Nothing New Under the Sun

I started reading Thomas Aquinas’s commentary on Aristotle’s Physics recently. The Physics isn’t actually about what we would call physics; it’s about what in modern terms would be called philosophy of nature. Anyways, Aristotle devotes large parts of this book to rebutting the opinions of other philosophers, and every time I see one of these rebutting sections I’m always amazed at how similar his contemporaries sound to modern philosophers. Here are a few parts I was reading over the past couple of days that particularly stood out to me. The Latin text is from the Corpus Thomisticum, and the translation is by yours truly.

Thomas Aquinas, Commentary on Aristotle’s Physics, book 2, reading 2

Postquam philosophus ostendit quid est natura, hic ostendit quot modis natura dicitur. Et primo ostendit quod natura dicitur de materia; secundo quod dicitur de forma, ibi: alio autem modo et cetera. Circa primum, sciendum est quod antiqui philosophi naturales, non valentes usque ad primam materiam pervenire, ut supra dictum est, aliquod corpus sensibile primam materiam omnium rerum ponebant, ut ignem vel aerem vel aquam: et sic sequebatur quod omnes formae advenirent materiae tanquam in actu existenti, ut contingit in artificialibus; nam forma cultelli advenit ferro iam existenti in actu. Et ideo similem opinionem accipiebant de formis naturalibus, sicut de formis artificialibus. Dicit ergo primo quod quibusdam videtur quod hoc sit substantia et natura rerum naturalium, quod primo inest unicuique, quod secundum se consideratum est informe: ut si dicamus quod natura lecti est lignum, et natura statuae est aes; nam lignum est in lecto, et secundum se consideratum non est formatum. Et huius signum dicebat Antiphon esse hoc, quod si aliquis proiiciat lectum ad terram, et ligna putrescendo accipiant potentiam ut aliquid ex eis germinet, illud quod generatur non erit lectus, sed lignum. Et quia substantia est quae permanet, et naturae est sibi simile generare, concludebat quod omnis dispositio quae est secundum quamcumque legem rationis vel artem, sit accidens: et illud quod permanet sit substantia, quae continue patitur huiusmodi dispositionum immutationem. Supposito igitur quod rerum artificialium formae sint accidentia, et materia sit substantia, assumebat aliam propositionem, quod sicut se habent lectus et statua ad aes et lignum, ita et quodlibet horum se habet ad aliquid aliud quod est materia ipsorum; ut aes et aurum ad aquam (quia omnium liquefactibilium materia videtur esse aqua), et ossa et ligna ad terram, et similiter est de quolibet aliorum naturalium. Unde concludebat quod illa materialia subsistentia formis naturalibus, sint natura et substantia eorum. Et propter hoc quidam dixerunt terram esse naturam et substantiam omnium rerum, scilicet primi poetae theologizantes; posteriores vero philosophi vel ignem vel aerem vel aquam, vel quaedam horum, vel omnia haec, ut ex superioribus patet. Quia tot de numero eorum dicebant esse substantiam omnium rerum, quot accipiebant esse principia materialia; et omnia alia dicebant esse accidentia horum, idest materialium principiorum, vel per modum passionis vel per modum habitus vel per modum dispositionis, vel cuiuslibet alterius quod reducatur ad genus accidentis. Et haec est una differentia quam ponebant inter principia materialia et formalia, quia dicebant ea differre secundum substantiam et accidens. Alia autem differentia est, quia dicebant ea differre secundum perpetuum et corruptibile. Nam quodcumque praemissorum corporum simplicium ponebant esse materiale principium, dicebant illud esse perpetuum: non enim dicebant quod transmutarentur invicem. Sed omnia alia dicebant fieri et corrumpi infinities: ut puta, si aqua sit principium materiale, dicebant aquam nunquam corrumpi, sed manere eam in omnibus sicut substantiam eorum; sed aes et aurum et alia huiusmodi dicebant corrumpi et generari infinities.

