Digressions&Impressions

On Newton's Refutation of the Mechanical Philosophy

In the recent philosophical reception of Newton there is an understandable tendency to focus on the inverse square law of universal gravitation. I don't mean to suggest this is the only such focus; arguably his views on Space have shaped -- through the good works of Stein and Earman -- also debates over spacetime theories. 

The effect of this telescoping has also impacted, I think, the way in which the debate between the mechanical and Newtonian philosophy has been understood. The former is said to posit a contact model in which contact between very small corpuscles explains a lot of observed phenomena. A typical mechanical philosopher creates a hypothetical model, a machine with pulleys and levers (etc.), that can make observed phenomena intelligible. In the mechanical philosophy, which itself was directed against a variety of Aristotelian and Scholastic projects, efficient causation -- once one of four canonical causes (including formal, final, and material) -- has achieved a privileged status.

The scholarly fascination with the status of action at a distance is, thus, readily explicable because it violates the very model of intelligibility taken for granted in the mechanical philosophy. As Newton notes in the General Scholium (first published in the 1713 second edition of the Principia), universal gravity "operates, not according to the quantity of the surfaces of the particles upon which it acts, (as mechanical causes use to do,) but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides, to immense distances, decreasing always in the duplicate proportion of the distances." 

Before I get to the main point of today's post, I offer two asides. First, with its emphasis on hypothetical explanations, the mechanical philosophers (and here I use the term to cover people as diverse as Beeckman, Descartes, Boyle, and Huygens) also exhibit a deep strain of skepticism about the very possibility of truly grasping nature's innards as it were. Spinoza's natura naturans and even Kant's ding-an-sich are the enduring expressions of this strain of skepticism (allowing that Kant is much less a mechanical philosopher). To put this as a serious joke: the PSR is, thus, not an act of intellectual hubris, but a self-limitation of the knower when it comes to fundamental ontology. Second, by showing that there is something wholly unintelligible about the way motion is supposed to be transferred from one body to the other (Essay 2.23.28), Locke, who gets so little credit among contemporary philosophers, had already imploded the pretensions of the mechanical philosophy on conceptual grounds.  Okay, so much for set up.

The mechanical philosophers were not so naïve to think that models that relied on mere impulse, matter in motion, could create hypothetical models of sufficient complexity to provide hypothetical explanations of the phenomena. This is especially a problem because the mechanical philosophers posited a homogeneous matter. So that in addition to matter and motion, they posited size and shape not merely as effects of motion, but also as key explanatory factors in the hypothetical models of visible phenomena (this can be seen in Descartes, Gassendi, and Boyle, whose "The Origin of Forms and Qualities according to the Corpuscular Philosophy" (1666), I take as a canonical statement of the mechanical philosophy). So that the mechanical philosophy is committed to privileging (to echo a felicitous phrase by Biener and Smeenk [here; and here]) geometric features of bodies.

Even leaving aside the inverse square law and its universal scope, Newton's experimental work on gravity demolished a key feature of the mechanical philosophy: size and shape are irrelevant to understand gravity. I quote from Henry Pemberton's View of Sir Isaac Newton's Philosophy (1728):

It will be proper in this place to observe concerning the power of gravity, that its force upon any body does not at all depend upon the shape of the body; but that it continues constantly the same without any variation in the same body, whatever change be made in the figure of the body: and if the body be divided into any number of pieces, all those pieces shall weigh just the same, as they did, when united together in one body: and if the body be of a uniform contexture, the weight of each piece will be proportional to its bulk. This has given reason to conclude, that the power of gravity acts upon bodies in proportion to the quantity of matter in them. Whence it should follow, that all bodies must fall from equal heights in the same space of time. And as we evidently see the contrary in feathers and such like substances, which fall very slowly in comparison of more solid bodies; it is reasonable to suppose, that some other cause concurs to make so manifest a difference. This cause has been found by particular experiments to be the air. --1.2.24 [emphasis added]

Pemberton (who was the editor of the third, 1726 edition of the Principia) goes on to give Boyle's famous vacuum experiments with falling feathers and stones as evidence for this argument. That is, Pemberton uses Boyle's experimental work to refute Boyle's mechanical philosophy. 

Now, in the Principia, references to Boyle's experiment got added only to the (1713) second edition in two highly prominent places: Cotes added a reference to it in his editor's introduction and Newton added a reference to it in the General Scholium at the end of the book. In both cases Boyle's experiment is used as a kind of illustration for the claim that without air resistance falling bodies are equally accelerated and for the plausibility of positing an interstellar vacuum. That is, if one reads the Principia superficially (by looking at prominent material at the front and end), it seems as if Newton and Boyle have converging natural philosophies.

Of course, neither Pemberton nor Newton rely exclusively on Boyle's vacuum experiment to make the point that shape and size (or geometry) is not a significant causal factor when it comes to gravity. The key work is done by pendulum experiments with different metals. (These can be found in Book II of the Principia, which is often skipped, although he drives the point home in Book III, Prop. 6 of Principia.) These show that quantity of matter is more fundamental than shape. And, crucially, shape & size and quantity of matter need not be proportional to or proxies of each other. This fact was by no means obvious, and at the start of the Principia. even Newton offers, as Biener and Smeenk have highlighted, a kind of geometric conception of quantity of matter in his first definition before suggesting that 'quantity of matter' is proportional to weight (and indicating his pendulum experiments as evidence thereof).

Let me wrap up. What's important here is that even if Newton had been wrong about the universal nature of the inverse square law, he showed that the mechanical philosophy cannot account for the experimentally demonstrated features of terrestrial (and planetary) gravity. (So, that the mechanical philosophy is not a natural way to understand Galilean fall.) And this means that in addition to Locke's conceptual claim, Newton shows that the mechanical philosophy's emphasis on just one kind of efficient causation, by way of contact, is not sufficient to explain the system of nature. 

What I say here is not surprising to students of Newton. But it's also not really much emphasized. To be sure, Newton, too, accepted a kind of homogeneous matter, but rather than its size and figure, he showed that an abstract quantity (mass) is more salient. Of course, how to understand mass in Newton's philosophy opens new questions, for as Ori Belkind has argued it should not be taken as a property of matter, but rather as a measure.

 

 

The story starts with a stolen Maupertuis

Actually, the story starts with me buying a copy of Maupertuis' (1738) La figure de la terre at auction online. I am a modest rare book collector; my principle of collecting is 'works that intersect with my scholarly research in neat ways' (all other things being equal, which is not always -- <think of prices> -- the case). So that means that unlike many collectors, I am not always after the first edition of a work and do not mind copies that show sign of some scholarly use (which also means I can afford them more easily). 

Now, my first scholarly projects starting with George Smith were on the Huygens-Newton debate over universal gravity and the shape of the Earth, and the measurements that settled it. Maupertuis' measurements in Lapland -- the title page of the 1738 work prefers 'polar circle' -- were part of the evidence that helped resolve the debate. While others (Maglo, Terrall, Shank, etc.) would publish with more detail on La Figure, I used this work by Maupertuis to make some modest, albeit distinctive claims about the philosophical particulars of Adam Smith's History of Astronomy. 

The pictures of the lot suggested a very clean copy, but one with a modern binding. Much to my surprise the bidding for it remained relatively calm even in the final minutes. And so for under 500€ (generally the most I am willing spend on a rare book) I was the proud owner of a work that is a joy to read, has an interesting story, and that shows up in non-trivial places in my own scholarship. I was elated! The seller sent it off with tracking, and the book arrived after a few days. I had last held a physical copy in my hand over twenty years ago in Chicago (presumably at the Newberry library, but I just noticed there is also a copy in Regenstein so maybe there).  

After opening the package, I opened the book and I had my first modest disappointment. The neat map I remembered at the front of the book was not there. My spirits started to deflate, but after looking through the book I found it at the back. (See here for a picture of the map at Gallica.) Interestingly enough, the copy of the English translation in the British Library, which seems to be one used by Google to scan it also has the map in front, whereas the French version has it in back (but the reproduction is badly done)! So, I wondered if I had misremembered and had only looked at the English translation. More on this below.

However, when I started to look through the book more slowly I had a true shock. There was an impressive library stamp on the page facing the frontispiece with "The Institution of Civil Engineers" and an address at "25 Great George Street, Westminster" in London. (See the picture below this post.) Now, I have bought books at auction before that had impressive library stamps in them. I always do due diligence before I bid and check out the provenance. Usually I find that the book had belonged to a seminary or school library that had closed or merged. Most sellers show a library stamp in the pictures that the seller usually supplies in auction. How could I have missed this?

