Saturday, October 18, 2014

The 'How Does it Work?' Objection to Dualism: #1 Different Substances

"How can the mind move the body?" This is one of the most familiar rhetorical questions for dualists about the mind. It is rhetorical since it is meant to make the point that dualists can't explain how the mind moves the body, and that this is a problem for dualism.

One problem is that this question is highly ambiguous. This is reflected in the literature by the fact that the phrase 'interaction problem' is used by different philosophers to refer to quite different arguments. When someone poses this question there are multiple objections someone could have in mind. Someone could be saying it's in principle impossible for dualists to provide an explanation. Or they could simply be saying there is no plausible candidate for an explanation. Or they could be saying it's very likely that non-physical causation never happens in our world. Moreover, they could pose these arguments for different reasons. So it's important to get clear on which objection we're talking about. I'll try to distinguish a few ways we can formulate this objection and then reply to these objections. In the first post I'll identify and respond to what I call the 'Different Substances Objection'.

#1: The Different Substances Objection

First, one might object that, since mind and matter on a dualist view are completely separate there is no way for them to interact. Everything is mental or material, but not both. So there could not be interaction between the two. The problem is that it's not generally true that entities from two mutually exclusive categories cannot interact causally. Everything is either a proton or a non-proton for instance, but that doesn't mean protons and non-protons cannot interact.

Another very similar form of this objection is that mind and matter are different types of substances, so the two cannot interact. Or a more particular version of this objection would say that the mind is non-extended and the body is extended, so the two cannot interact. One problem is that, in general, it is false that in order for substance x to interact with substance y of kind F, x must itself be of kind F. You don't need to be a human to interact with a human; you don't need to be a proton to interact with a proton; etc.

A final and more sophisticated way to formulate this version of the objection is that since mind and matter share no intrinsic properties, the two cannot interact. First of all, the main premise of this argument is not true. Being a substance is common to both our minds and our brains. Having causal powers is intrinsic to both (note: one need not presuppose causation between mind and body occurs to hold this is true, since one should at least admit mental to mental causation). They both have the property of having metaphysical components. Of course, they don't share any intrinsic physical properties (since the mind does not have physical properties). But at least some of what I have listed are plausibly intrinsic properties.

More importantly though, why do two substances have to have common intrinsic properties to causally interact? This principle would have to be motivated by some more general theory where two substances' having common intrinsic properties P1, ... , Pn plays a relevant role in their ability to engage in causal interaction. In particular, to be relevant, if x causes change C in y in some way, then these P1, ... , Pn must contribute some causal influence to C. I'm not sure how else one would motivate the main premise here.

But we can imagine situations where the common intrinsic properties of agents plays no relevant role in the interaction of the two. For instance, even though a Jedi and a table share the intrinsic properties of having mass or volume or other physical properties, when the Jedi uses the Force he doesn't in any way seem to take advantage of his having mass or volume or his other physical properties. Of course, this is just an imaginary situation, but it seems perfectly coherent and thus there can be no a priori reason for thinking common intrinsic properties must play a relevant role in all causal interaction (of course, this isn't to deny that sometimes they do).

In fact, there might be some cases which are actual counterexamples. For instance, consider the EPR paradox cases from quantum mechanics. Suppose you have a source emitting an electron-positron pair in a state of quantum entanglement, where the spin of each is anti-correlated with the other. In other words, if electron e has upward spin then p has downward spin, and if e has downward spin then p has upward spin. Suppose moreover you have two observers A and B in different locations who can measure the spin of the particles along some axis Z, and e is sent to A while p is sent to B. If A measures e as having an upward spin then B will measure p as having a downward spin with 100% probability. On the other hand, if A measures e as having downward spin, B will measure p as having upward spin with 100% probability. Since experimentation and Bell's Theorem rule out local causal explanation here, and supposing there is causal interaction between e and p, there must be some causation here where local intrinsic properties such as mass, volume, velocity, etc. do not play a role in the causal interaction.

