An Argument Against Newtonian ‘Absolute’ Time From the Identity of Indiscernibles

An interesting thought occurred to me recently while I was reading through the early pages of Bas C. van Fraassen’s An Introduction to the Philosophy of Time and Space. I would not be surprised if this thought is unoriginal (indeed, I might even be slightly surprised if Leibniz himself hadn’t already thought it), but, for what it’s worth, the idea did genuinely occur to me, so, for all I know, it might be original. In any case, I think it may be of some interest, so I’m going to try to briefly flesh it out.

In order to do so, I will have to set the stage by very briefly explaining some of the basics of an Aristotelian view of time (at least, insofar as they are pertinent), and juxtaposing that with a Newtonian view of time as absolute. I will come around, near the end, to a brief reflection on what this argument might tell us, if anything, about the philosophical status of the generic A-theory, or the generic B-theory.

Aristotle is well known for championing a view of time on which time is dependent upon motion. Granted, what Aristotle means by motion bears only mild resemblance to our modern (much more mechanistic) notion. Motion, for Aristotle, is analyzed in terms of potentiality and actuality (which are, for Aristotle, fundamental conceptual categories). Roughly speaking (perhaps very, very roughly speaking), for any property P and being B, (assuming that having property P is compatible with being a B), B either has P actually, or else B has P potentially. For B to have property P actually is just for it to be the case that B has the property P. For B to have property P potentially is just for it to be the case that B could (possibly) have, but does not (now) have, the property P. In other words, potentiality represents non-actualized possibilities. A bowling ball is potentially moving if it is at rest, just as it is potentially moving at 65 mph if it is actually moving at 80 mph. A phrase like ‘the reduction of a thing from potentiality to actuality,’ common coin for medieval metaphysicians, translates roughly to ‘causing a thing to have a property it did not have before.’ This account may be too superficial to make die-hard Aristotelians happy, but I maintain that it will suffice for my purposes here. Aristotle, then, wants to say that in the absence of any reduction from potentiality to actuality, time does not exist. Time, in other words, supervenes upon motion in this broad sense – what we might, in other contexts, simply call change. Without any change of any sort, without the shifting from one set of properties to another, without the reduction of anything from potentiality to actuality, time does not exist.

Newton is well known for postulating absolute time as a constant which depends, in no way, upon motion (either in the mechanical/corpuscularian sense, popular among empiricists of his time, or in the broader Aristotelian sense).[1] In this he was, there is little doubt, infected by the teachings of his mentor, Isaac Barrow, who overtly rejected the Aristotelian view;

“But does time not imply motion? Not at all, I reply, as far as its absolute, intrinsic nature is concerned; no more than rest; the quality of time depends on neither essentially; whether things run or stand still, whether we sleep or wake, time flows in its even tenor. Imagine all the stars to have remained fixed from their birth; nothing would have been lost to time; as long would that stillness have endured as has continued the flow of this motion.”[2]

Newton’s view of time was such that time was absolute in that its passage was entirely independent of motion. It is true, of course, that Newton fell short of thinking that time was absolute per se; indeed, he viewed time as well as space as being non absoluta per se,[3] but, rather, as emanations of the divine nature of God. However, since God was absolute per se, as well as necessary per se (i.e., because existing a se), time flowed equably irregardless of motion, just as space existed irregardless of bodies.

To illustrate the difference, imagine a world in which everything is moving along at its current pace (one imagines cars bustling along the streets of London, a school of whales swimming at 2500 meters below sealevel, planes reddying for landing in Brazil, light being trapped beyond the event horizon in the vicinity of a black hole in the recesses of space, etc.), and, suddenly, everything grinds to a halt. It is as though everything in the world has been paused – there are no moving bodies, the wind does not blow, there are no conscious experiences, light does not propagate, electromagnetic radiation has no effects. Does time pass? On the Newtonian view, it certainly does. This sudden and inexplicable quiescent state might persist for a short amount of time, or a very long time, or it may perdure infinitely. On the Aristotelian view, this is all nonsense; instead, we are simply imagining the world at a time. To imagine that this world persists in this state from one time to another is just to be conceptually confused about the nature of time; time doesn’t merely track change, its relationship to change is logically indissoluble. So, for Aristotle, time cannot flow independently of motion (i.e., of change), while, for Newton, time flows regardless of what, or whether, changes were wrought in the world.