I went online to check the lot I had bought and to my shock there was no picture of the stamp! I then went online to look for the Institution of Civil Engineers library, and found an impressive website, which suggested the library was flourishing although it had moved a few doors down. I checked the catalogue and it showed a copy of the book I was holding in my hand. At that moment, I realized I had almost certainly a stolen book in my hands (although part of me hoped they had sold off a duplicate).

I knew I had to move quickly, so I immediately wrote the auction house with my suspicion (so that they would keep my payment in escrow). (It was Friday afternoon after hours for the auction house so I knew I would not hear back before Monday at the earliest.) I then contacted the seller/dealer through the auction house message system in France; he responded quickly but in a dismissive fashion. (I return to that below.)

I decided to call the ICE library. The person who picked up the phone was a librarian, Debra Francis. I quickly explained the situation. It turns out the ICE library is supposed to have two French copies of La Figure (one part of a special collection). While we were talking she established one of these copies was missing. I was not surprised, I was holding it! At this point I knew the book had to be returned, but I was not wholly eager to take the loss. So, I gave her my yahoo email address, but little else info about me.

However, it was time to be more assertive with the seller. In our online interactions he revealed that he had bought the book a few months ago at another (reputable) auction house, and that these would have been cautious about provenance. (I was stunned how little he paid!) I decided to call the specialist listed on their website. I explained the situation to him, and after some back and forth he explained that the book was bought through an intermediary as part of a much larger estate of a deceased book-dealer. So, now I knew that my seller was not himself the thief or an accomplice in selling on stolen goods, and that the book was probably missing at least since 2020 or so. (My seller had merely looked the other way downstream.) The member of staff of this auction house told me they were insured against this kind of thing. So, I decided that my seller could probably get his money back there.

By monday, after some further communication between us, my seller agreed not to accept my money if I returned the book to the library in London. And much to my relief my auction house agreed to this approach provided I would supply them with pictures of the stamp and of the book, as well as a letter of the ICE library and me handing it back. I contacted my new librarian friend at ICE, Debra Francis, and she was eager to facilitate this.  

So, this morning I went to the lCE library right next to Parliament. I was stunned by how beautiful it was. And I was welcomed by Debra, who decided to give me a grand treat. First I was given a tour of the library and told its history. I was shown some of the special collections. And then we did the hand-over. But as we did the hand-over she showed me the copy of the 1738 La Figure from their special collection. It was much less pristine copy of the book than 'mine' that I was returning. But as we opened it, it did have the map on the facing page of the frontispiece just as I had remembered! 

For some reason this cheered me up greatly. In part, because it created a new puzzle why did some copies have the map in front and others in the back? (And more interestingly, which one was the original and which on the possible bootleg?) I have done a modest survey online today some seem to lack the map altogether, but other library copies do have the map and there is no clear pattern whether it's in front or in the back of the book.

Now, while Debra Francis was correcting some infelicities in the letter she had made out to my auction house, I had a chance to inspect the box with the original holdings of the library donated by (if I am not mistaken) Thomas Telford. Most of the books were clearly engineering specific. But my heart started to flutter when behind the glass I saw a copy of the Opticks. Judging by its tattered spine an original fourth edition. When my librarian friend returned we opened the case and it turned to be a fragile copy of the third edition.:)  [See picture below.] She had a quick peek in the catalog and informed me there should be more Newton holdings in the case. I scanned the list, and then looked more closely in the case, and immediately spotted a posthumous edition of Newton's work on fluxions. At this point, I had forgotten my misery over the Maupertuis and switched into scholar, teacher, and collector mode and started to pontificate on the significance of these holdings. Then I stopped mid-sentence, I had spotted the Principia!

When she took it out it was a pristine copy of the third edition donated by a Mr. Young in 1840. I immediately tried to remember Thomas Young's dates. I don't think I have ever held a third edition the Principia (the last one published during his life). Despite my excitement I was a bit sad there were no marginalia. However, as I was ruminating over this Debra Francis called me attention to a four page manuscript wedged in the front pages of the book. I have reproduced the first page below. (It's in English and fairly easy to follow.) I immediately took pictures of the whole manuscript and sent them to the great Niccolo Guicciardini to see if he could identify the author.

At this point my host invited me down to the basement where the members registry is held to see if we could identify which Young had donated the copy of the third edition of the Principia. (It turns out the relevant copy of the registry is in storage.)  As it happens the basement office is next to the vault, and I could not resist an offer of a tour of it (including learning the escape route on the other side of the vault). For, it turns out that the library has a special collection which houses just about every important book published in the 17th century on clocks and finding longitude.  So, for the next half hour I geeked out and excitedly explained the significance of each book I recognized to my patient host. And I was also struck by the presence of some works wholly obscure even to a specialist. By the time I left, I forgot to send the materials to the auction house because I was thinking of new research projects. 

 

 

Hudde and Spinoza's Monism, Pt 3

This is the third post in a series triggered by an invite from Karolina Hubner and Justin Steinberg to write on the Spinoza and Hudde (1628 – 1704)) exchange.  According to Spinoza (recall this post); and this one), Hudde's original request to Spinoza was to provide [1] "a demonstration of the Unity of God from the fact that his Nature involves necessary existence." (Curley 2016: 25) We can infer from Spinoza's response that in his final letter to Spinoza, Hudde raised two remaining concerns about Spinoza's monism:

[3a] It is unclear why Spinoza seems committed to the claim that it is a contradiction to conceive something whose definition involves existence (or what is the same, affirms existence) under a negation of existence. (Curley 2016: 29)

[3b] Spinoza seems to be unable to rule out the [real] possibility that there could not be many beings, existing through themselves, but differing in nature, just as thought and extension are different, and can perhaps subsist by their own sufficiency... (Curley  2016: 30) 

I doubt Spinoza's response to [3a] really would have been satisfying. Spinoza writes:

since the limited denotes nothing positive, but only the privation of the existence of the same nature which is conceived as limited, it follows that something whose definition affirms existence cannot be conceived as limited. For example, if the term extension involves necessary existence, it will be as impossible to conceive extension without existence as it is to conceive extension without extension. And if this is maintained, it will also be impossible to conceive a limited extension. For if it were conceived to be limited, it would have to be limited by its own nature, namely, by extension. And this extension by which it was limited would have to be conceived under the negation of existence.

For, Hudde is not worried with the possibility that something whose definition affirms existence can be conceived as limited. Rather, he is worried that one can hold the idea of something whose definition affirms existence at a kind of arms length by, say, putting it between brackets and negating it. (As I noted before Hudde pioneered working with negative numbers, so I this was not something he would have thought of as mere wordplay.) It's quite clear, also from the Ethics, that Spinoza does not consider this a real possibility because for Spinoza the thinking subject becomes unified in a certain sense with the clear and distinct (or adequate) idea s/he affirms and cannot simultaneously genuinely deny it, say, for the sake of argument. So, here Hudde and Spinoza seem to me to be talking past each other. (I actually wonder if this represents a fundamental in 17th century post-Cartesianism on the way of ideas.)

The point in the last paragraph is non-trivial because in a fascinating (1989) paper on the Hudde-Spinoza Correspondence, Wim Klever has suggested that Hudde is a kind of crypto Spinozist. (What makes the paper so fascinating is that Klever noticed that Hudde and Locke corresponded (via Van Limborch) over the same issues decades later.)+ I strongly doubt we need to infer that Hudde is a crypto-Spinozist from Hudde's position (as presented by Spinoza) and I don't see why we should ascribe crypto-Spinozism to Hudde.

In addition, Klever thinks that Hudde is worried about the substance-like nature of the attributes in Spinoza (which is a natural concern had Hudde read the Short Treatise), and that this motivates Hudde's concern with polytheism. This cannot be ruled out altogether; and to be sure, [3b] is compatible with Klever's reading because in it the self-sufficient subsistence of thought and extension are mentioned. But to me they seem more introduced as analogy not the source of Hudde's concern. 

The more natural reading of [3b] is that Hudde is worried about multiple self-causing, self-subsisting substances with different (and non-overlapping) natures or attributes existing simultaneously given Spinoza's commitments. And, in Part II, chapter II, of the Appendix Containing Metaphysical Thoughts of the Cartesian Principles of Philosophy, Spinoza himself had invited this concern in the passage on God's Uniqueness (which I had already suggested in the two previous posts on the exchange must have prompted Hudde's questions on other grounds). For in that passage Spinoza explicitly indicates that God has an open-ended number of attributes (including understanding). And Spinoza goes on to write, "If now you say that there are many Gods, or supremely perfect beings, they will all have to understand, in the highest degree." (Curley 1985: 318)

And what Hudde is noticing is that it not obvious that if there are many Gods, that they all have to understand in the highest degree. Spinoza seems to presuppose that to be a God one must have all the attributes (that is, have unity). So, Hudde's original question, 'why does Unity of God follow from the fact that his Nature involves necessary existence?' makes sense. The tought being that maybe all gods necessarily exist (by their own sufficiciency), but they otherwise have a division of labor involving different infinite attributes and they are unlimited in its own kind. So, again, I doubt Hudde needs to be a Spinozist to raise this proto-Leibnizian objection.