Of course, the particles do share the intrinsic properties of having spin. But it's not e's simply having spin which contributes causal influence to p's particular spin; rather, it is e's having an upward or downward spin which does so. For what the spin of p is depends on the actual spin of e. So it isn't clear that we can identify some common intrinsic property of e and p where's e's having this property causally influences p's having a particular spin.

This seems to me to be an adequate reply to the different substances objection. In the next post I'll talk about what I call the 'No Mechanism Objection', which poses the problem that there seems to be no familiar model which could make causal interaction between the mind and the body intelligible.

Monday, September 29, 2014

An Issue With Metaphysical Reduction

Take a fact F. In general, what does it mean to say that fact F metaphysically reduces to fact F'? Note I am speaking of metaphysical reduction as opposed to conceptual reduction. First of all, the latter has to do with concepts and propositions rather than facts. For example, when we say that being a bachelor just means being an unmarried male, or when we say the proposition that Alfredo is a grandfather just means that Alfredo is the father of a parent, these count as examples of conceptual reduction. These explications of meanings are just the result of fully specifying the nature of our concepts as they stand. These are very simple examples, but the more complex instances of conceptual reduction in philosophy follow the same general idea as these ones.

Metaphysical reduction on the other hand has to do with facts in the world and how they stand in relation to each other. I take it that the following necessary condition imposes a restriction on the relation of metaphysical reduction:

  • (R) If fact F metaphysically reduces to fact F' then (i) fact F holds in virtue of fact F' holding and (ii) the holding of fact F is nothing over and above the holding of fact F'.

As an example, physicalists often say that all mental facts are reducible to physical facts. I take it that this at least means that the mental facts hold in virtue of the physical facts and that they are nothing over and above the physical facts.

Now, (i) and (ii) seem to me to be in tension with each other. In fact, on the most straightforward reading of (ii) their simultaneously holding leads to a contradiction. Hence, we must find some other way to explain (ii), since it does not seem like a primitive relation. This is rather difficult. Let me explain.

By (i), reducibility must be an asymmetrical relation. This means that if F reduces to F' then F' does not reduce to F. For suppose F reduces to F'. Then F holds in virtue of F'. But the 'holding in virtue of' relation is asymmetrical, since otherwise there would be circular chains of ontological dependence. So if F holds in virtue of F', then F' does not hold in virtue of F, and thus by (R), F' is not reducible to F.

The problem is that the most straightforward reading of (ii) is that the holding of fact F is identical with the holding of fact F'. After all, suppose F and F' are not identical and we are dealing with a world of just F and F' (here I'm abbreviating, and I should really be saying the holding of F and the holding of F'). Then there is a perfectly clear sense in which F is something over and above F', viz. there are more things in the world than F! For if F =/= F', then for some x, x =/= F'. So there is something out there in the world which is extra-mentally distinct from F'. That seems to be a legitimate sense in which F is something over and above F'. So if F is not something over and above F' then F = F'.

But of course, if that were the case, then the 'in virtue of' relation here would not be asymmetrical, since if F = F' and F holds in virtue of the holding of F', then by substitution of equals F' holds in virtue of the holding of F. So reducibility would not, in fact, be asymmetrical. And that is a contradiction, since we earlier established it was.

One option is to say that the 'in virtue of' relation is not asymmetrical. But that seems deeply problematic insofar as it doesn't allow us to capture the reducibility we want to pick out. After all, every materialist will accept that all mental facts reduce to physical facts, but no materialist would ever dare say the physical facts reduce to the mental facts! (Personally I find the latter suggestion more plausible than the former, but regardless it is not something the materialist would ever claim.)

Instead, we have to find a sense in which one could say fact F is nothing over and above F' even though F is not identical to F'. And I'm not sure how to explain this. No idea if this works or not, or whether it is at all helpful, but here's a thought: Let us denote by 'a full truthmaker of P' a truthmaker of P which is not a constituent or part of some other truthmaker of P. Let Q be the proposition expressing the holding of F. Maybe we can say F is nothing over and above F' if the set of all full truthmakers of the proposition Q contains only F'. That would make (i) superfluous it seems. Or at least from pretty uncontentious premises (i) would follow as a consequence. This theory is a little weird though, since the question arises as to what, metaphysically speaking, explains why Q would be distinct from the proposition expressing the holding of F'.