Now, I want to try to construct an argument for thinking that this Newtonian view may be logically impossible. I will start with an appeal to no lesser an authority than Gottfried Leibniz, who was easily Newton’s intellectual superior. He famously championed a principle which has come to be called the identity of indiscernibles (though, McTaggart tried, unsuccessfully, to relabel it as the dissimilarity of the diverse).[4] As Leibniz puts it, “it is never true that two substances are entirely alike, differing only in being two rather than one.”[5] To put it in relatively updated language: “if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:

∀F(Fx ↔ Fy) → x=y.”[6]

The suggestion was that not only were identicals indiscernible (which is indubitable), but that absolutely indiscernible things must be identical. In other words, if there is not a single level of analysis on which two things can be differentiated, then the two things are really one and the same thing.

‘What is the difference,’ you might ask ‘between this ball here and that ostensibly identical ball over there?’ Well, for one thing, their locations in space (one is here, and the other is there – and this difference suffices to make them logically discernible), to say nothing of which of them is closer to me at this present time, or which one I thought about first when formulating my question (Cambridge properties suffice to make things discernible in the relevant sense). If two things do not differ with respect to their essential properties, they must (if they are genuinely distinct) differ at least in their relational properties, and if not in real relations, at least in some conceptual relations (or, what Aquinas would have called relations of reason).[7] This principle is a corollary, for Leibniz, of the principle of sufficient reason – for, the reason two indiscernible things must be identical is that, if they are truly indiscernible, then there is no sufficient reason for their being distinct. For any set of things you can think of, if they share all and only the very same properties (and, thus, are absolutely indiscernible), then they are identical – they are not a plurality of things at all, but merely all one and the same thing.

Assume that this principle is true (in a few moments, I will explore a powerful challenge to this, but spot me this assumption for the time being). Now, suppose there are two times t1 and t2, such that these two times are absolutely indiscernible. We can help ourselves here to the previous thought experiment of a world grinding to a halt; this perfectly still world is the world at t1, and it is the world at t2. No change of any kind differentiates t1 and t2. There is no discernible difference between them at all. But then, by the identity of indiscernibles, t1 and t2 are identical. To put it formally;

  1. For any two objects of predication x and y, and any property P: ∀P(Px ≡ Py) ⊃ x=y
  2. Times are objects of predication.
  3. Times t1 and t2 share all and only the same properties.
  4. Therefore t1 = t2.

This argument is so straightforward as to require little by way of clarification. I assume that times are objects of predication not to reify them, but simply to justify talking as though times have properties.

There are now two things to consider; first, what implications (if any) this argument’s soundness would have for the generic A-theory of time, and, second, whether this is a powerful argument. With respect to the first, obviously Newton’s view of time was what we would today call A-theoretical. On the A-theory, there is a mind-independent fact about time’s flow – there is a fact about what time it is right now, et cetera. Time, on the A-theory, may continue to flow regardless of the state of affairs in the world. On the B-theory of time, by contrast, there is nothing which can distinguish times apart from change (in particular, change in the dyadic B-relations of earlier-than, simultaneous-with, and later-than between at least two events). It seems confused to imagine a B-series where the total-event E1 (where ‘total-event’ signifies the sum total of all events in a possible world, at a time) is both one minute earlier than total-event E*, and where the total-event E1 is also (simultaneously?) a year earlier than the total-event E*. Indeed, to use any metric conventions to talk about the amount of time E* remained unchanging might be confused (even if one opts for a counterfactual account of how much time would have been calculated to pass had a clock been running, there is still a problem – clearly, had a clock been running, it would have registered absolutely no passage of time for the duration of E*). So, there is just no rational way of speaking about the duration of a total-event E* by giving it some conventional measurement in the terms of some preferred metric.[8] If the B-relations of earlier-than, simultaneous with, and later-than, are not in any way altered from one time to another, then the times under consideration are strictly B-theoretically indiscernible, and, thus, identical. On the A-theory, by contrast, one can provisionally imagine an exhaustively descriptive state of affairs being both past and present.[9] One can imagine its beginning receding into the past while it (i.e., this total-event E*) remains present. I am not sure that every version of the A-theory will countenance this possibility, but it seems right to say that only the A-theory will countenance this possibility.[10] If my argument is right, and the reasoning in this paragraph hasn’t gone wrong, then the A-theory is less likely to be true than it otherwise would have been (we don’t even need to apply a principle of indifference to the different versions of the A-theory, so long as we accept that the epistemic probability of each version of the A-theory is neither zero nor infinitesimal).

