Modernizing (and Medievalizing) Analyticity

A project I've been hoping to do eventually is to re-work the concept-containment notion of analyticity. Something has always seemed to me intuitive about it, at least in the "Bachelors are unmarried" sorts of cases. (From the 19th century onward, for various reasons, the analytic truths seem to have become equated with the logical truths; this seems wrong to me.)

I'd also like to see whether the notion of analyticity comes up at all in medieval philosophy, and whether any of the tools of medieval philosophy could be of use for this project (or, what would be just as interesting, whether they would find the concept-containment notion of analyticity hopelessly confused).

There are several problems for the concept-containment approach, but a big one is this:

1. Forms of Analytic Judgments: Kant (sometimes) defined analyticity in terms of conceptual containment, roughly as: A judgment of the form 'A are B' is analytic iff the concept B is contained in the concept A.

The worry is that there are many judgments that do not seem to have this form, but where they seem to also be true in virtue of 'meaning' or 'concepts' (or something close). Some examples, taken from SEP:

(11) If Bob is married to Sue, then Sue is married to Bob.
(12) Anyone who's an ancestor of an ancestor of Bob is an ancestor of Bob.
(13) If x is bigger than y, and y is bigger than z, then x is bigger than z.
(14) If something is red, then it's colored.

Other examples, from Jerrold Katz:

(15) Mary walks with those with whom she herself walks.
(16) Mary walks with those with whom she herself strolls.
(17) Poor people have less money than rich people.
(18) Rich people have more money than poor people.

It's not totally clear how all of these examples can be analytic (assuming they all are) if we take analytic truth to mean that the predicate-concept is contained in the subject-concept.

I don't have a worked-out answer to this yet, but I suspect that some of the work in cognitive linguistics might be helpful. In fact, Katz' own work might be helpful here, though from what I understand Katz is a Platonist (rather than a "conceptualist") about meaning, and so it would have to be properly adapted.

In addition to these strategies, where medieval philosophy might be useful here is in seeing how we might, in fact, be able to reformulate all "basic" sentences and then parse them out so that they technically obey the constraint of "subject-copula-predicate" form.

As Terence Parsons points out, medieval scholastic Latin is unique in that it is a natural language and yet there is no distinction between a sentence's ordinary surface grammar and its logical form.

Now, if one had a close enough association between words and mental concepts, one might then be able to get a nice conceptualist-type semantics going. And it seems certain medieval thinkers did have precisely this sort of close association between mental concepts and meaning, viz., in the theory of "subordination" (I'm thinking of Buridan and Ockham right now).

This suggests that we could translate basic ordinary-language sentences into medieval subject-copula-predicate sentences, and the concept-containment idea could become more useful again.

I'm not sure it will be as simple as that or that this will solve everything, but I suspect it will make things easier.

There are some other issues for a conceptual containment theory of analyticity too:

2. Conceptual Containment: There are really at least two problems here: (a) a theory of concepts, and (b) a notion of containment. Can we give a plausible and clear theory of both? (And, what would be even better: Can we give a theory of both that is mathematizable and subject to rigor and computation once we are given a case?) And how neutral can we be here with respect to different theories of concepts and containment?

How can medieval philosophy help here? Medieval philosophy certainly contains much discussion of concepts, and that should certainly be useful.

As for the notion of containment, I can't help but think of Scotus' theory of "repugnance" and "non-repugnance" by which he assesses the modal status of basic propositions -- the kinds of propositions concept-containment seems to be after (see page 162, here). What's interesting is that Scotus seems to define repugnance as a relation holding between terms. That seems to make it a semantic relation rather than a conceptual relation for Scotus; moreover, the relation's holding is said to be grounded in "notae," which are in some sense objective features of the external world.