My reading seems to be supported by the first sentence of Spinoza's response: "if we assert that something which is only unlimited in its own kind, and perfect, exists by its own sufficiency." This seems to be Hudde's worry as I understand it. But having said that, the way Spinoza refutes Hudde's worry is, in part, by relying on the idea that multiple substance-like attributes actually imply the existence of a single God/substance only might well be taken to support Klever's interpretation (although I deny that that's required). 

Okay, let's now turn to Spinoza's full response to Hudde's [3b]: 

if we assert that something which is only unlimited in its own kind, and perfect, exists by its own sufficiency, the existence of a being absolutely unlimited and perfect will also have to be conceded. This Being I call God. For example, if we want to maintain that extension or thought (each of which can be perfect in its own kind, that is, in a definite kind of being) exists by its own sufficiency, we will also have to concede the existence of God, who is absolutely perfect, that is, of an absolutely unlimited being.
    Here I should like you to note what I said just now about the term imperfection, namely, that it signifies that something is lacking to a thing which pertains to its nature. For example, Extension can be called imperfect only in relation to duration, position or quantity, because it does not last longer, or does not keep its position, or is not larger.
    But it will never be called imperfect because it does not think, since its nature, which consists only in extension, that is, in a definite kind of being, requires nothing of that sort. In this respect only limited or unlimited extension is to be called imperfect or perfect, respectively. And since the nature of God does not consist in a definite kind of being, but in a Being which is absolutely unlimited, his nature also requires everything which expresses being perfectly, since otherwise his nature would be limited and deficient.
    Since these things are so, it follows that there can only be one Being, God, which exists by its own force. For if we assert, for example, that extension involves existence, it must be eternal and unlimited , expressing absolutely no imperfection, but only perfection. Therefore, Extension will pertain to God, or it will be something which expresses God’s nature in some way. For God is a being which is, not just in a certain respect, but absolutely unlimited in being and omnipotent. And this, which is said of Extension (as an arbitrary example), will also have to be affirmed of everything we want to maintain as having such a nature.
    I conclude, then, as in my preceding Letter, that nothing outside God, but only God, subsists by its own sufficiency. I believe these things suffice to explain the meaning of the preceding letter. But you will be able to judge better than I concerning that. (Curley  2016: 30-31)

If I understand Spinoza correctly, Spinoza simply denies what Hudde takes to be possible on Spinoza's view is possible. And that's because if we conceptualize God and attributes properly, then God must have or express all the attributes: "since the nature of God does not consist in a definite kind of being, but in a Being which is absolutely unlimited, his nature also requires everything which expresses being perfectly, since otherwise his nature would be limited and deficient."

By itself this does not seem very compelling as a response to Hudde's worry as I understand it because it rules out polytheism by stipulation. Yet, Spinoza's position is not mere terminology or question begging against Hudde's proto-Leibnizian worry. The really interesting underlying point in the passage quoted above is that Spinozistic God is not the kind of entity that can figure in a question like, 'is there is one or more.' As Jonathan Bennett first suggested (I believe) in his field metaphysics (but relying on the Ethics not this letter), Spinoza's God is, grammatical appearances to the contrary, not a count-noun, but more like a mass noun (Bennett A Study of Spinoza's Ethics, 1984, p. 104).* I doubt that is obvious if one only read the Metaphysical Thoughts or Short Treatise (and, if one is interested in Spinoza's development, I suspect it may not have been obvious to Spinoza himself before Hudde's challenge). 

So, in my view the significance of Spinoza's three responses to Hudde is that they show Spinoza articulating, even developing key features of the PSR and the nature of his monism.  I leave open here, to what degree Hudde's later challenges to Locke reflects continued dissatisfaction with Spinoza's responses or an evolved understanding of the issue(s) (or both).

Spinoza, Hudde, and Monotheism, PT 2

This is the second post in a series triggered by an invite from Karolina Hubner and Justin Steinberg to write on the Spinoza and Hudde (1628 – 1704)) exchange.  According to Spinoza (recall this post), Hudde's original request to Spinoza was to provide [1] "a demonstration of the Unity of God from the fact that his Nature involves necessary existence." (Curley 2016: 25) From what follows in Spinoza's letter (OP 34) from 7 January 1666, it is clear that Spinoza understands 'unity' here as a kind of monotheism which rules out a plurality of Gods:

But from his true definition (as I have already demonstrated previously from the second and third hypotheses) the necessary existence of many Gods cannot be inferred. There follows, therefore, only the existence of one God. Q.E.D. (Curley 2016: 26)

Hudde was evidently not satisfied, and seems to have written two follow up letters. Spinoza's wording suggests that Spinoza wrote a response (now lost) to the initial follow up (from 10 February 1666), in which expressed his difficulty grasping Hudde's continued problems with Spinoza's argument. (All of Hudde's letters to Spinoza seem to be destroyed.) And after the second follow up (30 March, 1666), Spinoza takes Hudde's true worry to be: [2] "whether there is only one Being which subsists by its own sufficiency or power?" (Curley 2016: 26; Letter 35 OP, 10 April 1666.)

What's interesting about the formulation now attributed to Hudde by Spinoza is that the terminology of 'subsistence' is new here in their discussion. To the best of my knowledge, Spinoza does not use it when discussing substance or god. The one exception I have found is in the Cartesian Principles of Philosophy, in Proposition 16 where the incorporeality of God is demonstrated. (Curley 1985: 260) There Spinoza seems to use 'subsist' and 'exist' interchangeably. But, he is here clearly treating Descartes' position, not his own. And he is using 'subsist' in a conditional mode. So, I am inclined to suspect the terminology reflects Hudde's attempts to grapple with Spinoza's view. (As I noted, if Hudde is responding to Cartesian Principles of Philosophy, the argument is rather cryptic.) 

One advantage of this new formulation is that it gets at the worry that [i] it is not obvious why the kind of power that produces God should itself be limited in number. That's subtly different from the original version of the worry (recall) that I attributed to Hudde based on Spinoza's original response: this initial concern is the worry that [ii] it is not obvious why the power that produces God should be limited to producing only one God.* 

From the perspective of this re-formulation, Spinoza's new response to Hudde is frustrating. Because rather than focusing on the nature of such power (or sufficiency), Spinoza's new proof relies on the relationship between necessary existence and pure perfection (and we seem, as Wiep van Bunge suggests [in Dutch], in the real of ontological proofs). His fifth step in his new reformulation is: "whatever involves necessary existence cannot have in it any imperfection, but must express pure perfection." (Curley 2016: 27) This is then used to argue that there is only being with such pure perfection.

That Hudde was not fully convinced is clear. But rather than pressing the point about perfection, he seems to have rephrased his concern by splitting it in two as follows:

[3a] that it is a contradiction to conceive something whose definition involves existence (or what is the same, affirms existence) under a negation of existence. (Curley 2016: 29)

[3b] why there could not be many beings, existing through themselves, but differing in nature, just as thought and extension are different, and can perhaps subsist by their own sufficiency... (Curley  2016: 3o)

What's neat about [3b] is that it shows that (in light of the initial concerns of [i] and [ii]), Hudde de facto accepts something like the identity of indiscernibles.(I put this in Leibnizian fashion because I think [3b] clearly anticipates some of Leibniz's worries about Spinoza's position.) And Hudde concedes a principle like: same perfect power must produce same perfect entity. And so Hudde now recognizes that if there are to be (at least) two gods (self-causing, self-sufficient, necessarily existent, etc.) these must be at least different in nature. (This also shows that Hudde was not convinced by the language of perfection.) 

By contrast, the way I understand [3a] is as an instance of a more general worry at least in the vicinity of [3a] about Descartes and Spinoza's general approach when it comes to God/Substance. They seem to hold that one literally cannot be said to really think the denial of certain clear and distinct or adequate ideas, not even, as it were, at arm's length. And Hudde -- who pioneered the use of negative numbers -- clearly seems to think that one can at least conceive the denial of whatever one affirms (even if it is a thing with necessary existence or whose definition involves existence). 