In any case, the salient feature of what I’ve presented as the Newtonian view is that time may pass independently of any change in the world at all. I’ve suggested that there is a problem for the Newtonian view (whether or not such a view can be married to the B-theory) in the form of a violation of the principle of the identity of indiscernibles. The Newtonian might, of course, argue that God’s conscious awareness continues regardless of a quiescent world, so that God himself could act as a sort of clock for such a motionless universe. He, at least, would know how long it had been since anything was moving, or changed. In this case, however, the Newtonian is effectively conceding ground to the peripatetic; at least God, then, has to be reduced from potentiality to actuality (this suggestion will, of course, be repugnant, both to Aristotelians as well as to Catholics, but die-hard Newtonians typically aren’t either anyway).

Regardless, this argument may not be as strong as I initially hoped. After all, together with the principle of sufficient reason, the identity of indiscernibles has been the subject of sustained and impressive criticisms. While these criticisms may not present insuperable difficulties for defenders of the principle, they cannot be lightly dismissed. For a fair conceptual counter-example, one might think, in particular, about a perfectly symmetrical world in which there are only two physically identical spheres, neither of which has a single property that the other fails to have. Consider the following passage from Max Black’s ingenious paper, The Identity of Indiscernibles;

“Isn’t it logically possible that the universe should have contained nothing but two exactly similar spheres? We might suppose that each was made of chemically pure iron, had a diameter of one mile, that they had the same temperature, colour, and so on, and that nothing else existed. Then every quality and relational characteristic of the one would also be a property of the other. Now. if what I am describing is logically possible, it is not impossible for two things to have all their properties in common. This seems to me to refute the Principle.”[11]

There are no obvious and attractive ways out of this predicament for the rationalist, as far as I can see. One might be able to say that they have distinct potentialities (i.e., that to scratch or mutilate one would not be to scratch or mutilate the other, so that each one has a distinct potentiality of being scratched or somehow bent into a mere spheroid), but it isn’t clear how useful such a response is. One might argue that each one is identical with itself, and different from its peer, but it isn’t clear that self-identity is a bona-fide property. One may, out of desperation, ask whether God, at least, would know (in such a possible world) which was which, but it may be insisted, in response, that this is a pseudo-question, and that, while they are not identical, God could only know that there were two of them (and, of course, everything else about them), but not which one was which.

In passing, I want to recommend that people read through Black’s paper, which is written in the form of a very accessible and entertaining dialogue between two philosophers (simply named ‘A’ and ‘B’ – yes, yes, philosophers are admittedly terrible at naming things). Here is a small portion which, I feel, is particularly pertinent;

“A. How will this do for an argument? If two things, a and b, are given, the first has the property of being identical with a. Now b cannot have this property, for else b would be a, and we should have only one thing, not two as assumed. Hence a has at least one property, which b does not have, that is to say the property of being identical with a.

B. This is a roundabout way of saying nothing, for ” a has the property of being identical with a “means no more than ” a is a When you begin to say ” a is . . . ” I am supposed to know what thing you are referring to as ‘ a ‘and I expect to be told something about that thing. But when you end the sentence with the words ” . . . is a ” I am left still waiting. The sentence ” a is a ” is a useless tautology.

A. Are you as scornful about difference as about identity ? For a also has, and b does not have, the property of being different from b. This is a second property that the one thing has but not the other.