So this isn't exactly concept-containment analyticity; but still, in terms of its formal/logical properties, non-repugnance/repugnance behaves similarly to concept-containment/exclusion. (This seems to be an instance of a more "externalist," metaphysical picture of containment and exclusion relations; I get the sense that this sort of externalism is the norm in medieval philosophy, especially pre-Nominalism, though even after that as well.) Moreover, like repugnance-relations, concept-containment relations are supposed to ground the modal status of propositions, and moreover, they both seem to deal with the same sorts of propositions. So I can't help but think Scotus will be helpful here, even if he probably wouldn't have a view of analyticity like Kant's.

3. Rigor: How would a rigorous conceptual semantics go? Can we make it as formal, precise and mathematical as the non-conceptualist semantics have been? Some work has already been done on this sort of thing, but there's more to be said. Again, I wonder if the medieval logic might help us here, since Parsons and others have shown it to be entirely rigorous and fit for mathematical treatment. Medieval logic at its height was generally far more sophisticated than anything after it -- certainly more sophisticated than anything Kant did on logic -- and so I can only imagine it will make this project easier.

4. Externalism: Although the conceptual-containment approach seem plausible in certain cases, so does semantic externalism. Gillian Russell, a professor here at UNC, has done some brilliant work on updating analyticity to take these post-Kripkean insights into account. However, she tends toward the more externalist side of things, and I'd like to see whether we can salvage more of the connections between meaning, analyticity and concepts than she does, while still giving a reasonable account of the externalist insights (something I worry cognitive semantics a la Peter Gardenfors hasn't quite done -- see 4.1 here, for instance).

One thing I worry about in trying to find analyticity in medieval philosophy is that medieval philosophy seems to tend much more toward externalism about semantic content (though this is only a hunch I get -- I can't point to anything specific). But maybe I'm wrong and there is room for analyticity in medieval philosophy; and even if not, the project may still be worthwhile, since maybe we will find new reasons to either abandon or revise our conception of analyticity in interesting ways we've never thought of.

So I plan to do some research on medieval logic and semantics in the next few weeks, and maybe this will help my concept-containment project. Moreover, I think it is an interesting historical project in its own right to see whether something like analyticity can be found (or reformulated) in terms of medieval semantic categories.

Pure Actuality

Many scholastic theologians, most notably Aquinas, make the claim that God is "pure actuality." This is supposed to do a lot of philosophical and theological "work"; it is by showing that there exists a being which is pure actuality that Aquinas is able to deduce many of the divine attributes. However, it is not immediately clear what this even means if one is not familiar with the metaphysical context of medieval philosophy.

A charitable interpreter who has read some medieval philosophy may be able to see how scholastics use this claim and identify certain inferences from this claim as being valid and others not. But it'd be nice if we had a more precise characterization of what it means to say God is 'pure actuality', so that we can see if all that Aquinas says follows actually does follow from this claim. Moreover, once we have a precise characterization of what Aquinas is even asserting, we can begin to more clearly assess the plausibility of the claim itself and whether Aquinas has established it. I propose the following definition:

• x is pure actuality if and only if for all (intrinsic) P, if x is P then x is actually P.

For completeness and wider scope of application, I also propose the following definitions of a thing's being 'composed of' or 'having' actuality and potentiality:

• x is composed of potentiality if and only if for some (intrinsic) P, x is P and x is potentially P
• x is composed of actuality if and only if for some (intrinsic) P, x is P and x is actually P.

Suarez's Modal Distinction and the Eucharist

Sorry for the lack of posts and for being bad about approving comments. I've been very busy this quarter as I'm taking three math classes, and this consumes most of my time. Here is an explanation (albeit somewhat oversimplified) of Suarez's idea of the 'modal distinction'. Suarez is an excellent, extremely clear late medieval philosopher. I wish more of his works were in English and I hope he will be canonized some day. The reference for Suarez's theory of distinctions is his Metaphysical Disputation VII.