 

After the Philosopher has shown what nature is, he here shows how many meanings “nature” has. And first he shows that nature is said of matter; second that it is said of form, there: “But in another way,” etc. Concerning the first, it must be noted that the ancient natural philosophers, unable to arrive at prime matter, as was said above, held some sensible body to be the first matter of all things, like fire, or air, or water: and thus it followed that all forms came to matter as to something already existing in act, as occurs with artificial things; for the form of a knife comes to iron that already exists in act. And therefore they held a similar opinion on natural forms and artificial forms. He [Aristotle, citing objections?] says then first that to some it seems that this is the substance and nature of all natural things, that which is in each of them first, which considered in itself has no form: as if we should say that the nature of a bed is wood, and the nature of a statue is bronze; for wood is in the bed, and considered in itself is not formed. And Antiphon said that a sign of this fact is this, that if someone throws a bed to the ground, and the wood by rotting actualizes [?] its potency to have something germinate out of it, that which is formed will not be a bed, but wood. And because substance is that which remains, and it is characteristic of nature to create something similar to itself, he concluded that every arrangement that follows some law of reason or some skill, is accidental: and that which remains is substance, which uninterruptedly undergoes such arrangements and changes. Given then that the forms of artificial things are accidents, and their matter is their substance, he adopted another proposition, that as a bed and a statue is to wood and bronze, so also any of these things is to any other thing that is its matter; as bronze and gold are to water (for the matter of all liquefiable things seems to be water), and bones and wood to earth, and it is similar with any other natural thing. From this he concluded that those materials underlying natural forms, are their nature and substance. And because of this some have said that the earth is the nature and substance of all things, namely the first theologizing [?] poets; philosophers afterward said that fire or air or water, or some of these, or all of them [were the nature and substance of all things], as is clear from what was said above. For they said as many of those were the substance of all things, as they held to be material principles*; and everything else they said were accidents of these, that is of the material principles, either in the manner of passion [“passion” in the sense of receiving rather than causing change; opposed to action] or in the manner of a habit* or in the manner of an arrangement, or of whatever other thing that falls under the genus of accident. And this, they said, is one difference between material and formal principles, for they said they differed as substance and accident. And another difference is, that they said they differed as permanent and corruptible. For whichever of the aforementioned simple bodies they said was a material principle, they said that that was permanent: for they said that they [the principles] were not changed into each other. But all other things they said came into being and passed away an infinite number of times: as for example, if water was a material principle, they said water never passed away, but remained in all things as their substance; but bronze and gold and other such things they said passed away and came into being an infinite number of times.

(*I’m not entirely sure how to translate “principium”; literally it just means “beginning,” but it often carries the connotation that it’s a source rather than just a beginning. Translations of Aquinas usually just translate “principium” as “principle” everywhere, so since I’m not entirely sure what Aquinas means, I’m just falling back on that. Similarly, I’m also not sure how to translate “habitus”; literally it just means “a[n act of] having,” which could mean any one of a number of things. But most translations of Aquinas just render this as “habit,” so I’m falling back on that.)

It might be hard to understand this if you don’t know all the technical terminology Aquinas uses, but the basic idea is that the ancient philosophers thought that any complex thing exists only as a feature or arrangement of the parts that make it up, rather than the whole being a thing in itself. They thought that the elements were never created or destroyed, only rearranged to form different things. They also thought that there was no ontological difference between living things and artificial machines. All of these are positions taken for granted by modern philosophers and scientists, though we have different elements now. This contrasts with the position Aristotle came up with; he held that natural things (“natural” being defined as “having within itself a principle of motion and rest, which is in it primarily and essentially and not accidentally” (book 2, reading 1)) are things in their own right rather than simply sums of their parts.

ibid., book 2, reading 7

… sicut Empedocles, qui dixit quod aer non semper adunatur superius supra terram quasi hoc ei sit naturale, sed quia ita accidit a casu. Dicit enim quod quando mundus est factus, lite distinguente elementa, accidit quod aer se collegit in istum locum, et sicut tunc cucurrit, ita semper stante isto mundo cursum habebit: sed multoties in aliis mundis, quos ponebat infinities fieri et corrumpi, ut supra dictum est, aer aliter ordinatur inter partes universi. Et similiter dicebat quod plurimae partes animalium fiunt a fortuna; sicut quod in prima constitutione mundi fiebant capita sine cervice.

