it might ideally demand of us.

Intuitionism and constructivism command our respect in the same way that Euclidean geometry commanded the respect of the ancients: we might not demand that all reasoning conform to this model, but it is valuable to know that rigorous standards can be formulated, as an ideal to which we might aspire if nothing else. And and ideal of reason is itself an ethos of reason, a norm to which formal thought aspires, and which it hopes to approximate even if it cannot always live up the the most exacting standard that it can recognize for itself.

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Studies in Formalism

1. The Ethos of Formal Thought

2. Epistemic Hubris

3. Parsimonious Formulations

4. Foucault’s Formalism

5. Cartesian Formalism

6. Doing Justice to Our Intuitions: A 10 Step Method

7. The Church-Turing Thesis and the Asymmetry of Intuition

8. Unpacking an Einstein Aphorism

9. Methodological and Ontological Parsimony (in preparation)

10. The Spirit of Formalism (in preparation)

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Tuesday


In earlier posts to this forum I have discussed the dissatisfaction that comes from introducing an idea before one has the right name for it. An appropriate name will immediately communicate the intuitive content of the idea to the reader, as when I wrote about the civilization of the hand in contradistinction to the civilization of the mind, after having already sketched the idea in a previous post.

Again I find myself in the position of wanting to write about something for which I don’t yet have the perfect intuitive name, and I have even had to name this post “an unnamed principle and an unnamed fallacy” because I can’t even think of a mediocre name for the principle and its related fallacy.

In yesterday’s Defunct Ideas I argued that new ideas are always emerging in history (though they aren’t always being lost), and it isn’t too difficult to come up with a new idea if one has the knack for it. But most new ideas are pretty run-of-the-mill. One can always build on past ideas and add another brick to the growing structure of human knowledge.

That being said, it is only occasionally, in the midst of a lot of ideas of the middling sort, that one comes up with a really good idea. It is even more rare when one comes up with a truly fundamental idea. Formulating a logical fallacy that has not been noticed to date, despite at least twenty-five hundred years of cataloging fallacies would constitute a somewhat fundamental idea. As this is unlikely in the present context, the principle and the associated fallacy below have probably already been noticed and named by others long ago. If not, they should have been.

The principle is simply this: for any distinction that is made, there will be cases in which the distinction is problematic, but there will also be cases when the distinction is not problematic. The correlative unnamed fallacy is the failure to recognize this principle.

This unnamed principle is not the same as the principle of bivalence or the law of the excluded middle (tertium non datur), though any clear distinction depends, to a certain extent upon them. This unnamed principle is also not to be confused with a simple denial of clear cut distinctions. What I most want to highlight is that when someone points out there are gray areas that seem to elude classification by any clear cut distinction, this is sometimes used as a skeptical argument intended to undercut the possibility of making any distinctions whatsoever. The point is that the existence of gray areas and problematic cases does not address the other cases (possibly even the majority of the cases) for which the distinction isn’t in the least problematic.

Again: a distinction that that admits of problematic cases not clearly falling on one side of the distinction or the other, may yet have other cases that are clearly decided by the distinction in question. This might seem too obvious to mention, but distinctions that admit of problematic instances are often impugned and rejected for this reason. Admitting of no exceptions whatsoever is an unrealistic standard for a distinction.

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Saturday


The arch-atheist Jean-Paul Sartre

Despite having posted on this twice recently in A Note on Sartre’s Atheism and More on Sartre’s Atheism, I haven’t yet finished with this (as though one could ever be finished with an idea!).

I have, in a couple of posts, quoted a line from Sartre’s “Existentialism is a Humanism” lecture that ends with I must confine myself to what I can see:

I do not know where the Russian revolution will lead. I can admire it and take it as an example in so far as it is evident, today, that the proletariat plays a part in Russia which it has attained in no other nation. But I cannot affirm that this will necessarily lead to the triumph of the proletariat: I must confine myself to what I can see.

For corroboration from a fellow Frenchman and a fellow novelist consider this from Balzac’s Louis Lambert (not his most admired novel, but perhaps his most philosophical novel), delivered by the novel’s protagonist:

“To think is to see,” he said one day, roused by one of our discussions on the principle of human organization. “All science rests on deduction, — a chink of vision by which we descend from cause to effect returning upward from effect to cause; or, in a broader sense, poetry, like every work of art, springs from a swift perception of things.”