Suarez makes three types of metaphysical distinctions. There are two which most philosophers of his era admit to exist: the real distinction and the distinction of reason. A real distinction holds between A and B just in case A can exist without B and B can exist without A. A prime example of a real distinction is between two substances, like me and my chair. A distinction of reason on the other hand holds between A and B just in case A and B are really the same and thus mutually inseparable, yet we conceive A and B using distinct and incomplete concepts. So, one of the primary examples Suarez appeals to is the divine attributes. Given the theory of divine simplicity (the idea that God has no proper parts at all) it seems to follow that God's justice is really the same as God's mercy. They are both mutually inseparable in the sense that neither can exist without the other. However, we use different and necessarily incomplete concepts to think about each of them. This explains why it is not obviously true that God's mercy is identical to God's justice, even though both phrases and their corresponding concepts refer to the same being.

Aside from these two Suarez admits a third distinction, called a modal distinction. The motivation for this distinction comes in large part from problems about the relationship between an accident and its inherence in a substance. The problem is raised by Bl. John Duns Scotus, taking as his starting point the case of the Eucharist (though his argument doesn't really depend on this example in particular).  We know in the case of the Eucharist that the accidents of the bread such as the quantity remain even though the substance of the bread does not. Hence, the accidents no longer inhere in the substance. So suppose that the quantity of the bread were not really distinct from its relation of inhering in the substance of the bread. Then since the quantity of the bread exists after transubstantiation, so would its inhering in the substance of the bread. But clearly the quantity's inhering in the bread cannot exist unless it inheres in the bread! This is a contradiction, since in the case of the Eucharist the accidents no longer inhere in the bread. Hence, it seems to follow there is a real distinction between a quantity and its relation of inhering (similar arguments can be run for other relations of union or composition).

But this leads to problems of its own. Let I be the relation of inhering between an accident a and substance b. Suppose I is really distinct from a as Scotus's argument appears to show. Then since I is an accident of a (it's a feature of a connecting it to b), it follows there must be some relation I* between I and a in virtue of which I inheres in a. But then there must be some relation I** between I* and I in virtue of which I* inheres in I, and so on. This creates an infinite regress, which is problematic to say the least. So it seems whichever way we go we have an issue. If the relation of inhering is really distinct from the accident, we have an infinite regress. If it is not really distinct from the accident, we have a contradiction.

While nominalists like Ockham have their own solution to this quandary, Suarez is a metaphysical realist, and thus unlike the nominalists he thinks as a matter of semantic principle that there must correspond to the term 'inheres' some extramental being. It is with this concern in mind that Suarez develops his notion of a modal distinction. A modal distinction is a distinction which obtains between a being and its mode. Suarez is using the word 'being' here in a strong sense, to denote a real, particular individual, in scholastic terminology a 'res' (though this need not be a substance). A mode on the other hand is just a way in which a being or 'res' can exist. So Suarez wants to say that instead of letting an accident's inhering be a really distinct relation, we let it simply be a mode or way of being of the accident. Suarez considers this modal distinction to be a distinction intermediate between a real distinction and a distinction of reason, because the accident can exist separately from its mode (at least by the power of God), but the mode cannot exist separately from the accident. Since this is the only intermediate distinction Suarez admits, he takes A and B to be modally distinct just in case A can exist without B but B cannot exist without A, or vice versa (but not both).

Clearly then Scotus's problem was with his first argument; Scotus assumed that if the quantity of the bread and its inhering are not really distinct then it follows they are both mutually inseparable. Suarez on the other hand allows that it is possible for a being to be separable from its mode even though they are not really distinct; after all, a being's mode is not in itself a 'being' in the strong sense, so it is not some separate 'being', and thus it is not really distinct. With his modal distinction laid out Suarez has the tools to give a very nice solution to the problem of the Eucharist. The accidents of the bread and wine can continue to exist even without the substance because it is not part of their essence that they inhere in something; inhering is only one of their modes. While it is obviously not a natural occurrence that an accident exist without its mode of inhering, it is not metaphysically impossible, and thus God can bring it about by his power.