 

… like Empedocles, who said that air does not always rise upward above the eath as if this is natural to it, but because it occurs thus by chance. For he says that when the world was made, with strife [incompatibility? repulsion?] separating the elements, it happened that air went to that place, and as when it ran there then, so will it always take that course as long as the world stands thus: but often in other worlds, which he thought were created and passed away an infinite number of times, as was said above, air is otherwise ordered among the parts of the universe. And similarly he said that most parts of animals occur by chance; as when in the first creation of the world heads were made without necks.

And here we have the multiverse with the laws of nature changed at each iteration.

ibid., book 2, reading 12

Circa primum sciendum quod ponentes naturam non agere propter aliquid, hoc confirmare nitebantur removentes id ex quo natura praecipue videtur propter aliquid operari. Hoc autem est quod maxime demonstrat naturam propter aliquid operari, quod ex operatione naturae semper invenitur aliquid fieri quanto melius et commodius esse potest, sicut pes hoc modo est factus a natura, secundum quod est aptus ad gradiendum; unde si recedat a naturali dispositione, non est aptus ad hunc usum; et simile est in ceteris. Et quia contra hoc praecipue opponere nitebantur, ideo dicit quod potest opponi quod nihil prohibet naturam non facere propter aliquid, neque facere semper quod melius est. Invenimus enim quandoque quod ex aliqua operatione naturae provenit aliqua utilitas, quae tamen non est finis illius naturalis operationis, sed contingit sic evenire; sicut si dicamus quod Iupiter pluit, idest Deus vel natura universalis, non propter hunc finem, ut frumentum augmentet, sed pluvia provenit ex necessitate materiae. Oportet enim, inferioribus partibus ex propinquitate solis calefactis, resolvi vapores ex aquis; quibus sursum ascendentibus propter calorem, cum pervenerint ad locum ubi deficit calor propter distantiam a loco ubi reverberantur radii solis, necesse est quod aqua vaporabiliter ascendens congeletur ibidem, et congelatione facta, vapores vertantur in aquam; et cum aqua fuerit generata, necesse est quod cadat deorsum propter gravitatem: et cum hoc fit, accidit ut frumentum augeatur. Non tamen propter hoc pluit ut augeatur; quia similiter in aliquo loco frumentum destruitur propter pluviam, ut cum est collectum in area. Non tamen propter hoc pluit, ut destruatur frumentum, sed hoc casu accidit, pluvia cadente; et eodem modo videtur casu accidere quod frumentum crescat per accidens, pluvia cadente. Unde videtur quod nihil prohibeat sic etiam esse in partibus animalium, quae videntur esse sic dispositae propter aliquem finem: utpote quod aliquis dicat quod ex necessitate materiae contingit quod quidam dentes, anteriores scilicet, sint acuti et apti ad dividendum cibum, et maxillares sint lati et utiles ad conterendum cibum. Non tamen ita quod propter istas utilitates natura fecerit dentes tales vel tales: sed quia dentibus sic factis a natura propter necessitatem materiae sic decurrentis, accidit ut talem formam consequerentur, qua forma existente sequitur talis utilitas. Et similiter potest dici de omnibus aliis partibus, quae videntur habere aliquam determinatam formam propter aliquem finem.

Et quia posset aliquis dicere quod semper vel ut in pluribus tales utilitates consequuntur; quod autem est semper vel frequenter, conveniens est esse a natura: ideo ad hanc obiectionem excludendam, dicunt quod a principio constitutionis mundi, quatuor elementa convenerunt ad constitutionem rerum naturalium, et factae sunt multae et variae dispositiones rerum naturalium: et in quibuscumque omnia sic acciderunt apta ad aliquam utilitatem, sicut si propter hoc facta essent, illa tantum conservata sunt, eo quod habuerunt dispositionem aptam ad conservationem, non ab aliquo agente intendente finem, sed ab eo quod est per se vanum, idest a casu. Quaecumque vero non habuerunt talem dispositionem sunt destructa, et quotidie destruuntur; sicut Empedocles dixit a principio fuisse quosdam generatos, qui ex una parte erant boves, et ex alia parte erant homines.