B. All you are saying is that b is different from a. I think the form of words ” a is different from b ” does have the advantage over ” a is a ” that it might be used to give information. I might learn from hearing it used that ‘ a ‘ and ‘ b ‘ were applied to different things. But this is not what you want to say, since you are trying to use the names, not mention them. When I already know what ‘ a’ and ‘ b ‘ stand for, ” a is different from b ” tells me nothing. It, too, is a useless tautology.

A. I wouldn’t have expected you to treat ‘ tautology’ as a term of abuse. Tautology or not, the sentence has a philosophical use. It expresses the necessary truth that different things have at least one property not in common. Thus different things must be discernible; and hence, by contraposition, indiscernible things must be identical. Q.E.D


B. No, I object to the triviality of the conclusion. If you want to have an interesting principle to defend, you must interpret ” property” more narrowly – enough so, at any rate, for “identity ” and “difference ” not to count as properties.

A. Your notion of an interesting principle seems to be one which I shall have difficulty in establishing.”[12]

And on it goes – but I digress.

Now, if such a world (with two identical spheres) is logically possible, it looks as though the spheres in it are indiscernibles even if they aren’t identical. No fact about their essential properties, or relations, will distinguish them in any way (and this needn’t be a case of bilocation either, for we are supposed to be imagining two different objects that just happen to have all and only the same properties and relations). If that’s correct, then (I take it) the identity of indiscernibles is provably false.

So, my argument will only have, at best, as much persuasive force as does the identity of indiscernibles. It persuades me entirely of the incoherence of imagining a quiescent world perduring in that state, but I doubt whether the argument will be able to persuade anyone who rejects the identity of indiscernibles.

[1] Strictly speaking, I’m not entirely sure that Newton would have said that time can continue to flow independently of any change of any kind, but I do have that impression. Clearly, for Newton, time depends solely on God himself.  Below, I will consider one response a Newtonian could give which suggests that time flows precisely because God continues to change – however, to attribute this to Newton would be gratuitous and irresponsible. I am not a specialist with regards to Newton’s thinking, and I do not know enough about his theology to say whether, or to what extent, he would have been happy to concede that God changes.

[2] The Geometrical Lectures of Isaac Barrow, J.M. Child, Tr. (La Salle, III.: Open Court, 1916), pp. 35-37.

Reproduced in Bas C. van Fraassen An Introduction to the Philosophy of Time and Space, (New York: Columbia University Press, 1941) 22.

[3] William Lane Craig, Time and the Metaphysics of Relativity, Philosophical Studies Series Vol. 84. (Springer Science & Business Media, 2001), 114.

[4] See C.D. Broad, McTaggart’s Principle of the Dissimilarity of the Diverse, Proceedings of the Aristotelian Society, New Series Vol. 32 (1931-1932), pp. 41-52.

[5] G.W. Leibniz, Discourse on Metaphysics, Section 9;

[6] Peter Forrest, “The Identity of Indiscernibles,” in The Stanford Encyclopedia of Philosophy ed. Edward N. Zalta, (Winter 2016 Edition);

[7] See W. Matthews Grant “Must a cause be really related to its effect? The analogy between divine and libertarian agent causality,” in Religious Studies 43, no. 1 (2007): 1-23.

[8] I will not, here, explore the idea of non-metric duration.

[9] Interestingly, McTaggart would likely have begged to disagree. Indeed, one may be able to construct an argument along McTaggart’s lines for the impossibility of a world remaining totally quiescent over time by arguing that the A-properties of pastness and presentness were incompatible determinations.

[10] It is entirely possible, upon reflection, that I am dead wrong about this. Perhaps this is just my B-theoretic prejudice showing itself. Why, if the A-properties of Presentness and Pastness aren’t incompatible determinations of a total-event E*, think that the B-relations of being earlier-than and simultaneous-with are incompatible determinations of a total-event E*? I continue to persuade and dissuade myself that there’s a relevant difference, so I’m not settled on this matter.

[11] Max Black, “The identity of indiscernibles,” in Mind 61, no. 242 (1952): 156.

[12] Max Black, “The identity of indiscernibles,” in Mind 61, no. 242 (1952): 153-4,155.