Honoré de Balzac, Louis Lambert, translated by Katharine Prescott Wormeley, Boston: Roberts Brothers, 1889, p. 39

Fellow Frenchman and philosopher Descartes offers more than corroboration: he stands at the foundation of the tradition from which both Balzac and Sartre come. In his most systematic work, the Principles of Philosophy (Book I, ix), Descartes presents an all-encompassing conception of thought, as is appropriate for the philosopher who is the locus classicus of the cogito:

By the word thought, I understand all that which so takes place in us that we of ourselves are immediately conscious of it; and, accordingly, not only to understand (INTELLIGERE, ENTENDRE), to will (VELLE), to imagine (IMAGINARI), but even to perceive (SENTIRE, SENTIR), are here the same as to think (COGITARE, PENSER). For if I say, I see, or, I walk, therefore I am; and if I understand by vision or walking the act of my eyes or of my limbs, which is the work of the body, the conclusion is not absolutely certain, because, as is often the case in dreams, I may think that I see or walk, although I do not open my eyes or move from my place, and even, perhaps, although I have no body: but, if I mean the sensation itself, or consciousness of seeing or walking, the knowledge is manifestly certain, because it is then referred to the mind, which alone perceives or is conscious that it sees or walks.

On the one hand, one can view these accounts as tributes to the visible and the tangible, except that Descartes, who stands at the origin of the tradition, can in no way be assimilated to materialism. On the other hand, and more interestingly, all of these accounts can be understood as expressions of various degrees of constructivism — mostly unconsciously formulated constructivism, but nevertheless an awareness that our thought must be disciplined by experience in a rigorous way if it is not to go terribly wrong. This is also a Kantian orientation, as we observed in Temporal Illusions, and Kant is counted as an ancestor of contemporary constructivism.

Skeptics have always demanded that truths be exhibited. We saw this in our previous posts about Sartre’s atheism, taking Doubting Thomas as the paradigm of the skeptic, who must needs touch the wounds of Christ with his own hands before he will believe that it is the same Christ who was crucified and subsequently risen.

It is a feature of constructivist thought, and most especially intuitionism, to reject the law of logic that is called (in Latin) tertium non datur or the Law of the Excluded Middle (LEM, or just EM). This simply states that, of two contradictory propositions, one of them most be true (“P or not-P“). Intuitively, it seems eminently reasonable, except that we all know of instances in ordinary experience that cannot be adequately described in a black-or-white, yes-or-no formulation. Non-constructive reasoning makes unlimited use of the law of the excluded middle, and as a consequence holds that all propositions have definite truth values even if we haven’t yet determined the truth value or even if we can’t determine the truth value. This can lead to strange consequences, like the famous Aristotelian example of the sea fight tomorrow: either there will be a sea battle tomorrow or there will not be a sea battle tomorrow. We don’t know at present which is true, but if we accept the logic of non-constructive reasoning, we will acknowledge that one of these propositions is true while the other is false.

The law of the excluded middle implies the principle of bivalence — the principle that there are two and only two logical values, namely true and false — and bivalence in turn implies realism. Realism as a philosophical doctrine stands in opposition to constructivism. Plato is the most famous realist philosopher, and believed that all kinds of things were real that common sense and ordinary experience don’t think of as being “real,” while at the same time disbelieving in the reality of the material world. Thus Plato is something of an antithesis to the kind insistence upon the tangibility and visibility upon which the skeptic and the materialist rely.

It is interesting, then, in the context of Sartre’s atheism and his insistence upon relying upon the seen, which we have now come to recognize as a kind of constructivism, to contrast the very different viewpoint represented by William James. One of James’ most famous essays is “The Will to Believe” in which he lays down the criteria for legitimate belief even where sufficient evidence is lacking. William James offers, “a defence of our right to adopt a believing attitude in religious matters, in spite of the fact that our merely logical intellect may not have been coerced.” Among the criteria that James invokes is when a choice is forced, which he describes like this:

…if I say to you: “Choose between going out with your umbrella or without it,” I do not offer you a genuine option, for it is not forced. You can easily avoid it by not going out at all. Similarly, if I say, “Either love me or hate me,” “Either call my theory true or call it false,” your option is avoidable. You may remain indifferent to me, neither loving nor hating, and you may decline to offer any judgment as to my theory. But if I say, “Either accept this truth or go without it,” I put on you a forced option, for there is no standing place outside of the alternative. Every dilemma based on a complete logical disjunction, with no possibility of not choosing, is an option of this forced kind.