 

Concerning the first, it must be noted that those who held that nature does not act for an end, tried to prove this by taking away the cases because of which nature especially seems to work for an end. And this is what most seems to show that nature works for an end, that out of the operation of nature a thing is always found such that it can be so much the better and more convenient, as the foot is made in this way by nature, so that it is fit for stepping; so that if it departs from its natural arrangement, it is not fit for this use; and it is similar in everything else. And because they wanted to argue against this especially, therefore he [Aristotle, citing objections?] says that it can be objected that nothing prevents nature from not acting for an end and always making what is better. For we find all the time that out of some work of nature some useful thing comes forth, which is still not the end of that natural operation, but happens to occur this way; as if we say that Jupiter rains [?]*, that is God or all of nature [?]*, it is not for this end, that it should make fruit grow, but the rain comes forth out of the necessity of matter. For it is necessary, when lower areas have been warmed by their closeness to the sun, for vapors to be released out of water; and these ascending because of their heat, when they have arrived at a place where heat is insufficient because of its distance from the place where the rays of the sun are rebounded, it is necessary that the water, ascending as a vapor, be congealed there, and once it has congealed, that the vapors be turned into water; and when the water has been formed, it is necessary that it fall downward because of its weight: and when this occurs, it so happens that fruit grows. But it is not for the sake of this, so that the fruits should grow, that it rains; because similarly in another place fruit is destroyed because of rain, as when it is gathered together in an area. But it is not for this purpose, that the fruits should be destroyed, that it rained, but this happened by accident, when the rain was falling; and in the same way it seems to occur by chance that the fruit grows accidentally, while the rain is falling. From which it seems that nothing prevents things from also being this way with the parts of animals, which seem to be so arranged for some end: namely that someone should say that out of the necessity of matter it so happens that some teeth, that is the front teeth, are sharp and fit for cutting food, and molars are broad and useful for grinding food. But it is not that nature made teeth in such or such a way for these uses: but that, when teeth had been so made by nature because of the necessity of matter running down [?] in this way, it happened that it followed such a form, and once such a form existed, such a use followed. And it can similarly be said of all other parts, which seem to have some definite form for some end.

(*I think this might be one of those cases where the ancient Greeks and Romans used the name of a god metonymically to stand for the thing that that god is a god of. So in Virgil, you often find lines where he says “Venus” but means “love.” Here, I’m guessing Aristotle is saying “Zeus” to mean “the sky,” or “all of nature” as Aquinas says, and since Aquinas is using a Latin translation (he didn’t know Greek), that’s rendered as “Jupiter.”)

And because someone could say that such uses follow always or for the most part; that is, always or frequently, it is fitting that this be by nature: therefore to preclude this objection, they say that from the beginning of the formation of the world, the four elements came together to the formation of natural things, and the many and varied arrangements of natural things were made: and whichever things happened to be fit for some use, as if they had been made for this, only those were preserved, because they had an arrangement fit for preservation, not from some agent intending that end, but from that which in itself is empty, that is by chance. On the other hand whatever did not have such an arrangement was destroyed, and is destroyed every day; as Empedocles said some people were formed in the beginning, who in one part were bulls, and in the other part were men.

 

Now, is it just me, or does this whole section, and particularly the underlined part (the underline is mine, by the way), sound exactly like evolution and natural selection?


After Aristotle devoted so much of this book to rebutting these philosophers, it looks like nothing has changed.

One More Thing: Boolean Conditionals

Uncle1

I don’t mean to beat a dead horse, but I just thought of another thing to say about Boolean logic. When I wrote my first post on Boolean logic, I just dismissed the idea that conditionals are true if the condition never comes true by saying, “I don’t see in what sense it’s true that if Mars is green, then I don’t need glasses.” But recently I actually thought of some reasoned counter-arguments that aren’t just appeals to common sense.

Under the Boolean interpretation, complex propositions are analyzed in terms of truth tables. In a truth table, the possible combinations of truth values (truth or falsity) of the simple propositions that make up the complex propositions are listed, along with the truth value of the resulting complex proposition in each case. The truth table for a conditional proposition looks like this:

p  |  q  |  If p, then q
T     T     T
T     F     F
F     T     T
F     F     T

So the statement “If I am 18 years old, then I am legally an adult” is true because the first proposition, “I am 18 years old,” is true, and the second, “I am legally an adult,” is as well. But the statement “If Kobe Bryant is with the LA Lakers, then Ronald Reagan was not a Republican” is false because the first proposition, “Kobe Bryant is with the LA Lakers,” is true while the second proposition, “Ronald Reagan was not a Republican,” is false. For convenience, the first proposition is called the antecedent, and the second is called the consequent.