With that said, I don't know if that's on the right track. And even if it gets the extension of the relation right it might not even produce a deeper understanding. The point being, I don't myself know how to explain (ii). Like I said though, it doesn't seem like this is a primitive or undefinable relation. I wonder then what we can say about it.

Monday, September 1, 2014

What God Knew and Abraham Didn't

The traditional story of Abraham and Isaac is one of the most perplexing parts of the Bible, at least for philosophers. There seems to be some sort of implicit contradiction in the idea of God commanding someone to sacrifice a human being, especially an innocent boy. Moreover, it seems like if one were commanded to do this one should not do it. Before thinking about this more we should review the story very quickly.

In the recounting of the story in Genesis 22, God wishes to test Abraham and see whether he "fears God." To this effect, God commands Abraham to go and sacrifice his only son, Isaac. On the third day of their journey Abraham takes Isaac up to a mountain to sacrifice him. Before going up, Abraham tells his servants with him, "We shall worship and come back to you." (Genesis 22:5) Abraham then binds Isaac and prepares to sacrifice him. When Abraham grabs his knife to kill Isaac an angel sent from God stops him by telling him not to kill the boy. God speaks through the angel and says that he now knows that Abraham fears him, and because of his actions God will shower blessings upon Abraham and his descendants.

Sometimes opponents of Christianity will say that this verse proves an inconsistency in the Christian conception of God. On the one hand, God is supposed to be a perfect being, and a perfect being, it seems, would never command something intrinsically evil such as sacrificing an innocent person to him. On the other hand, the Bible says he does. Let's give a precise argument which captures the force of this more vaguely formulated one.

  • (1) Suppose God commands Abraham to sacrifice another innocent human being to him. [assumption]
  • (2) God commands someone to do an action A only if it is morally licit to do A. [premise]
  • (3) So it is morally licit to sacrifice another innocent human being to God. [by 1 and 2]
  • (4) But it is not morally licit to sacrifice another innocent human being to God. [premise]
  • (5) So God did not command Abraham to sacrifice another innocent human being to him. [by 1 through 4]
But the conclusion of the argument contradicts Christianity, first of all and primarily because it asserts that something which the Christian Scriptures say happened actually didn't happen. But I'd argue that even if one didn't think we had to take the story literally, the story of the sacrifice of Abraham and Isaac is in another sense central to Christian teaching, and the conclusion would still disprove Christianity.

Throughout the New Testament the story is frequently cited with approval as a prefigurement of what God would do with Christ. Moreover, Abraham and the way he acted here is constantly given as a paradigmatic instance of true faith and fear of God. (For verses, see e.g. Acts 3:25; Romans 4:1; Romans 8:32; Hebrews 11:17) So, if one could show that the story couldn't have happened (in both the metaphysical and the deontic sense) then the New Testament is theologically mistaken, both in comparing the central mystery of Christ's sacrifice to Abraham's, and in upholding Abraham as an example of faith.

It's important then for Christians to diffuse the argument above. I want to respond to the charges in a way that is somewhat less common. Some people try to criticize premise (4) and say that actually since God commanded a sacrifice of an innocent human being it was morally licit to do so. Instead, leaving (4) aside, I want to criticize premise (2). Premise (2) seems true though. God, a perfect being, could not command something evil, could he? Despite appearances, I think that premise (2) is false. However, the exceptions to (2) are far and few between. One could even argue that the exceptions are precisely those cases which are like the Abraham and Isaac case. 

Suppose that, as (4) says, it is not morally licit to sacrifice another innocent human being. However, suppose Abraham doesn't know this. One might wonder how Abraham could fail to realize this unless he was morally obtuse, and we know that Abraham was a pretty decent guy. However, one might begin to at least doubt one's own moral intuitions if one were appeared to by God in all his glory and commanded to do something one previously thought was wrong. It's quite easy for us to say that (4) is true when we don't have the Almighty before us saying otherwise, but one should at least be somewhat sympathetic if Abraham doubts it, given his circumstances.