The other neat thing about [3a] and [3b], from the perspective of the original worry [1], is that Hudde now is decomposing different levels at which concern about Spinoza's argument might enter in. One is at the level of what can be thought/conceived by the meditator. The other is at level of what God(s)'s nature/identity might be. And what he puts his finger on is that in Spinoza's philosophy these two levels seemingly get intertwined.  In my next post, I'll explore Spinoza's final known letter to Hudde in response.

 

The PSR, Spinoza and Hudde

I shall presuppose that:
(1) The true definition of each thing contains nothing beyond the simple nature of the thing defined.
From this it follows that
(2) No definition involves or expresses any multiplicity or any definite number of individuals since it involves or expresses nothing but the nature of the thing, as it is in itself.
For example, the Definition of a triangle contains nothing but the simple nature of the triangle, not some definite number of triangles, just as the definition of the Mind, that it is a thinking thing, or the definition of God, that he is a perfect Being, contains nothing but the nature of the Mind, or of God. It does not contain a definite number of Minds or Gods.
(3) There must necessarily be a positive cause of each existing thing, through which it exists.
(4) That this cause must be affirmed to exist either in the nature and definition of the thing itself—because existence pertains to its nature, or its nature necessarily contains existence—or outside the thing.

From these presuppositions it follows that [A] if some definite number of individuals exists in nature, there must be one or more causes which were able to produce precisely that number of Individuals, neither more nor fewer. For example, if twenty men exist in nature—to avoid all confusion I shall suppose that they exist together and without predecessors in nature—it will not be sufficient, to give a reason why the twenty exist, to investigate the cause of human nature in general. [B] What must also be investigated is the reason why neither more nor fewer than twenty men exist. For (according to the third hypothesis) concerning each man a reason and cause must be given why he exists. But (according to the second and third hypotheses) that cause cannot be contained in the nature of the man himself, for the true definition of man does not involve the number of twenty men. Therefore (according to the fourth hypothesis), the cause of the existence of these twenty men, and hence of each of them separately, must exist outside them.--Spinoza to H [Hudde], Letter 34, Voorburg, 7 January 1666. Translated by E. Curley, The Collected Works of Spinoza, Vol. II, (Princeton 2016), pp 25-26. [Emphasis added.]

This post is triggered by an invite from Karolina Hubner and Justin Steinberg to write on the Spinoza and Hudde (1628 – 1704)) exchange. If we only had the second quoted paragraph above, and not the earlier part of the letter, we might infer that the third hypothesis is a causal principle in the spirit of “ex nihilo, nihil fit” (“from nothing, nothing comes”). What's notable is that rather than using what we may call its negative formulation (ex nihilo, nihi) 'from nothing, nothing...', Spinoza opts for what we may call a positive formulation: "(3) There must necessarily be a positive cause of each..."

The positive formulation of Hypothesis (3) echoes Axiom 11, from Spinoza's (1663) The Principles of Cartesian Philosophy,:

Nothing exists of which it cannot be asked, what is the cause, or reason, why it exists. See Descartes’ Al.
Since existing is something positive, we cannot say that it has nothing as its cause (by A7). Therefore we must assign some positive cause, or reason, why [a thing] exists—either an external one, i.e., one outside the thing itself, or an internal one, i.e., one comprehended in the nature and definition of the existing thing itself. (Curley (1985), Vol 1, p. 246; emphasis in original)

It is worth noting that Spinoza here is explicitly riffing on Descartes' Replies to the Second Objections (of the Meditations), and in the context of his treatment of the Cogito; and that Spinoza does so, as he tells us, because it is "impossible for" him "to think that something may come from nothing." (PCP, Vol 1, p. 242) 

In their SEP entry, Yitzhak Melamed and Martin Lin claim that Axiom 11 is "Spinoza’s earliest statement of the PSR." (They omit the causal principle on p. 242 perhaps because it's possible to read it as Spinoza attributing it to Descartes.) It's worth mention that there is a version of the PSR in the Short Treatise, which may well date from before 1663. (I thank John Grey and Daniel Schneider for alerting me to this.) In part 1, Chapter 6 (the one on predestination), paragraph 4, Spinoza writes:

Regarding our second question: whether there is any thing in Nature of which one cannot ask why it exists? our saying this indicates that we must investigate through what cause a thing exists. For if that [cause] did not exist, it would be impossible for this something to exist.
We must seek this cause, then, either in the thing or outside it. But if someone asks what rule we should follow in this investigation, we say it does not seem that any at all is necessary. For if existence belongs to the nature of the thing, then certainly we must not seek the cause outside it. But if existence does not belong to the nature of the thing, then we must always seek its cause outside it. And since the former is true only of God, this shows (as we have already proven before) that God alone is the first cause of everything. (Curley (1985), VOL 1, p. 86)

Be that as it may, let's return to the first letter to Hudde. Let's stipulate, for the sake of argument that Spinoza's conclusion, which I labelled [A], follows from the four 'hypotheses.'* My interest is in the final clause, "neither more nor fewer." That [A] includes 'neither more nor fewer' [nec maiorem, nec minorem] looks, at first glance, a kind of redundant exactitude requirement. To count as a proper explanation (or ground, etc.) the cause of the existence of some entity (or group) may not overshoot or undershoot. I call it 'redundant' because Spinoza already has stated 'precisely' [in Latin: illum iuste].+ [A] anticipates a principle we find in the Ethics, “if a certain number of individuals exists, there must be a cause why those individuals, and why neither more nor fewer, exist.” (E1p8s2) 

But in the letter to Hudde, from the exactitude requirement in [A] Spinoza infers the requirement/demand [B].++ And [B] seems to demand that the cause X of some entity (or number of entities) Y also explains the omissions of possible entities (Yn) such that only Y. If you think that my gloss on [B] is too strong, fair enough. But it is not wholly improbable interpretation because later, in the Ethics, Spinoza articulates an even stronger version of this principle: “For each thing there must be assigned a cause, or reason, both for its existence and for its nonexistence”. (E1p11dem). And so it looks like [B] anticipates some such demand for providing causes of nonexistence(s).

I should note that depending on how one thinks of what a cause or reason is, it's not silly to think that an explanation for Y simultaneously helps rule out why all kinds of not Ys do not obtain. If I can show why a projectile with a particular velocity breaks a particular window at a particular time, I can probably also show why given that velocity it is only breaking that window (and not other windows) at that time. If you agree with Spinoza that a definition is a kind of (formal) cause you can run this example through properties of triangles (and which help explain why it's not a hexagon).

So, crucially, then, compared to the Short Treatise and the Cartesian Principles of philosophy, in the letter to Hudde, Spinoza starts packing quite a bit more into what counts as a proper causal explanation of things existing in nature and so also starts developing a heavier duty version of the PSR to be used in explanations of nature.

The foregoing also helps explain why Hudde was confused in the first place. His question to Spinoza was (according to Spinoza) to provide "a demonstration of the Unity of God from the fact that his Nature involves necessary existence." In the Cartesian Principles of philosophy, at the end of his demonstration to proposition 11 ("there is not more than one God") Spinoza had added the following remark:

It should be noted here that it follows necessarily from the mere fact that some thing involves necessary existence from itself (as God does) that it is unique. Everyone will be able to see this for himself, provided he meditates attentively. I could also have demonstrated it here, but not in a way perceptible by everyone, as has been done in this proposition. (Curley (1985), p. 255)**

Spinoza returns to this material in Chapter 2 of the Appendix. And he says somewhat cryptically, "I advise the Reader that by right we infer God’s Unity from the nature of his existence, which is not distinguished from his essence, or which necessarily follows from his essence." (Curley (1985), p 319)

Clearly Hudde -- himself a very accomplished mathematician and natural philosopher [not to say eventually one of the most powerful people in Amsterdam and Holland [and so Europe]] --- had tried to meditate attentively, but had failed in seeing it for himself. And the reason why he had failed in this is, I submit, that Spinoza had actually not yet articulated [A] and [B].

For without such precification or extension of the causal principle it is not obvious how one can even begin to rule out multiple Gods. (I am not suggesting that Spinoza has successfully done so here. Clearly some folk think even the Ethics version fails.) This is especially so if one thinks, not implausibly, that the cause of (a) God can itself be not limited in particular ways  (since it it is powerful enough to cause God and neither involves any multiplicity or any definite number of individuals).