So here’s my first problem with this interpretation of conditional statements. Suppose I said, “If I have eaten sushi, then I am Japanese.” It just so happens that I have never eaten sushi in my life, so the antecedent is false. Therefore, this conditional statement is true in the Boolean interpretation.

But then suppose I were to pay a visit to the sushi station in my college’s cafeteria and have some sushi for the first time in my life. Now the antecedent has become true. But obviously even if I were to eat sushi, I wouldn’t become Japanese, so the consequent would remain false. So now the antecedent is true and the consequent is false. If you look at the truth table, this means that the conditional as a whole is false.

Now, the thing is, if the conditional was true before I ate sushi and then became false after I ate sushi, then how was it true to begin with? The whole point of conditionals is to predict what will happen when the condition becomes true. A conditional that starts out true but then turns false when its antecedent is fulfilled is completely useless. If the conditional statement will turn false when its antecedent is fulfilled, then it should be false to begin with. If I say, “If it rains tomorrow, I will die,” and then it rains tomorrow but I don’t die, you wouldn’t say that the conditional started true and then turned false. You would just say that I was wrong to say in the first place that I would die if it rained. But this is not what the truth table analysis says.

Second, notice that in the sushi example we could tell, even though the antecedent hasn’t come true, that if it were to come true the conditional would be false. If humans really thought in terms of truth tables, then you’d expect that we wouldn’t be able to come to that conclusion. We should still think that “If I have eaten sushi, then I am Japanese” is a true statement, since the antecedent is still false.

This shows that humans do not in fact think of conditionals in terms of truth tables. So how do we think of them? I would contend that we think of them in terms of Aristotle’s four causes.

For example, take “If Socrates is a (healthy) man, then he can walk.” We know that this is true because part of what it means to be a (healthy) man is to be able to walk; simply by being a man Socrates has the potential to walk. In Aristotelian terms, Socrates’s being a man is the formal cause of his being able to walk.

The next cause in the list is the material cause… but I’m actually not entirely sure about this one. In the Physics, Aristotle defines the material cause as “that out of which something is made and which exists in [the thing even after it is actually made].” I think an illustration of material causality in a conditional would be something like, “If Socrates is a man, then Socrates is subject to gravity.” Here, the consequent doesn’t follow from Socrates’s being a man insofar as he is a man, but from Socrates’s being a man insofar as a man is something made up of particles that carry mass. Here, the consequent doesn’t follow from what Socrates is (viz. a man) so much as from what he is made of.

For antecedents that describe change, two causes come into play. Take “If a match is struck, it will catch fire,” for example. Here, the match’s being struck is the cause (in the colloquial modern English sense) of its catching fire. Thus the match’s being struck is what in Aristotelian terminology is called the efficient cause of its catching fire. But besides the efficient cause, the final cause also comes into play here. A lot of people think that the final cause just refers to the purpose of something. That is one meaning of final causes. But the more basic meaning is simply what a thing is directed toward, regardless of whether it’s directed consciously or not. In this case, catching fire is the final cause of striking a match. Whenever you strike a match, unless something else gets in the way, the result is always fire, never a duck, or music, or anything else. If the act of striking a match were not inherently such that it always produced that outcome all else being equal, then you’d expect that it might just as well produce fire as anything else. The fact that it does inherently produce fire is all Aristotle means by final causality. It’s because of this inherent ordering that we can confidently say that if I strike a match, it will catch fire; whereas when there’s no connection of final causality between one thing and another, we can’t say for sure whether the presence of the one entails that of the other.

Under this analysis, it’s easy to see why it’s false that if Mars is green, then I don’t need glasses. The antecedent here has no connection to the consequent at all. Here, since we aren’t talking about change, the causes in question are the formal and material causes. But the formal cause of my needing glasses is my eyeball being too long for its lens to focus light onto my retina, and the formal cause of that would be my eye’s stiffness which causes it to retain the shape it happened to take when I was growing up. The efficient cause of my eye taking this shape probably has something to do with genetics and/or my tendency to hold up handheld video games and books too close to my face. Mars being green has no causal connection, formal, material, efficient, or final, either to my needing glasses or to the length of my eyeball, since those are already sufficiently explained by other things. This, not anything to do with truth tables, is the reason we can tell easily that “if Mars is green, I don’t need glasses” is false.