While Suarez's account seems secure there is one objection. Someone like St. Thomas Aquinas might object that the essence of an accident includes mention of the substance of which it is a part. However, at least in the case of the Eucharist, even Aquinas makes exceptions, and thus this account must obviously be modified. And Suarez can easily modify it by saying that accidents are beings whose definition include that it is metaphysically possible that they inhere in a subject. Substances by contrast are beings for which it is metaphysically impossible that they possess the mode of inhering. So it seems Suarez's modal distinction provides a coherent solution to all the puzzles set out above.

Thomistic vs. Molinist Predestination Part II

In my last post I explained that God does not cause1 our free actions, but only cause2's them; hence, there can be no conflict between God's efficaciously willing that one do an action and our doing it libertarianly freely. I'd argue that one's free actions being caused is only inconsistent if we are using 'caused' in the sense of cause1. This is how I understand physical determinism:

(PD) The past state of the world, together with the laws of nature are sufficient to render necessary one unique future.

Clearly then God doesn't determine my next action A in this sense in cause2ing it, since God could have just as well created everything with the laws of nature and the past state up to my current time and yet cause2ed me to do ~A. It's only the case that I must do A under the supposition that God wills I do A, but it's not absolutely speaking necessary that I do A, since God could have willed otherwise.  In other words, libertarian freedom is possible, since even given the laws of nature + the past state of the world I could have done otherwise if God had so willed.

But maybe God's cause2ing me determines me in some morally relevant sense (where a form of determinism is morally relevant just in case if it were true it would preclude moral responsibility and freedom) since his causing is 'logically prior' to my acting. So we can generalize determinism from physical determinism to 'logical determinism' as follows:

(LD) An event E is logically determined by some state S just in case (a) necessarily the proposition expressing E (i.e. the proposition that E is the case) is true if the proposition p expressing S is true and (b) p is true.

Since necessarily if God wills that I do A then I do A, and God wills I do A, by this definition I'm logically determined to do A. So if this is a genuine morally relevant form of determinism, then God's cause2ing determines our actions and removes freedom. The problem with LD however is that it's not clear that it is a morally relevant form of determinism. After all, necessarily, if I do A then God wills I do A, and I in fact do A, but I don't determine God in any relevant sense to will that I do A. But if LD was a morally relevant form of determinism then I would.

I would simply hold to this: necessarily, God wills I do A if and only f I do A. This is true, but this is only meant to secure the efficacy and dependence of everything else for its existence on God's will.  This is similar to supervenience relations, and just like supervenience relations it only implies a necessary covariance; it does not necessarily imply any causal priority either of God's willing or my acting. To come back to the original point, we are working on different "causal plains" so to speak; I cause only in the sense of cause1, and God causes only in the sense of cause2. There is no causal priority of either of God's willing or my acting to the other.

Hence, I'm not sure this form of determinism, viz. logical "determinism", is a genuine form of determinism. I mean we can call it determinism (nomina significat ad placitum) but the question is whether it is a morally relevant kind, i.e. one which removes free will and moral responsibility. In the next and final post I'll come to the point about whether Aquinas's picture of predestination works.

Thomistic vs. Molinist Predestination Part I

This post comes out of a very large and high-quality discussion on predestination on Facebook. If you don't have Facebook you should really get it, if only because (among other things) we have a thriving Thomism group on there. I will be posting in three parts.

So, I'm kind of agnostic between Thomistic and Molinist views of predestination at the moment (though sympathetic to the Thomistic view). I'm worried about the Thomistic view since if God's will is efficacious then he should be able to bring about the salvation of all, and so the only explanation for why not all are saved is that God does not will it, which is contrary to Scripture. Aquinas replies by distinguishing between God's consequent and antecedent will. So God in general ('antecedently') wills that all men be saved, but taking all things into consideration ('consequently') wills that only some are saved; just as a judge wills that all men should live but taking into consideration particular cases wills that some should die. However, the difference between the two cases is that God's will can never be thwarted or perverted.