 

On Throwing Out Philosophical Babies with the Bathwater

Newton's Corollary VI, however, is not in the Principia for mere ornament. Newton needs it to establish that to a first approximation, the system of a planet and its satellites can be treated as an isolated gravitating system if one ignores the shared orbital motion around the sun. Thus we have a case--treating the sun's gravitational field in the region of the system in question as essentially homogeneous--of what Einstein was to call the "principle of equivalence." Indeed, Newton's sixth Corollary (which deals with a homogeneous field of acceleration), and Huygens's discussion of centrifugal force (which deals with an inhomogeneous one), together adumbrate the principle, exploited so fruitfully by Einstein, that the dynamical states and behavior of bodies in no way distinguish between, on the one hand, a certain kinematical state, and on the other, a second kinematical state implying the same distances and rates of' change of distance, together with a suitable applied field of force. It is a little surprising that Mach, with his relativistic view of motion and his interest in seventeenth-century mechanics did not at all notice these things.--Howard Stein "Some Philosophical Prehistory of General Relativity." Minnesota Studies in the Philosophy of Science, 8 (1977): 20.

Last week, after my digression on Harman's rediscovery of Adam Smith, I mentioned in a correspondence with Nathan Ballantyne, that Howard Stein also had documented a case in which a philosophical move/insight/distinction had been lost (and then recovered). And after stating this confidently, I thought it prudent to re-read the Stein piece I had in mind (and only belatedly realizing I had blogged about this material before--today's post is thus a retracing of steps). Before I get to the Stein piece a few words of introduction.

Let's stipulate that due to linguistic or geographic isolation or the (deliberate and accidental) destruction of sources sometimes philosophical moves or distinctions are not available at a later date. These may well be cases of linguistic injustice (recall), but do no present further philosophical challenges.

Then there are cases -- now known as Kuhn-losses -- in the sciences, where insights in a discarded paradigm are not ready-at-hand in a new ruling, scientific paradigm. I use 'ready-at-hand' in order to make clear that not all such cases of Kuhn-loss have to involve strict incommensurability.  The insight from the discarded paradigm may just be thought unintuitive or unlikely-to-work in a new paradigm. (This is especially likely to occur in complex policy contexts.) In so far as paradigms structure the availability of intellectual choices (we might call them theoretical affordances), Kuhn-losses are just a natural effect of the disciplining of an intellectual community by text-books and a shared sense of salient experiences (statistical regularities, decisive experiments, etc.). I say 'natural' because time and cognitive attention are scarce goods, and so at the margin there will be a trade-off between the cost of memory and the costs of advancing the paradigm (etc.). The previous sentence may seem abstract, but some such reasoning was (and is) often used to remove the history of the discipline from the graduate curriculum in a field of expertise/science. There is more to be said about such matters, but hopefully that's sufficient for present purposes.

Now, since philosophy does not have paradigms in the scientific sense, and since graduate education in philosophy is not standardized in the way the sciences and the discipline's history is preserved within the graduate curriculum, the existence of the philosophical analogue to Kuhn-loss in philosophy is prima facie a puzzle. Because Kuhn-loss is a term within the philosophy of science about science, and I both deny that philosophy is a science and -- more polemically -- think it a bad idea to think about philosophy in terms familiar from the philosophy of (Kuhnian) science (because unhealthy to the flourishing of philosophy), I use (after nudging from Ballantyne) 'throwing out the baby in the bathwater' when discussing prima facie puzzling cases of the loss of philosophical insight/moves, and distinctions.

And as I noted last week, Harman felt the force of the puzzle. As it turns out, in my reconstruction of the case, it was Sidgwick's strategy, to turn philosophy into a text-book-driven field with the aim of both (i) demarcating normative philosophy from empirical psychology and (ii) to treat ethics as aiming at (and now I use the felicitous phrase of Aaron Garrett) "comprehensive and coherent normative moral theories" that basically caused Smith's The Theory of Moral Sentiments to be dropped from quasi-standard reading lists in philosophy. And this entailed that some relatively cutting edge responses to objections to impartial spectator theories were not ready at hand when the topic was revived. This opened the door to what we may (in honor of Liam Kofi Bright) call historical arbitrage. 

I think such arbitrage is needed when whole eras of philosophy are treated with disdain in subsequent ages. It's pretty clear that the early moderns actively promoted disdain toward and a lack of acquaintance with scholastic philosophy. And this meant that lots of distinctions and concepts developed by the scholastics were removed from philosophical vocabulary or emptied from a lot of previous significance. And without wishing to raise a prejudice against the practice, we can see that post-Kantian university philosophy in Germany and later in Anglophone world re-introduces a lot of these distinctions and terms back into mainstream philosophy. (To what degree these are really the same concepts given shifting background metaphysics I leave aside.) 

Now, re-reading Stein (one of my doctoral supervisors) was instructive.  First, I was reminded that my own rejection of the ban on using anachronistic terms -- a ban common among certain historians of philosophy (inspired by a species of contextualism)--, is anticipated by Stein (whose paper I read in graduate school).  His version of the argument is instructive:

For the avoidance of anachronism, it is neither necessary nor sufficient to restrict conceptual vocabulary to that of the period under discussion. To impose such a restriction is to inhibit flexibility of thought without any important compensating guarantee against error. It is an intellectual stratagem analogous to that of the shallow empiricism in science that seeks security in rules for the construction of concepts, and achieves only a hobbling of theory. (p. 14)

Stein is explicit that Mach is an example of such shallow empiricism. (p. 14; recall also.) But perhaps forms of operationalism  may also be classified as such. Be that as it may, Stein is right that one can still be anachronistic in interpreting the past even if one only uses actor's categories. For, one may well add apply these categories in a way that is a-historical and at odds with the historical sources. I once claimed (rather too polemically in a NDPR review) that this had happened among scholars who polemically rejected looking at the past through the prism of contemporary issues, but who had tacitly projected a version of the fact-value distinction (in fact, I now understand it was Sidwick's) onto the past that was anachronistic. Moreover, as Daniel Schneider taught me, by using actor's categories, which may well be contested concepts, one is likely to take sides (without always realizing it) in past debates. So, Stein seems to me right that the deployment of anachronism can be illuminating of the historical actors' actual positions (etc.). Stein himself does this throughout the article.  

Okay, now let's turn to the baby with the bath-water. First, in the major key (as it were), Stein himself is an anti-Kuhnian. He concludes his essay with the the claim that "I see, from the seventeenth century up to today a profound community of concerns and a progressive development that has involved both cumulative growth and deepening structural understanding." (27) Stein does not deny a 'conceptual revolution' by Einstein (building on Riemann).

Second, in the minor key (as it were), but my present interest, Stein recognizes that within this profound community of concerns, historical cul-de-sacs and forgetting are possible. Mach really misses something that was available to Newton and Huygens. And while Stein does not  harp on this, plenty of folk influenced by Mach (even after the Einsteinian revolution) missed the point when describing seventeenth century relativity and its development. That the later folk do not see as clearly is especially striking because not only is the seventeenth century mathematical vocabulary is relatively impoverished relative to the later ones, but also there is intellectual continuity from late seventeenth century thinking through the nineteenth century. No major texts are lost and the philosophical vocabulary of the seventeenth and eighteenth century about physics and astronomy does not pose major difficulties to the nineteenth century mind. 

Now, while Mach's case happens within science (broadly conceived), it also involves what we may call the metaphysical principles of science and so, also part of (natural) philosophy proper. (Mach's own institutional position reflects this in his own shifts from mathematics and physics to becoming one of the first professors in the history and philosophy of science.) I put it like that because full awareness of the implications of the "principle of equivalence" seems to have been missed. Now I don't think of myself as an expert on 19th century physics, so take this with a grain of salt. But it's pretty difficult to test empirically the principle of equivalence and so was, perhaps, not of active concern to practicing physicists and natural philosophers. In addition, and this seems to me crucial to Stein's argument, later reflection on relativity was shaped primarily by Leibniz's views (who was treated as the standard bearer for relativistic thinking).

I think this happened in part because of the effect of the Leibniz-Clarke correspondence on philosophical thought of the eighteenth and nineteenth century. This displaced interest in Huygens' views (some of which were hardly accessible) and let people to miss that Newton himself had important stuff to say on the topic. While I am pretty convinced that Leibniz-Clarke shaped people's views of Newton's natural philosophy (to this day, alas), I also say this with some nervousness because I don't know if anyone has checked in a systematic way what folk did with or commented on Newton's sixth Corollary. Of course, and this I feel confident in saying, in many places people studied physics through text-books that while Newtonian in some expanded sense did not follow Newton slavishly at all. Even so, because Newton's achievements were culturally so central to the eighteenth and nineteenth centuries, it is really striking that some of his most profound insights were only appreciated in the development of a physical theory that surpassed his. 