Logical disjunction is another name used for the law of the excluded middle. Here James reveals himself as a realist, if not a Platonist, in matters of the spirit, just as we saw that Sartre revealed himself as a constructivist, if not an intuitionist, in matters of the spirit. The point I am making here is that this is not merely a difference of belief, but a difference in logic, and a difference in logic and reaches up into the ontology of each and informs an entire view of the world. People tend to think of logic, if they think of logic at all, as something recondite and removed from ordinary human experience, but this is not the case. Logic determines the relationship that we construct with the world, and it organizes how we see the world.

Nietzsche wrote in a famous line (or, perhaps I should say, a line that ought to be more famous than it perhaps is) that the nature and degree of an individual’s sexuality reaches into the highest pinnacles of his spirit. I agree with this, but I would add that the nature and kind of an individual’s logic — be it constructivist or non-constructivist — also reaches into the highest pinnacles of his spirit and indeed informs the world in which his spirit finds a home… or fails to find a home.

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Saturday


Jean-Paul Sartre: existence precedes essence.

Jean-Paul Sartre: existence precedes essence.

Sartre’s skepticism regarding human nature (discussed in Human Nature) is not arbitrary and nihilistic skepticism, but has a theoretical basis in Sartre’s pure philosophical work. And while Being and Nothingness is a daunting and difficult work, in the same famous lecture we have quoted in which Sartre expressed his skepticism regarding human nature, Sartre also summarized many of his technical doctrines, and even reduced them to aphoristic sententiousness, as with existence precedes essence.

What do we mean by saying that existence precedes essence? We mean that man first of all exists, encounters himself, surges up in the world – and defines himself afterwards. If man as the existentialist sees him is not definable, it is because to begin with he is nothing. He will not be anything until later, and then he will be what he makes of himself. Thus, there is no human nature, because there is no God to have a conception of it. Man simply is. Not that he is simply what he conceives himself to be, but he is what he wills, and as he conceives himself after already existing – as he wills to be after that leap towards existence. Man is nothing else but that which he makes of himself. That is the first principle of existentialism. And this is what people call its “subjectivity,” using the word as a reproach against us. But what do we mean to say by this, but that man is of a greater dignity than a stone or a table? For we mean to say that man primarily exists – that man is, before all else, something which propels itself towards a future and is aware that it is doing so. Man is, indeed, a project which possesses a subjective life, instead of being a kind of moss, or a fungus or a cauliflower. Before that projection of the self nothing exists; not even in the heaven of intelligence: man will only attain existence when he is what he purposes to be.

Jean-Paul Sartre, “Existentialism is a Humanism” 1946, translated by Philip Mairet

In what sense are we to take “precedes”: in a temporal sense, or an ontological sense, or both? One could well maintain that the relation is one of deductive precedence, so that once given the extant, such as it is, the essential can be systematically derived. This is one form of ontological precedence, but it seems to be almost the negation of what Sartre was suggesting. The obvious interpretation, though not the only possible interpretation (or even the only plausible interpretation), is that the precedence of existence before essence is a temporal precedence: first there are existing things, and then there are the essences of existing things. This alone doesn’t tell us anything about the nature of essence. It does not even imply the derivative character of essence (in contradistinction to the non-derivative character of existence) as does an interpretation of “existence precedes essence” in terms of deductive (or ontological) precedence, as mentioned above.

The famous Cafe de Flore in Paris, where Sartre held court.

The famous Cafe de Flore in Paris, where Sartre held court.

To make the point that essence is derivative while existence is primary (that is to say, primitive, non-derivative), and to retain a naturalistic interpretation of the world, one must insist that the slogan “existence precedes essence” must be interpreted both in terms of deductive and temporal precedence. But in so doing, it becomes obvious that a great many other considerations have been imported into the formula: not least the imperative to maintain a naturalistic understanding of the world, however grossly nature is undervalued. But expressing an ontological doctrine in the space of an aphorism is likely to result in a certain degree of compression and thus ambiguity, so we ought not to fix too much on this simple formula, as Sartre’s longer treatment is readily available elsewhere.

Given a formulation of a philosophical principle as clear and as simple as existence precedes essence, it would seem obvious that Sartre’s principle can easily be confronted with its opposite by inverting the formula: essence precedes existence. How are we to interpret this? We must travel rather beyond the bounds of popularized philosophy to find an adequate philosophical embodiment of this, and we can find it, to a certain extent, in Alexius von Meinong.

Alexius von Meinong: being is independent from being-so.

Alexius von Meinong: being is independent from being-so.