On (Possibly) Being Unable To Avoid Speaking Falsely

I was thinking yesterday about Thomas Aquinas’ rather strict view on the duty to never lie, even, as he says, when we lie for the sake of a joke. He admits, of course, that lying in the cause of a joke (a jocose lie) is not a mortal sin, but he does insist that it is at least venially sinful.

Ergo mendacium iocosum et officiosum non sunt peccata mortalia.[1]

I thought to myself that Aquinas probably means jokes which only work if the audience accepts a falsehood asserted before the punchline. I am reminded here of a (probably apocryphal) anecdote about Dominican friars teasing Aquinas by saying “look, out the window – flying pigs!” in response to which he looked out the window, to their great amusement. He retorted to their laughter by saying that he would sooner believe that pigs could fly than that his Dominican brethren could lie. Clearly, in such a case, Aquinas would say that what these friars did was sinful (at least venially). However, I don’t think Aquinas would offer the same analysis of sarcastic jokes, where what one says is actually the opposite of what one affirms by saying it. In sarcasm, one expresses a truth P by expressing a token-sentence K which, under normal circumstances, affirms not-P, but which, when used sarcastically, is understood by everyone to affirm P. To utter K sarcastically is to affirm P, and everyone knows this. This got me thinking about a strange situation.

Suppose one is in a court of law and must answer any question with a simple affirmative or negative. Suppose, then, that for some question, the token statement which is an affirmative is true in one language game, and false in another language game, and the token statement which is the negation is true in one language game and false in another. Call these tokens Y and N, and let us suppose that half the audience is playing the first language game, and the other half is playing the other. If one answers Y, then half the audience will believe something true, while the other half of the audience will believe something false, because they are unconsciously playing two different language games. If one answers N, the same situation results. Suppose you are fully aware that Y will communicate a falsehood to some, and that N will communicate a falsehood to others. Suppose, further, it isn’t possible to elaborate on Y or N (you can tell any story you like here – maybe you speak a totally different language, and you have a designated translator in court who is committed to translating whatever you say into simply Y or N – or any other scenario you like, so long as you aren’t able to avoid affirming Y or N).

In such a strange case, would you have to lie? It seems like you would have to communicate something false (imagine, for simplicity, that your silence would be taken as an affirmation of Y, or N, or would be a sort of speech-act by omission which, in any case, would communicate a falsehood), which you knew to be false.

If such a situation arose, it wouldn’t be possible to avoid telling a lie (at least where the sufficient conditions of lying are speaking falsely with a knowledge that what you’re saying is false). Therefore, it wouldn’t be possible to do the right thing (except in terms of telling the lesser lie, whatever that is). Does this pose much of a problem for Aquinas’ view? I’m actually not sure. If we really can construct a situation in which there is no way to avoid sinning, that would plausibly provide us with a reductio ad absurdum and should cause us to carefully review what we think qualifies as a sin. However, it is still open to the especially devout Thomist to bite the bullet here, or to find some way of arguing that the situation I propose arises in no logically possible worlds. It might help our case if we could provide some kind of hypothetical example. Here’s one: consider the question “is God infinite?” Clearly, those speaking the language of Duns Scotus are going to take a rejection of this as a false statement, and they (playing their language game) would be right to do so. On the other hand, those speaking the language of modern mathematicians would recognize the affirmative to be a straightforward falsehood (for God is not infinite in any quantitative sense). There is no unqualified answer (in the form of an affirmation or denial) which does not communicate a falsehood which one knows to be false (presuming one is sufficiently well theologically informed).

[1] ST, II-II, Q. 110, Art. 3, ad. 3.

Arguing that the B-theory (or the A-theory) is a metaphysically necessary truth

I have profound sympathy for the intuition that, for either the A-theory of time, or the B-theory of time, if it is true, then it is necessarily true. It obviously follows, therefore, from either one’s metaphysical possibility, that it is a necessary truth. However, the force with which this intuition imposes itself notwithstanding, it turns out to be extremely difficult to prove this modal thesis, and there may, in fact, be a really good objection to it.

Does it really follow from the A-theory’s being true (supposing it is) that it is necessary, or from the B-theory’s being true (supposing it is) that it is necessary? Suppose our world is an A-theory world; could God really not have created a B-theory world?