At this point one may be impatient and suggest that in fact the case at hand while no Kuhn-loss is the effect of paradigmatic thinking in science, which can, in fact, obstruct the insights of (what we may call in homage to Kuhn) the scientific-legislator of the paradigm. And that by creating a division of labor in science (among different fields, but also among theory and experiment), it was left to relatively few to study relativistic theories while Newtonianism ruled. And, in fact, once Maxwell's equations and concerns about the ether opened the door, relativistic principles were explored by (say) Poincare in the late nineteenth century. So the critic may refuse to accept the example as a case about lost philosophical babies.

Fair enough. But, of course, one of the effects of the split between philosophy and science, and the relatively high status of physical science, is the tendency toward paradigmatic thinking in science and philosophy. And one may well conclude, as I do, that in so far as paradigmatic thinking and the prestige of science within philosophy as such shape philosophy we should expect the bathwater, even one nourished with the fruits of science, to carry away important insights. Of course, documenting such cases involves a kind of practical contradiction because in the very act of retrieval the baby is saved.

 

 

 

 

 

 

 

On Crooked Timber.

The last two months have been challenging for me, hence my lack of blogging. They aren’t limited to losing my advisor. But what I have seen running throughout many of these challenges is a kind of a deep psychological that I will call wounds of the heart.

A wound of the heart is an emotional hurt that generates intense, seemingly unbearable psychic stress and that can create long-term damage to one’s personality due to overpowering negative moral emotions, like resentment and hatred, and that may last for the rest of one’s life. They are typically caused by some act by one’s close friends, family, or community. The wounded person believes the act signals that the offending group bears him or her bad will, and that the group does not love or support the wounded person in the way he or she had counted upon in the past. It can overwhelm the wounded person’s agency, leading them to lash out and creating a new harm, and perhaps wounding the hearts of others. When multiple parties to a relationship have wounds of the heart, that can spell the death of the relationship, even if the relationship continues pro forma.--Kevin Vallier The Wounds of the Heart

Because one of my entries into the history of philosophy was by way of Isaiah Berlin, I have always associated his quotation from Kant that "Out of the crooked timber of humanity no straight thing was ever made" with an important truth. To this day the core idea informs my own skeptical liberalism.

But as always the story has wrinkles.

So for years I shared Ingrid Robeyns' sense, appropriately shared at the mother of all philosophical blogs, CT, that Berlin's translation improved on the original, Aus so krummem Holze, als woraus der Mensch gemacht ist, kann nichts ganz Gerades gezimmert werden. I still do. However, it is not often remarked that Kant added a footnote, to this very sentence; and it is worth noting it, too:

The role of man is very artificial. How it may be with the dwellers on other planets and their nature we do not know. If, however, we carry out well the mandate given us by Nature, we can perhaps flatter ourselves that we may claim among our neighbors in the cosmos no mean rank. Maybe among them each individual can perfectly attain his destiny in his own life. Among us, it is different; only the [human] race can hope to attain it."*

There are really two fine issues here: first, that we may be part of a larger family of planetary denizens. This is an idea that excited Huygens and Newton. And from Kant's pre-critical writings we know (recall) that Kant was much impressed by Newton's ideas on this point. And Kant assumes that, once we get into the habit of  this, we will adopt a perspective in which we are judged by such aliens. Maria Pia Paganelli has suggested -- in commenting on a similar idea in Adam Smith -- that this can be traced by to Fontenelle's Conversations on the Plurality of Worlds. It's plausible this also influenced Kant because Kant's earlier Universal Natural History is clearly shaped as I argued (based on a suggestion by Martin Schönfeld) by Fontenelle's work. So, Kant's cosmopolitanism here is truly cosmopolitan. I assume this is known among Kant experts, but the thought always delights me. 

Second, in the note Kant articulates the thought that that any attainable future worth having is a collaborative or shared project. I can think no better way of characterizing the liberal project in that it simultaneously holds that we should assume the unreformable weakness of individuals and that as humanity we're in it together. This is why, the more I reflect on it, the more I recognize that global, maybe cosmic (yeah for Star Trek!) federation is the liberal political destiny. 

This morning, in a wistful, apprehensive mood,  I returned to Seneca Letter 50. The letter is really about the comic-from- without-maddening-from-within realization that the more we run away from our problems, and disown them, the more we find them not just sneaking up on us, but defining us:

For what else are you busied with except improving yourself every day, laying aside some error, and coming to understand that the faults which you attribute to circumstances are in yourself? We are indeed apt to ascribe certain faults to the place or to the time; but those faults will follow us, no matter how we change our place.

And yet, I was in no mood to be preached to by Seneca that the way forward is a regimen of self-improvement. My mind drifted back toward's Vallier's post quoted above. As the reach of life has shrunk during this pandemic, and in my solitude, I more easily and directly encounter evidence of how my past wounds create new harms; I re-read, and I recognize myself in the self-portrait he draws. Kevin writes of 'soldiering on.' I wince at the bellicose nature of the phrase, despite seeing the tenderness in the rest of Kevin's words. The soldiering on reminds me of the bit of the part of Seneca -- preparing for death -- I like least.    

Without realizing it I had read on in Seneca. And there, I was surprised to read (in  Richard Gummere's 1917 translation), There is nothing that will not surrender to persistent treatment, to concentrated and careful attention; however much the timber may be bent, you can make it straight again.  [Nihil est, quod non expugnet pertinax opera et intenta ac diligens cura; robora in rectum quamvis flexa revocabis. Curvatas trabes calor explicat et aliter natae in id finguntur, quod usus noster exigit; quanto facilius animus accipit formam, flexibilis et.]

    Of course, Seneca must believe that self-improvement is possible, I think.

But, as I re-read I realize that Seneca thinks this, too, is a collaborative project: "we begin to mold and reconstruct our souls before they are hardened by crookedness" ["ante animum nostrum formare incipimus et recorrigere quam indurescat pravitas eius]. In Kevin's vocabulary, we soldier on in a platoon. Of course, the larger context of the Letter suggests that Seneca thinks we do this under the guidance of a mentor. 

I then remembered Kant. And now looking at what I have written, I am struck by the thought that I have been eavesdropping on a great debate between the two wings of cosmopolitanism: disagreeing about the means, but both claiming that we're in this together. My gloom dissipates. 

 

 

Some dis-analogies between Two Basic Quantities (Space and Time) in Newton's Principia

Thus far it has seemed best to explain the senses in which less familiar words are to be taken in this treatise. Although time, space, place, and motion are very familiar to everyone, it must be noted that these quantities are popularly conceived solely with reference to the objects of sense perception. And this is the source of certain preconceptions; to eliminate them it is useful to distinguish these quantities into absolute and relative, true and apparent, mathematical and common.

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (precise or imprecise) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heavens, where the dimension is determined from the situation of the space with respect to the earth. Absolute and relative space are the same in species and in magnitude, but they do not always remain the same numerically. For example, if the earth moves, the space of our air, which in a relative sense and with respect to the earth always remains the same, will now be one part of the absolute space into which the air passes, now another part of it, and thus will be changing continually in an absolute sense.--Newton, Scholium to the Definitions, Principia, translated by Whitman & Cohen) 1999: 408-409).

My present interest is to articulate four dis-analogies in the paragraphs labeled, '1' and '2'.* For the purposes of analysis, I distinguish in Newton's thought between four basic quantities and three fundamental distinctions that Newton applies to these four basic quantities. The four basic quantities are “time, space, place, and motion." The three fundamental distinctions are "absolute and relative';' "true and apparent;" and "mathematical and common.” In what follows I focus only on basic quantities. Here I stipulate that such a quantity is abstract (see Smeenk & Schliesser 2017). And my interest here is primarily in the significance of the measures of two such basic quantities (time and space).

The first dis-analogy is related to the first sentence of each paragraph: ‘true, and mathematical’ are present as modifications of (absolute) time and absent as modifications of (absolute) space. The second is related to the second sentence of each paragraph: that “apparent, and common” are present as modification of (relative) time and absent as modification of (relative) space. Katherine Brading (2017) and I (see here in 2013) have given different interpretations of the significance of these two dis-analogies, but I will bracket that today.

Third, there is an asymmetry in the measures Newton proposed. In order to measure time (an abstract quantity) Newton proposes to use the motion of bodies. However, in order to measure space (another abstract quantity) Newton proposes to use the “situation” of a part of space to another part. Crucially, the measure of space is identical in “species and in magnitude” to the thing it is a measure of (space). This identity (in species and magnitude) is omitted in the measure of time. Motions of bodies, even the regular motions of the solar system or pendulum clocks,  are not identical in species and magnitude to duration.