Ok, now I think I’m done with Boolean logic.

Existential Import, Pt. 2

Okay, I finally got time to write the rest of my thoughts on the Boolean interpretation. If you haven’t already, you might want to see this post so you can understand what the heck I’m talking about; in particular, you’ll want to at least read up to “but there’s one problem with the Boolean interpretation: it uses two different senses of ‘true’ and ‘false,'” and then read the edit at the end. Speaking of which, if you’ve already seen the original post but haven’t seen the edit, you should probably take a look at that to make sense of this.

Boole’s entire system rests on the claim that logical propositions are primarily concerned with asserting or denying existence. This is the basis of his claim that A’s and E’s are not contrary and his claim that all statements about subjects that don’t exist are true.

But this presupposition is not sound, which is evident from the simple fact that logical propositions are syntactically different from existential statements. In English, existential statements begin with “there is/are.” Logical propositions do not begin with “there is/are.” Therefore, logical propositions are not existential statements. Nor would appeals to different languages help. In Ancient Greek and Latin, the languages in which logic was first extensively studied in the West, existential statements took the form of the 3rd person of “to be” (ἔστι or εἰσί in Greek, est or sunt in Latin) and the nominative form of the thing that is said to exist. But this is not the way logical propositions were phrased in Greek or Latin either. In those languages, logical propositions were phrased in sentences of the form “P belongs to S” (“P ὑπάρχει τῷ S” in Greek). Thus logical propositions have not historically been thought of as existential statements, nor would they be thought of in this way now if this interpretation were not imposed on them by modern logicians.

And then there’s the obvious fact that A statements are positive statements. Yes, “all unicorns have horns” does imply that there are no unicorns that have no horns. But it seems odd that that should be interpreted as the primary meaning of that statement, when anyone would tell you that it is a statement about what unicorns do have, not about what kinds of unicorns don’t exist.

This is not to say that logical propositions say nothing about existence, but they do so only incidentally. Suppose, for example, that I told you that a triangle is a figure consisting of three lines joined together at the endpoints. Now, it just so happens that using that information, you can deduce that a triangle is also a figure whose interior angles add up to 180 degrees. But this doesn’t mean that I told you that a triangle is a figure whose interior angles add up to 180 degrees; or, if I did, I did so only incidentally, as a side effect of what I was really trying to tell you. Similarly, though “all unicorns have horns” also incidentally means that there are no unicorns that lack horns, that is not what it means per se. This is why the Boolean interpretation carries some plausibility; an A proposition does necessarily carry some incidental existential information. But this, as the Scholastics* would say, is a property, not its essence; it follows from what the statement is, but it does not define the statement.

(*Have I ever talked about the Scholastics? In case I haven’t, they were the proponents of the medieval tradition of thought derived from Aristotle.)

So if logical propositions are not existential statements, the question of what kind of statements they really are remains to be answered. I would argue that logical propositions are statements about the natures of things, in other words what it means to be a given thing. This seems to be supported by the fact that anyone would interpret a statement in the form “S is P” or “S does P” as a statement about the subject, and specifically about what kind of thing the subject is, not about what actually exists or does not. So, an A proposition states that the nature of a thing necessarily entails that it have some attribute, an I proposition states that the nature of a thing at least allows for it to have some attribute, an E proposition states that the nature of a thing absolutely excludes its having some attribute, and an O proposition states that the nature of a thing at least allows that it should sometimes lack some attribute. From this, all the relationships on the Square of Opposition can easily be seen to follow. Corresponding A and E propositions are contrary because the nature of a thing cannot both include and exclude an attribute. An I proposition is the subaltern of its corresponding A because if the nature of something necessarily includes an attribute, then of course it must have that attribute all the time, let alone some of the time. Corresponding A and O propositions are contradictory because stating that the nature of something always includes some attribute necessarily denies that its nature ever allows for it to lack that attribute, and conversely, saying that a thing’s nature allows for it to lack an attribute necessarily denies that it must always have that attribute. An O proposition is the subaltern of its corresponding E because saying that the nature of something absolutely excludes some property entails that it must lack that attribute all the time, let alone some of the time. E and I statements are contradictory because stating that the nature of something never allows it to have some attribute necessarily entails a denial that its nature allows for it to have that attribute even some of the time. I and O propositions are subcontraries because if a thing’s nature does not allow for it to have some attribute even some of the time, then it must always lack that attribute, which by subalternation means that it must lack that attribute at least some of the time. And lastly, by the same token, if a thing’s nature does not allow for it to lack some attribute even some of the time, then it must always have that attribute, which by subalternation means that it must have that attribute at least some of the time.