The problem with the Molinist view in my book is that I don't think it fits well with God's providence/omnipotence. The Molinist will reply that there's no problem, since it's not contrary to God's omnipotence if God can't bring about something that's impossible, and God's causing someone to freely choose him is impossible, since a free action can't be determined. But here I see no reason why God cannot bring about either of two contraries of a person's choice (i.e. either action A or not-A) and the action still be free--for God and creatures are working on different causal plains so to speak; God creates 'ex nihilo' by giving the whole of existence to particular states of affairs, whereas creatures cause in the sense of interacting with each other. It is only causing in the latter sense of interacting with by coercing or forcing that is incompatible with free will, and this is not the sense in which God is a cause.

To elaborate on the Thomistic point about how God can cause free actions we must distinguish different senses of the word 'cause.' First there is the sense of 'cause' in terms of interacting. Let's call this 'cause1'. So, for instance, this is what it means when I push you and 'cause' you to fall down, or when neurons cause arms to move, or if Cartesianism is true what happens when the soul causes the body to move. God does not cause in this sense; God does not cause1.

There is another sense of cause which means to create ex nihilo at evey moment, to 'sustain' or give being to things (although I have some reservations about the word 'sustain' since I think it can be misleading, since God isn't in time). We can call this cause2. God causes in this sense by being the cause of all being other than himself. He gives existence or 'esse' to everything. This is a very central doctrine to Thomism. God is the only person who causes in this sense; God is the only person who can cause2. God can cause2 anything that is possible. And on libertarian free will either of two contraries--i.e. either of action A or ~A--is possible, so God can cause2 either. Though I would agree he can't cause1 them, since that would entail determinism.

Now, maybe one can argue that even in the sense of cause2, this counts as a form of determinism which limits moral responsibility, and hence we should revert to the Molinist response. In Part II I'll respond to this point.

Classical Theism vs. Neo-Theism I: Divine Simplicity

In contemporary debates about the existence of God it is common to hear reference to 'the traditional divine attributes.' These include properties like omniscience, omnipotence, omnibenevolence, immateriality, eternality, and personality. It is supposed that if God exists he 'exemplifies all of these great-making properties'. This is the 'orthodox' conception of God in contemporary philosophy of religion and philosophical theology as heard from Craig, Plantinga, Swinburne, and most others.

Unfortunately, right from the get-go, there is a perfectly good sense in which this conception of God is unorthodox. According to the Fourth Lateran and First Vatican Councils of the Catholic Church, the doctrine that God is a perfectly simple being--one without any composition--is defined as infallible, binding dogma, denial of which amounts to heresy. Hence, the doctrine has some degree of pedigree in that it has been held by billions of Christians to be a very important doctrine. But even aside from this I would argue that the contemporary view--what I will call 'neo-theism'--is directly contrary to the truly 'classical theistic' view of God's nature. Classical theism has been the majority opinion for thousands of years. It is the view of the great pagan philosophers like Aristotle and Plotinus, the Christian Saints Athanasius, Augustine, Anselm, Bonaventure, Thomas Aquinas, and Bl. Duns Scotus, as well as other monotheistic thinkers like Maimonides, Averroes, and Avicenna. Such classical theists would deny that God is 'personal' or 'perfectly good' or 'eternal' in the sense that neo-theists take God to be. Distinctively classical theistic doctrines which are unpopular among the neo-theists of today include divine immutability, timelessness, and simplicity. I will focus on this last doctrine as an example of a fundamental difference between the two views, and argue that the classical theist view maintains God's perfection in a way which the neo-theist view does not.