Brading (2019) explains what’s going on in the third dis-analogy. In her terminology, rods (that is, measures of space) are geometrical just as space is. Whereas clocks (that is, a regular motion of bodies) are, for Newton, dynamical systems. And whatever time “in and of itself and of its own nature,” might be it is not natural to think of it as a dynamical system. That is to say, there seems to be no possible gap between the measure(s) of space and space (Brading 2019: 160-161); there does seem a possible gap between the measure(s) of time and time (Brading 2019: 162).  

The reason why clocks are a dynamical system on Newton’s account is very nicely explained by Brading:

“It is central to the project of the Principia,” she writes, “that forces and the motions of bodies are inter-dependent. Newton emphasizes this in the Preface to the first edition:

For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces (Newton, 1999, p. 382)

This means that all clocks in the Principia are dynamical systems, because they are systems of bodies in motion, and motions and forces are inter-related,” (Brading 2019: 162).”

That there is a possible gap between the measure of time and time in of itself is not just caused by the fact that the measure is a dynamical system and it seems odd to say this about time itself (where forces and bodies are absent), but also, and more important, because while time “flows uniformly” according to Newton’s stipulation (Brading 2019: 164), there is no guarantee that any measure, which is a natural process of bodies in motion, does so. And even when one constructs an artificial measure (a pendulum clock) or an abstract measure (a mathematical equation of time), there is no guarantee that its regularity and time’s uniformity are identical (Brading 2017: 34).

Now, it worth noting that Brading's use of "rods" is anachronistic because Newton uses "situations." Unfortunately, Newton does not explain what a 'situation' is. I think we can infer it is a kind of mental inspection or abstraction from other phenomenal details. Obviously, if you want to stabilize situations, rods are tempting instruments. 

As an aside, in his Essay, Locke, who I am treating here as an independent guide on contemporary use (not a source), treats 'situation' as an ingredient of complex ideas of (solid) bodies (2.23.9) and sometimes as a way to convey a relationship among sensible parts (2.4.4). 

The more important point, and here I am drawing on a note from Chris Smeenk is that "situation of the space with respect to bodies” (August 28, 2020) involves bodies apart in some sense; because unoccupied spaces are invisible and so difficult to use as markers of situations. Now, Smeenk worries, I think, this reintroduces time or dynamics. If that is so, then the gap that Brading diagnoses on the measure of time vs time side, may also exist on the space vs measure of space side. 

The reason why I think that there need not be such a gap between the measure of space and space is that one can evaluate/inspect a situation at an instance if a situation is small enough. I say this for two reasons: (a) in the early modern period it is often thought that some ideas are secure, or adequate, if they can be inspected at once  or instantaneously (without intermediate relata).** And perhaps Newton thinks that some relatively small situations can function as foundational measures in this way such that situations and spaces are the same in "species and in magnitude." And (b) keeping situations small echoes the manner in which pendulums (a body in motion) can be a reliable measure of time (by keeping the arc small, as was well known to Newton and Huygens)

This (b) also helps qualify the nature of the gap between the measure of time and time diagnosed by Brading. (What follows is also indebted to Smeenk.) For, once the ideal time keeper has been mathematically articulated and shown to be possible, Newton can bound the amount of error associated with departures from this ideal case. In fact, from the mid 1680s Huygens shows how to start doing this for a pendum in practice. And so that the right thing to say here, and this is very much in the spirit of George Smith's teaching on Newton (which Brading, Smeenk, and I share as common ground), is that Newton also creates a research program of successive approximation into theoretically and empirically establishing the error bounds and methods for correcting them among our measures; in Smeenk's terms of "systematically improving time measurements to approach the ideal of a truly periodic system." (And so Newton helps initiate a research project into measure-theory.)+ And so, if there is a gap, there is also a forward-looking attempt to learn how to recognize and close it over (ahh) time.

The fourth dis-analogy is that the measure of time (bodies in motion) presupposes space or its measure while the measure of space (a situation) does not presuppose time (if the situation can be accessed at an instant). This point is clearly something Newton had reflected on. For in his earlier criticism of Descartes’ physics, Newton argues in De Gravitatione that in order to be able to conceptualize and analyze motion, one must make reference to some “motionless being such as extension alone or space in so far as it is seen to be truly distinct from bodies,” (Newton 2004: 35) One need not agree with Newton’s metaphysics here, to see that some fixed or ordered coordinate system, independent of the bodies, is required for the analysis of motion (with a starting place and a subsequent places, etc.).

Celebrating George E. Smith (Tufts)

I am in Boston this week, part of a fest-program, A Question of Evidence, to celebrate George Smith's contributions to scholarship and teaching. Remarkably, one of his courses, a year long class on Newton's Principia -- roughly Semester/Part 1 puts the student in a position to read the Principia; Part 2 is the reading of the Principia. This course has shaped and re-shaped scholarship on Newton through its impact on students of all levels who have taken a version of the course at Tufts (George's home institution), Notre Dame, and Stanford.  I took the course in 1991/92, as an undergraduate at Tufts. (I believe it was the third installment of the course.) When I first walked into the class-room -- I was an IR/Econ major -- I thought I must have made a mistake: I saw a bunch of MA students and faculty from different departments (including some of my own economics professors). As I hesitated walking in I saw that some students were the known campus nerds. 

I had met George on the university's budget and priority meeting where I represented student interests. He had impressed me as its chair. It was clear he was an engineer who had worked in corporations, and he seemed to know what we were doing as we negotiated rather steep budget cuts.  When I looked him up in the course catalogue, I couldn't find him in the big book (this is pre-internet days). But I did find somebody with his name in the philosophy department offering an undergraduate course on Isaac Newton. 'That's me,' he said. 'But you're an engineer.' 'I am a philosopher, too.' (It's true see here.) Much later I learned he wrote a dissertation on modal logic at MIT.

I stuck with the course, first, because I wanted to know what distinguished successful science (physics) from the failures (political science/economics, etc.). [I wouldn't put it like that anymore.] The Berlin Wall had collapsed in my first semester in college, and i had been baffled by my social science professors -- some of the world's leading scholars -- inability to forecast and even understand it as the process was unfolding in real time. I had no intrinsic academic interest in the fall of the Berlin Wall, but I wanted to join the IMF or some such institution that could help run the world, and it seemed pointless to me to get a degree in a field promising to help you run the world but that was based on quicksand. But, the more important reason to stick with the course was George. George lectured. And he did so partially reading from amazing lecture notes. (He would put these on reserve after class (and editing).) But what made him mesmerizing was that he took us, the students  of all level, seriously as genuine interlocutors in this shared adventure of understanding Newton's method. And what made the whole point even more remarkable: many sessions would start with his excitement of his latest discovery -- sometimes overnight discovery -- of the evolution and development of Newton's thought. (I return to this below.) Our paper assignments were all clearly designed to contribute to a collective endeavor of understanding Newton's breakthroughs (in the context of the very high baseline set by Huygens and Galileo, especially).

George's pedagogic methods break every rule of the education consultants (that the 'managers' at my university hire to help improve 'learning outcomes'): he sets very high expectations from his students, assigns challenging primary texts (and a lot of them), often lectures for three hours on end (in the evening), does not include amusing (irrelevant) anecdotes, and he does not flip the class room. What he does do, and he does this amazingly well, is prepare you qua student to be a co-equal in this astounding intellectual adventure. He makes sure you acquire all the technical background, one firm step at the time, and then puts you in the position to contribute to active research, if you so wish. (A lot of students end up writing term papers that could be the basis of a journal article.) Along the way, he invites you out on frigid winter nights to stare through a telescope to experience what Galileo might have experienced when he turned one toward the Moon. (George makes sure to let you try to see anything with the magnification Galileo used.)

George changed my life not just through the course, which enlarged my sense of intellectual possibility, but because after my graduation (as a BA student), he roped me into a joint (and ongoing) project on Huygens's empirical challenge to Newton's account of universal gravity (see here).  (At the time, under the influence of Koyré, most historians and philosophers assumed, falsely, that the resistance to Newton was mostly driven by a metaphysical rejection of action at a distance and a stubborn adherence to the methods of the mechanical philosophy.) After that apprenticeship, I wanted to become a scholar. The amazing thing about our joint project was that George decided to redo all of Huygens's and Newton's relevant calculations. This is something he had also done in the budget process/debates we were involved in a few years ago. What's important here is that George did not merely eye-ball or even check the calculations, he re-did them (after getting hold of the original data from the manuscripts). Because George does that work his research turns out to be more durable (and more standard-setting) than a lot of other scholarship. 