One other problem with the Boolean interpretation: If all universal statements about things that don’t exist are true, what do we do about statements like “all unicorns exist”? I asked my logic teacher about this, and he said that supporters of the Boolean interpretation solve this problem by saying that existence is not a predicate. Now, I assume that if asserting existence of something is not a predication, then it would have to be classified as an existential statement. But if we’re going to oppose predicates and existential statements, and argue that “all unicorns have horns” is a valid statement while “all unicorns exist” is not because the former is a predicate as opposed to an existential statement while the latter is an existential statement as opposed to a predicate, then Boolean logic falls apart because, as was said earlier, Boolean logic depends on the presupposition that all logical propositions are kinds of existential statements. If “all unicorns have horns” is not denying the existence of a certain type of unicorn but predicating a certain attribute of unicorns, then A and E propositions become contrary again because we can’t both predicate an attribute of something and deny it. Taking this route is trying to have the cake and eat it too.

Contrast this with the way this problem can be dealt with if we go with the traditional interpretation. In the traditional interpretation, a statement like “all unicorns exist” would be stating that the nature of unicorns necessarily entails existence. Because we do not hold that A statements are essentially negative existential statements, this does not lead us to a contradiction. Now, as it turns out, the only thing that exists by nature is Pure Act unmixed with any potency, a.k.a. God, so the statement “all unicorns exist” couldn’t possibly be true. (I’ll probably talk more about that in a later post, after I finally get around to talking about Aristotelian metaphysics.) But we are not forced to deny the validity of the statement a priori; we are still allowed to at least ask the question of whether “all unicorns exist” is a true statement.

Lastly, one other thought on why the Boolean interpretation might seem to carry some plausibility. I can think of four different meanings of the present tense in English. One of them, which doesn’t really come into play in logic, is to indicate an imminent action: “Hand over the money, or the kid gets it!” Other times, the present tense signifies an action that a person does habitually; for example, “I eat pizza every Tuesday.” For some verbs that indicate a kind of state rather than an action, it indicates that that state is presently occurring: “I know that you killed Jethro,” or “I have a toothache.” And sometimes, the present tense indicates a truth that always holds regardless of time; “Triangles have three sides” and “Nice guys finish last,” for example, are not statements about any particular time, but statements that apply to all times. The Ancient Greek and Latin present tenses also carried all these meanings except for the one about imminent action. In addition, they also included what English expresses as the present progressive. Now, I think this is one of the reasons Boole came to such a different conclusion from Aristotle and the Scholastics: the latter interpreted the present tense in the timeless sense, while Boole interpreted it in the presently-occurring-state sense. So, I think that Aristotle would have interpreted “All dogs are living things” as “Dogs are always living things,” whereas Boole seems to interpret it as “Currently, all dogs are living things.” The former interpretation necessarily implies that we are talking about natures rather than about any particular instances of the thing in question, because the only sense in which a thing exists timelessly is in that its nature or form exists timelessly (not as a separate thing (substance in Aristotelian terms), but as an idea conceived of by some mind). The latter interpretation, on the other hand, makes more sense if we are talking about particular, existing things rather than about natures. After all, natures themselves do not exist as particular, changeable things that might have an attribute at one time but not another. So it seems to me that Boole arrived at the conclusions he did at least partly because of how he interpreted the present tense.

Ok, I’m pretty sure that’s all I have to say on this subject. Now I can finally move on to other topics without feeling bad.