So, this gets to why I think (2) is false. Suppose God knows that if he were to tell Abraham to sacrifice Isaac then Abraham would doubt (4). (Note: One need not appeal to Molinism here, since this counterfactual about doubting could be true regardless as to what Abraham would freely do in the situation.) Then, I contend, God could command a morally illicit action to test Abraham's faith, so long as God does not intend for it to actually come about in the end. By doing so, God does not engender any evil volitional attitudes in Abraham, since Abraham could be unsure about the truth of (4), at least when commanded otherwise by God, and Abraham could then take God's omniscience and moral authority as sufficient justification for trusting that whatever he does must be morally OK.

In other words, Abraham could (without fault) begin to doubt the truth of (4), because of his very concrete and vivid experience where the almighty God commanded him to do something contrary to it. Then, since he knows the all-knowing and perfectly good God commanded it, Abraham can (without fault) place his trust in God that he is not doing something wrong and intend to bring it about. 

Of course, throughout all this, God knows that if Abraham were to actually bring about the slaughter of his innocent son, then Abraham would have done something which is not morally licit. And so God doesn't actually intend for Abraham to do it. But Abraham doesn't know this. Since Abraham doesn't know this, Abraham is in a state where God can truly test him, not only to see whether Abraham is willing to give up everything he has for him including his only son, but also whether Abraham trusts in God's goodness and moral authority. Since God is doing this only to test Abraham's faith, and does not actually intend to bring about any evil whatsoever, nor does he make Abraham do anything evil, it is not contrary to God's goodness to command an evil action in these circumstances. 

So, in sum, (2) is false, because God can command a morally illicit action if (i) God does not intend to actually let it be brought about, (ii) the people he commands do not know that it is morally illicit and (iii) God wants to test their faith and obedience to him in some way. And these conditions are satisfied in the case of Abraham and Isaac.

Sunday, August 31, 2014

The Universe is Contingent (And Therefore Needs an Explanation)

One common fallacy is the fallacy of composition, where one argues from the fact that each part of a thing has a certain feature to the conclusion that the whole thing has that feature. For instance, one could argue that every brick of the house is cube-shaped, therefore the house is cube-shaped. Or one could argue that each part of one's brain is unconscious, therefore the whole brain is unconscious. These inferences are fallacious.

However, I think it is worth noting that not all inferences from properties of parts to properties of the whole are invalid. If each part of a wall is made entirely of stone, then the whole wall is made entirely of stone. Similarly, if each part of the ball is entirely red, then the whole ball is entirely red. And so on.

Contingency seems to be like this, at least in this case. So here's an argument that the universe must be contingent:

(1) Each part of the universe is essential to the universe; in other words, *this* particular universe we live in would not be the same universe without all its parts.
(2) If each part of the universe is essential to the universe, and some part of the universe is contingent, then the whole universe is contingent.
(3) Some part of the universe is contingent.
(4) So the whole universe is contingent.

And then of course we can run the cosmological argument:

(5) Whatever is contingent requires an explanation for its existence.
(6) So the universe requires an explanation for its existence. (by 4 and 5)

It might not be immediately obvious, but premise (2) can actually be proven by the definitions of the term 'essential' and 'contingent'. So the only real premises are (1) and (3).

Let me give a proof for (2):
(A) Suppose each part of the universe is essential to the universe.
(B) And suppose some part of the universe is contingent.
(C) By (B), it is possible for some part of the universe to not exist. [Definition of 'contingency']
(D) By (A), if some part of the universe does not exist then the universe does not exist. [Definition of 'essential']
(E) By (C) and (D), it is possible for the universe not to exist; so the universe is contingent.
(F) So, If each part of the universe is essential to the universe and some part of the universe is contingent, then the universe is contingent. [by (A) through (E)]

Premise (1) might be contentious. However, let's stipulate what we mean by 'universe'; once we define this term, we can take the conclusion of the argument to hold of whatever entity we define 'universe' as denoting. Now, I understand the universe to be the sum of all space, time, energy, and matter. Under this definition, premise (1) is true, since the universe is a mereological sum.