Meinong’s principle of independence — that being is independent of being-so — may be contrasted to Sartre’s dictum that existence precedes essence, which is a principle of both ontological and temporal dependence. For Meinong, in other words, the way a thing is, or how a thing is (its “being-so”), is independent of the fact that a thing is. Meinong’s principle of independence would appear to be more strictly and purely ontological than Sartre’s principle. We know for a fact that with human manufactures essence precedes existence, and therefore for at least one class of existents — the class of manufactures — that Meinong’s principle holds: the being-so of what it is to be an article of manufacture is independent of its being. A design may or may not be put into production; there is, with the principle of independence, a recognition of the disconnect between idea and reality. An architect can design a building that is never in fact built, as with Étienne-Louis Boullée’s Cenotaph for Newton. Thus also Meinong’s principle of independence does not hold for the complement of the class of entities for which Sartre’s principle holds.

Étienne-Louis Boullée’s design for a Cenotaph for Newton, which remains unbuilt. This is perhaps one of the most famous unbuilt structures in the history of architecture.

Étienne-Louis Boullée’s design for a Cenotaph for Newton, which remains unbuilt. This is perhaps one of the most famous unbuilt structures in the history of architecture.

A doctrine of relative degrees of independence could be readily formulated, (i.e., being might be dependent to a greater or lesser extent upon being-so), as could a doctrine of relative independence analogous to relative identity, (i.e., some individual aspects—properties—of an object might possess independence while others did not). Independence, like identity, is a concept that invites interpretation in terms of totality and absolutization, as exemplified by the implied tertium non datur : either being is independent of being-so (Meinong’s principle) or being is not independent of being-so (the negation of Meinong’s principle). If being is not independent of being-so, there are many ways in which it might be dependent, but if being is independent of being-so, then it is independent and there is nothing more to say.

One way in which being might be dependent upon being-so, or vice versa, is if existence always precedes being-so, that is to say, if existence precedes essence. So we see that Meinong’s principle of independence is somewhat more general that Sartre’s principle of existentialism. As we have seen, there are many ways for existence to precede essence, any many ways for being to be dependent upon being-so (and there is at least once sense in which the two coincide), but the independence of being and being-so (or, if you like, the independence of being and essence) seems to be of a more general character — a more sweeping principle, as it were.

There is not a perfect symmetry between Sartre’s principle and Meinong’s principle, although the two are sufficiently interrelated to be suggestive. But if we go beyond the realm of pure philosophy we can find a doctrine more perfectly in symmetrical opposition to Sartre. The inversion of Sartre’s principle – the principle that essence precedes existence – is clearly a teleological principle, and as such it could be considered a central principle of theism. Existentialism, under this interpretation, is not opposed to any other philosophical doctrine as much as it stands in opposition to theism.

But even here we run into trouble. In the same lecture of Sartre’s quoted above, Sartre makes a distinction between act and potential not unlike that promulgated by the schoolmen, and, again like the schoolmen, gives action priority over potential (this is a doctrine especially associated with St. Thomas Aquinas). Indeed, it could fairly be said that Sartre rejects potential as invidious to the understanding of human action.

“…in reality and for the existentialist, there is no love apart from the deeds of love; no potentiality of love other than that which is manifested in loving; there is no genius other than that which is expressed in works of art. The genius of Proust is the totality of the works of Proust; the genius of Racine is the series of his tragedies, outside of which there is nothing. Why should we attribute to Racine the capacity to write yet another tragedy when that is precisely what he did not write? In life, a man commits himself, draws his own portrait and there is nothing but that portrait. No doubt this thought may seem comfortless to one who has not made a success of his life. On the other hand, it puts everyone in a position to understand that reality alone is reliable; that dreams, expectations and hopes serve to define a man only as deceptive dreams, abortive hopes, expectations unfulfilled; that is to say, they define him negatively, not positively.”

Jean-Paul Sartre, “Existentialism is a Humanism” 1946, translated by Philip Mairet

This is a radical doctrine. And there is a sense in which it is astonishing that there should be any commonality between Sartre and the scholastics, not merely because Sartre was an explicit atheist, but rather because Sartre’s atheism runs deep, at a primordial level, and, though felt profoundly, was expressed in abstract and theoretical terms.

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Saint Thomas Aquinas: Absolutely speaking, act must be prior to potency, both in nature and in time, because every potential being is made actual by some actual being.

Saint Thomas Aquinas: Absolutely speaking, act must be prior to potency, both in nature and in time, because every potential being is made actual by some actual being.

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