The way that God's attributes are defined in contemporary philosophy of religion as above implicitly contradicts divine simplicity from the start. According to the contemporary view, when we predicate perfect moral goodness of God as in the sentence 'God is good', the referent of the term 'God's goodness' is the property of goodness. Likewise, if we say 'God is omniscient', the referent of the term 'God's omniscience' is the property of omniscience, and similarly for omnipotence, immateriality, and so on. However divine simplicity says that the referents of all intrinsic predications about God are identical, for to say otherwise would be to introduce metaphysical complexity into God. Hence, it is common to hear classical theists saying that God's goodness IS his omniscience, which IS his omnipotence, and so on. But it would seem to follow that omnipotence and goodness are the same property, which is clearly false; indeed, it would follow that God is himself a property!

Obviously the classical theist doesn't want to commit himself to such seemingly absurd claims, and it would be stupid to suppose 2,000 years of great thinkers were simply willing to accept a manifest falsehood. The more reasonable inference is that contemporary and classical thinkers are working with very different metaphysical presuppositions, and this is correct.

One neo-theist assumption is the Platonist, relational ontology within which Plantinga phrases the objection presented above. For Plantinga and other contemporary detractors reality consists of concrete individuals, platonic properties, and relations of exemplification. The platonic properties are abstract objects, which means they lack efficient causal power, while the causally efficacious concrete individuals exemplify these properties. Clearly God is an individual, since as creator of the universe he possesses causal power, in which case it follows he could not be an abstract object; hence he could not be identical to any of his properties, and thus divine simplicity is false. But certainly none of the classical presenters of simplicity accepted this ontological framework. Rather, following Aristotle, they would take a thing's features to be ontological constituents of a subject. This is the picture found in Aristotle's Categories for instance, where accidents such as color or size are said to be 'present in' a subject. Among contemporary philosophers D.M. Armstrong's theory of universals seems to be an example of a constituent ontology as well. Within such a framework it's not obviously incoherent to suppose that God is identical with his constituents so long as we can admit the idea of an improper constituent (analogous to an improper part or improper subset), since it doesn't follow from the very meaning of the term 'ontological constituent' that the constituent in question is a property; 'ontological constituent' is a category-neutral term, and doesn't necessarily imply Plantinga's relational ontology.

More generally though we can make sense of divine simplicity in terms of truthmakers. The neo-theist assumes that the referents of abstract singular terms like 'Alfredo's audacity', or in our case 'God's goodness', are platonic properties. This is what makes it impossible for God's to be identical with his goodness, for this to be identical to his omniscience, and so on. However, those who embrace divine simplicity can deny this account of predication. Rather, a classical theist will accept a truthmaker account, which says that if an intrinsic predication of the form 'a is F' is true, then a’s F-ness exists, where this entity is to be understood as the truthmaker for 'a is F.' So divine simplicity says God is identical with the truthmakers for each of his intrinsic predications. This makes sense because a truthmaker is an entity in the world in virtue of which a proposition is true. Clearly by this understanding truthmakers need not be properties (they can sometimes be). They can also be substances, as is the case with God--to deny this would at least have to be argued for and such a denial is on the face of it implausible. Hence, it is perfectly coherent to say God is his omniscience, which is his omnipotence, and so on. All this is saying is that God is identical to that in virtue of which he is omnipotent, that he is identical to that in virtue of which he is omniscient, and so on; and moreover, by the transitivity of identity, these things are each identical to each other. This picture shows that divine simplicity is not obviously contradictory and deserves much more than the charges of 'unintelligibility' and 'incoherence' ignorantly thrown at it today.

With these charges of absurdity put to one side we can see that divine simplicity is at least prima facie coherent. Certainly we will need to be given better arguments than Plantinga's cavalier dismissal of 2000 years of philosophy based on the presupposition of his own anachronistic ontology. But to argue something is logically coherent isn't to argue that it's true. In another post I will provide an argument to the effect that only a  simple God can truly be said to exist of himself and thus be perfect.