Though I decided to define 'universe' this way, presumably it is still a substantial conclusion that this entity must have an explanation for its existence. Depending on what version of the principle of sufficient reason you hold, (5) and (6) can be modified and made stronger or weaker, giving a stronger or weaker conclusion. I think that from (4) one can actually prove the existence of God.

Friday, August 29, 2014

Quantifier Variance and the Semantics of Quantifiers

In my previous post I explained the basic idea behind quantifier variance. Now I want to criticize it. In particular, I said I want to point out some problems with the quantifier variantist's simultaneously affirming the following two statements:

(i) the different quantifiers behave the same logically; and

(ii) the different quantifiers have different meanings.

Let's do a little basic semantics. Let's define the truth function τ[ψ]U,g relative to models U and g for the cases of quantified formulas ψ as follows. The following definitions are true for all models M, all variable assignments s, all variables x, and all formulas φ. If a formula is not assigned to T it is assigned to F:

τ : {<ψ,U,g>|ψ is a formula, U a model, g a var. assign.} → {T,F}
  • (τ-)τ[∀xφ]M,s = T ⇔ for all variable assignments s′, if for all variables v, s(v) ≠ s′(v) ⇒ v = x, then τ[φ]M,s′ = 
  • (τ-)τ[∃xφ]M,s = T ⇔ for some variable assignment s′, for all variables v, s(v) ≠ s′(v) ⇒ v = x, and τ[φ]M,s = 

The definition (τ-) could of course be derived from the definition (τ-and the following definition of existential quantification (or vice versa): 

  • (-ABV): τ[∃xφ]M,s = ⇔ τ[¬∀x¬φ]M,s = T

It is easier though for illustrative purposes to use the earlier definitions.

Of course, the definitions could be worded slightly differently, but the slight variations in wording don't make a difference to the argument I want to make. Besides, at the very least, one should admit that these definitions are at least extensionally correct; in other words, they get the truth right all of the time, and thus one could adopt these definitions and get all of the same logical and semantic results as the other variant definitions.

The reason these definitions of truth for quantified phrases are important is that they are the definitions which allow us to prove soundness and completeness. This is strong evidence in their favor. The point about soundness is particularly important. We want to be able to say that our inference rules for our quantifiers are valid, otherwise we would have to abandon these inference rules! With this in mind, and in conjunction with the quantifier variantist's affirmation of (i), he should want to endorse the semantics presented here as holding true for any quantifier, be it c or a.

But this opens a big question. Where is the quantifier variance taking place? The answer seems to be (in all its quantificational irony): Nowhere! If the semantics for c and a have literally the exact same wording then how could the quantified claims (such as (A)) of a compositionalist hold true in a given model while at the same time those of an anti-compositionalist do not? 

Notice that in the definiendum clauses in (τ-) and (τ-) there are meta-language quantifiers. They range over variable assignments and variables. If there is quantifier variance then it's going to have to hold with respect to these meta-language quantifiers. So, once again: Where does the quantifier variantist think the quantifier variance is taking place? 

Presumably there is no variance when quantifying over variables, or at least I would hope not! These quantifiers seem entirely univocal. But maybe there exists variance when quantifying over variable assignments? 

A host of thorny issues arise when we ask these questions. In my next post I'll investigate the issue more. In doing so I hope to make it even more clear what quantifier variance is saying, and also lay down some criticisms based on my own view of the nature of quantification and ontological debates.

Monday, August 25, 2014

Basics of Quantifier Variance

When I say that there are tables is it unambiguous what I'm saying? Quantifier variantists say no. Or at least they would say that in certain contexts it is not. In particular, the sentence is ambiguous when we are engaging in metaphysical debate about the existence of the table, as in the following case.