George's scholarship has transformed our understanding of Newton's Principia and the research that it stimulated over two centuries (see "Closing the Loop" [an amazing paper] here) and is doing so for a number of other research areas. Yet, while he was trained as a philosopher at MIT in the 1970s (and it shows in the clarity of his prose and the rigor of his arguments), it is very difficult to insert George's work into standard philosophical debates. That it does not do so is, in part, a consequence, I think, of the fact that philosophers had abandoned understanding how scientific discovery really works in practice (treating it as a mysterious black box) or got focused on confirmation theory (driven by toy examples).+ But while he makes enormous contributions to the history of science, and, as I've witnessed, is treated with enormous respect by historians of science, the work is driven by philosophical questions about the epistemic and evidential status of scientific theories.  

Some other time, I'll blog more about the content of George's works and its significance. Here I want to close with a (moralized) observation. There is a tendency, even by very well-meaning people, in efforts to push back against the one-sided attention to 'research' (say in status, academic reward, and grant recognition) to emphasize, say, the social significance or transformative potential of 'teaching.' Here I want to say something closely related, but I think distinct. And, that is, that it should not be forgotten that the impact of research, one's own and others, can also be felt in the classroom. This is not just true on the more general level that we, qua teachers-intellectuals, are shaped by the research we have done, or the more specific level in the material (itself a product of research) we teach, but also that we can treat teaching as an occasion to engage in a collaborative intellectual enterprise with our students not just in the advanced graduate seminar or the research lab meeting, but also in the undergraduate classroom. 

Huygens on Causal Isolation, Light, and Simultaneity (again) [part II]

Yesterday, I suggested that in rejecting both Descartes's vortex theory and Newton's cosmology (including the law of universal gravitation), Huygens landed with an apparent tension. One the one hand, Huygens claims that solar systems are causally isolated from each other. They are separated by an universal ether* that on my interpretation has five properties I wish to highlight today: (i) it keeps the planetary vertices that make up a solar system in stable equilibrium ("because the æther round it, which is at rest, keeps the parts of it from flying out" ) and (ii) it keeps each solar system causally isolated from each other ("And as their motions do not all intermix or communicate with one another;"). So, I attributed a further property to the Huygensian ether: (iii) that it absorbs and neutralizes any motion/energy from the motions of the solar systems.

Now, one may reasonably doubt that the universal ether is responsible for (ii). For, a more literal reading suggests it is the immense distances among solar systems that is responsible ("in my opinion must the Vortices of Stars be plac’d as not to hinder one anothers free Circumrotations.") This would put Huygens close to the 'solution' that Newton later adopts in the General Scholium. (Newton had worried about solar systems collapsing into each other given universal gravity.)

Yet, the immense distances cannot do the assigned task (of preventing communication of motion among the solar systems) if one is working with a plenum physics. For in a plenum physics, motions can be transmitted along immense causal chains. So, for now I stick with (i-iii).

Discussion with Marius Stan and Chris Smeenk made me realize, however, that there are two ways to understand what Huygens says about the ether: first, one one approach, the ether fills the space(s) between/among solar systems, but is absent inside the solar system. That is, the universal ether is a different kind of material (fluid) from vertices of the solar system. Because of (i) [and (iii)] it also entails that (iv) this ether must have mass (and so is a qualitatively different ether from the one Newton considers--his ether has negligible mass). 

The other approach is to treat the ether as a genuinely universal ether that fills all spaces.* (This is how Newton conceives of his ether.) The planetary vertices of the solar system then are carried through this ether. And then according to Huygens somehow this ether maintains the stability of each vortex and the system of vertices. The main problem with this second approach is that ether must have both negligible mass (so as not to retard the planetary motions) as well as considerable mass (so as to keep the system in stable equilibrium from without). Another non-trivial problem is that in the Principia, Newton had shown the orbits would  not be ellipses if they had to move through fluids (but spirals); yet Huygens explicitly accepts Newton's result that Keplerian motion is elliptical. So, I reject this approach, and continue to stick with the former conception of the ether.

To return to the apparent tension. On the other hand, Huygens's (v) universal ether explicitly propagates light from one solar system to another.  Here, in order to avoid misunderstanding, we need to distinguish between how the wave theory of light is often presented and how Huygens understands his own theory For him light always just is matter in motion, in particular a particle. But the way this is manifested is wave-like. How this is supposed to work in Huygens is unclear (and he himself appealed to God's providence at precisely this point in the Cosmotheoros) because his geometric proofs of the wave light character of light are divorced from his mechanical understanding of light. It is an interesting fact that later, Huygens's wave theory came to be divorced from his own ontology (such that a particle theory of light came to be thought an alternative associated with Newton).

As I hinted yesterday, because Huygens insists that the underlying ontology of light involves particles, he causes two kinds of problems for himself: first, his ether must have negligible mass (so as not to disperse light beams) and, as we have already seen, this is in apparent tension with (v), that is, the ether of having considerable mass (to keep the system of vertices of a solar system in equilibrium). Second, the motions of the solar systems are not causally isolated because particles of light are being transmitted among them across (as Huygens emphasizes) immense distances. I am unsure he recognized the tensions and how he would resolve them.

My interest in these matters was prompted by thinking about how Huygens (and Newton) would have to think about simultaneity. To re-introduce the issue(s) let me recall  how Huygens and Newton think about time and also insert some special terminology. The main measures of time were the motions of astronomical bodies (relative to some bodies held fixed, usually the 'fixed stars'). In a series of breakthroughs, Huygens had shown (and Newton had agreed), that it was possible to construct a mathematical equation of time for each planet and use it to calibrate clocks. In addition, Huygens had shown mathematically (see Joella Yoder's great book) that the cycloid was an isochronous curve and that one could construct a pendulum clock which was ischronous. One could treat, as Newton suggested, a solar system as the kind of entity in which the individual equations of time can be coordinated (and unified) with reference to a point external to it. This can help define (at least in thought) a 'temporal frame' (akin to an inertial frame).

Now, let's distinguish between local simultaneity and absolute simultaneity. Local simultaneity is roughly the idea that moments in time are shared within such a temporal frame of a solar system. Absolute simultaneity is the thought that a moment of time spreads out through all the spaces of the universe.  Once, in a paper, building on ideas of Nick Huggett, I had claimed that Newton's physics only required local simultaneity. And that this was true for each solar system.  But that only theological concerns drove Newton into embracing absolute simultaneity. 

I knew this couldn't be the whole truth because Newton's law of gravity was universal, but I had noticed (in the Opticks) that Newton allows the genuine possibility that different galaxies could be governed by different laws of nature (a point I develop in a paper with Zvi Biener). Even so, my approach was treated to very insightful criticism in a wonderful paper by Katherine Brading, who writes, “contra Schliesser, that all three of Newton’s conceptual distinctions between absolute and relative, true and apparent, and mathematical and common time have empirical import (section 5) and are necessary for the project the Principia (section 6).” (emphasis in original)." For now, I leave it to our readers to adjudicate our disagreement.** So, if Brading is right then for Newton, local simultaneity just is a special instance of absolute simultaneity.

By contrast, Huygens was a relativist*** -- in fact, as Howard Stein has shown an amazingly insightful relativist -- about motion. At first glance, it would seem for him there is really no scientific reason to accept absolute simultaneity (recall). This last point seems strengthened by the fact that for Huygens the motions of solar systems are explicitly causally isolated.  And, in fact, as I noted yesterday, Huygens's way of thinking seems to allow that different solar systems could have different ways of being locally stable (and so have different kinds of locally apt force laws).+

There is a further reason why Huygens might be cautious about introducing what I am calling absolute simultaneity.++ Imagine two solar systems, A & B, far apart from each other, each with their own temporal frame. We can ask: are equal intervals of time [according to the coordination of the equations of time] for system A *regular* compared to equal intervals of time [according to the coordination of the equations of time] for system B? Here we need a much lower degree of isolation (between A & B) for the problem to arise, at least in principle.+++ 

Now, the question remains if for Huygens the propagation of light through the ether does not generate pressure to insist on the existence of absolute simultaneity. For this propagation shows (assuming I am right above) that solar systems are not isolated causally. Given that Huygens knows the speed of light and at least some of the the relative distances among solar systems,**** it is at least conceivable for him that one day the motions of a group of solar systems could be brought together (by focusing on light emitted by their Suns) relative to some fixed point (even if within these solar systems there are different empirical force laws governing the  motions of system of vertices). While this does not get one from local simultaneity to absolute simultaneity, it would force him to take some steps down that road.++++