Consider the debate between what I will call compositionalism and anti-compositionalism. Compositionalism is the thesis that there are composite material objects, while anti-compositionalism is the thesis that there are not. Take the case of a world with just a table and its parts, and suppose we are considering a form of compositionalism which says there are tables. Assume further that there are exactly n atoms which, according to this form of compositionalism, are proper parts of the table. Note that we are using a philosophical definition of 'atom', according to which an atom is a material object which has no proper parts. Anti-compositionalism says there is no table; there are just the n atoms. 

In essence, compositionalism says (A) there are n+1 distinct things (viz. the n atoms, plus the table), while anti-compositionalism says (B) there are n things and there are no more than n things. Note that (A) and (B) can be adequately translated into a quantified language which only contains variables, quantifiers, sentential connectives, and the identity sign with the usual interpretation. For example, (A) would be translated as follows:

∃x1∃x2...∃xn((x1≠x∧ ... ∧ x1≠xn+1) ∧ (x2≠x3 ∧ ...  x2≠xn+1) ∧ ... ∧ (xn≠xn+1))

(B) could be done pretty easily too, but having a translation of (A) is enough to characterize the dispute between compositionalists and anti-compositionalists. Compositionalists assert (A) whereas anti-compositionalists deny it. So it seems that the two parties are disagreeing here, and thus only one view can be correct.

However, appearances are misleading, or at least so the quantifier variantist says. Quantifier variantists assert that, in the hands of a compositionalist, (A) will mean something different than in the hands of an anti-compositionalist. Thus, when an anti-compositionalist denies (A) and asserts not-(A) she is saying something different than if the compositionalist were to deny (A) and assert not-(A). Hence, the two parties are not actually disagreeing but merely talking past one another.

It was important to translate (A) as we did into our sparse quantified language. The translation makes it clear that, assuming identity, negation, and conjunction are not ambiguous, the only possible connective left for the two parties to disagree about in their interpretation is the existential quantifier. Hence the name 'quantifier variance'. According to the quantifier variantist the existential quantifier can mean something different depending on the context of assertion.

On the face of it this may seem like a trivial thesis. Of course we can interpret the symbol '' however we want. But quantifier variance is saying more than this. First off, for ease of discussion, I will refer to the existential quantifier plus the putative compositionalist interpretation by 'c'. I will refer to the existential quantifier plus the putative anti-compositionalist interpretation by 'a'. At the expense of some precision, I will talk as though these symbols are actually different quantifiers. Really though they just refer to the normal '' symbol along with the allegedly different meanings assigned to it.

With that said, quantifier variance isn't just a restatement of the triviality that '' can have multiple interpretations. It is also saying that 'c' and 'a' behave the same logically speaking insofar as they both have the same logical rules of use associated with them. These include rules like existential generalization and existential instantiation; these are legal inference patterns for both quantifiers. They also behave syntactically as quantifiers (and thus cannot be used as names, predicates, etc.).

Most importantly, quantifier variance claims that, under each quantifier, claims about the world are objectively true or false. Under 'c' the claim that there are n+1 things is true, while under 'a' the claim that there are n+1 things is false. This is not because the way the world is is somehow indeterminate or dependent on one's perspective or conceptual scheme. It's simply because both of these meanings are equally good at describing the way the world is while at the same time remaining different ways of doing so. The two quantifiers are saying different but equally true things. 

Quantifier variance says that this is what happens in metaphysical disputes between compositionalists and anti-compositionalists. Both sides are asserting true things about the world, it's just that their evaluative attitudes are not about the same proposition because of their respectively different quantifier meanings. 

In my next post I will try to elaborate on and criticize the thesis of quantifier variance on the basis of some semantic considerations. In particular, I will look at the tension which comes from the quantifier variantist's simultaneously affirming:

(i) the different quantifiers behave the same logically; and

(ii) the different quantifiers have different meanings.

Thursday, August 21, 2014

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.

Here P is taken to range over all and only intrinsic properties, i.e. properties which in some sense have to do only with the being in question, as it is "in itself". So it does not include so-called extrinsic properties, such as being smaller than Socrates or being Socrates's father. It does include properties such as weighing 50 grams, having an intellect, being round, etc.

As far as what being actually P means, this is in contrast with being potentially P. These phrases clearly modify predicates -- e.g. something can be actually hot or potentially hot -- but there probably isn't a precise definition to be given of them because they are such basic and fundamental concepts. It is better to look at indubitable examples to see what sort of feature of the world these terms pick out.

Suppose I am about to boil some water, but have not yet done so. I put the water in my pan and turn on the heat. At this point it is merely potentially boiling. Once the water reaches a certain temperature and bubbles start to appear the water is now actually boiling. Another example: Suppose I am asleep. I am not at that very moment conscious, though I am potentially conscious. When I wake up and start realizing what's going on around me, at that point I have become actually conscious. This is all clear enough.

As an aside, I think it is consistent with the duality of actuality and potentiality that some things be neither actually nor potentially P (though they cannot be both). Sherlock Holmes is neither potentially alive nor actually alive. Whatever else they are, non-existents are neither potentially nor actually anything. (We sometimes say that merely possible entities potentially exist, but I think this is just a roundabout way of saying they possibly exist.) I would also argue that the only things which are actually or potentially anything are present entities. Maybe this is all contentious and more work needs to be done here, but it seems right to me. Regardless, the important point is that we have some grasp on the distinction between something's having a feature potentially and something's having it actually.

Now let us test our definition. Let's see whether some of Aquinas's claims about God actually do follow from his being pure actuality. Consider the discussion on immutability:

"First, because it was shown above that there is some first being, whom we call God; and that this first being must be pure act, without the admixture of any potentiality, for the reason that, absolutely, potentiality is posterior to act. Now everything which is in any way changed, is in some way in potentiality. Hence it is evident that it is impossible for God to be in any way changeable." (ST Ia Q.9 a.1)

Aquinas's talk about potentiality being posterior to act is supposed to be justification for his claim that the 'first being' must be pure actuality. Let's assume simply for the sake of argument that this justification is right; then his first premise is that there exists a being (God) which is pure actuality. So, applying the definition I gave: for all P, if God is P then God is actually P. But, second premise: if something x changes, then for some P, x is potentially P. But this clearly would contradict the first premise. So we can indeed conclude that God does not change.

The problem is that Aquinas appears to make a further inference here, that it is impossible for God to change. But the argument can be amended. Suppose God is possibly changing with respect to some intrinsic property P. Then, since God is pure actuality, God actually exists and is possibly changing with respect to P. But, I would argue, if something actual can be changed with respect to P, then there exists something actual which has the potentiality to bring about such a change. But x has the potentiality to bring about a change in y with respect to P only if y is potentially P. So God is potentially P for some P, contradicting the thesis that God is pure actuality. Hence, God is not possibly changing with respect to any property P. So God cannot change.

Let us consider another case, where Aquinas argues God cannot be composed of matter:

"First, because matter is in potentiality. But we have shown that God is pure act, without any potentiality. Hence it is impossible that God should be composed of matter and form." (ST Ia Q.3 A.2)

This argument is simple. Using the definitions earlier, the first premise is that anything which is material or has matter is potentially P for some (intrinsic) P. God is not potentially P for any intrinsic P. So God is not material. Whether the premises work or not, the validity of the argument is clear under our interpretation.

My purpose in this post has not been to defend Aquinas's arguments. I merely hope to have made slightly more clear the meaning of claims involving potentiality and actuality. If the definitions I've given above help to make Aquinas's arguments seem more clearly sound, then this supports them as accurately representing what claims of potentiality and actuality are supposed to mean in the hands of medieval philosophers. And even if the soundness of these arguments remains contentious, on the above interpretation of potentiality and actuality I would argue it is at least easier to see why the arguments are formulated as they are.

There still remains a ton of work to be done on the logic and semantics of potentiality and actuality, and much to be done on the metaphysics of it. Nevertheless, taking the predicate modifier status of 'potentially' and 'actually' as basic and defining other phrases in terms of them seems to me to be a promising framework. Since the examples are so incontrovertible, these definitions provide powerful tools for rebutting the claims of those who feign incomprehension whenever arguments involving these terms are brought forward.