Interestingly, while I was rereading a paper today from Joshua Rasmussen, my attention was drawn to one of his footnotes, in which he outlines a sort of modal-ontological argument from the possibility of presentism (typically considered to be a version of the A-theory – though, I note in passing, he was arguing in the paper that presentism is strictly compatible with the B-theory) to its necessity. His argument went roughly as one might imagine (note: he uses ‘Tenseless’ as an abbreviation for the thesis that he argues for in the paper, and which needn’t directly concern us here):

Here’s the argument: (i) suppose it’s possible that Tenseless and presentism are true; (ii) then it’s possible that presentism is true; (iii) necessarily, if presentism is true, then presentism is necessarily true; therefore, (iv) if it’s possible that presentism is true, then it’s possible that presentism is necessarily true; (v) if it’s possible that presentism is necessarily true, then presentism is true (by S5); therefore, (vi) presentism is true.[1]

This caused me to review one of my (many, many) old blog post drafts, in which I tried to argue that if the A-theory is true, then it is a necessary truth, and if the B-theory is true, then it is a necessary truth. Here’s (roughly) what that looked like:

I have been asked, in the past, why I maintain that if the B-theory is true in any possible world, then it is true in all logically possible worlds (from which it follows that it’s true in the actual world), and that the same can be said for the A-theory. Upon reflection, I suppose I was reasoning in something like the following way:

  1. God exists in every possible world (assumption).
  2. If God exists in every possible world then his necessary essence is exemplified in every possible world.
  3. God either is by his necessary essence, or is necessarily not, simple and/or immutable in the classical senses.
  4. The B-theory is true if and only if God is essentially simple and/or immutable.
  5. Either the B-theory is true, or the A-theory is true (and not both).
  6. If the B-theory is true in one logically possible world, it is true in all logically possible worlds.
  7. Therefore, if the A-theory is true in one logically possible world, it is true in all logically possible worlds.

The weakest point of the argument, now that I lay it out and think about it, seems to be premise 4, for although it seems right to say that if God is simple and immutable then the B-theory must be true, it seems wrong to say that if the B-theory is true then God must necessarily be simple and/or immutable. Why think that if God weren’t simple and/or immutable then He couldn’t create a B-theory world? I then tried to construct a more elaborate argument for the conclusion that if the B-theory is true, then it is necessarily true, and if the A-theory is true, then it is necessarily true. It went something like:

  1. God’s existence is possible (assumption).
  2. God is a metaphysically necessary being. (by definition)
  3. For any metaphysically necessary being, if it exists in a single logically possible world it exists in all logically possible worlds.
  4. God exists in every possible world (assumption).
  5. If God exists in every possible world then his necessary essence is exemplified in every possible world.
  6. There is a logically possible world in which God’s essence includes being metaphysically simple and immutable. (Assumption)
  7. Therefore, in all logically possible worlds God is metaphysically simple and immutable.
  8. If God is metaphysically simple and immutable, then necessarily: if there is a contingent world, then the B-theory is true.
  9. There is a contingent world.
  10. Therefore, the B-theory is true.

This argument isn’t very good. For one thing, it highlights a really big problem for the idea that the A-theory of time and the B-theory of time are mutually exclusive and logically exhaustive disjuncts. Indeed, if there is no contingent world, there are surely no A-properties, but there are also no B-properties (it is hard to imagine a B-theory on which only ‘atemporal simultaneity’ is preserved – that is so depreciated that it isn’t clear whether it would even qualify as a version of the B-theory). It looks like this problem for Rasmussen’s argument as well (why accept his (iii)?).

I also had some rough notes on a third argument, which went something like this:

  1. God’s existence is metaphysically possible. (assumption).
  2. God is a metaphysically necessary being (and his essence, whatever it is, is metaphysically necessary).
  3. God either is essentially, or essentially is not, simple and immutable in the classical senses.
  4. There is a contingent world. (assumption)
  5. If there is a contingent world, then the A-theory is true, or the B-theory is true (and not both).
  6. The A-theory is true if and only if God stands in real relations to the world which are grounded in himself.
  7. If God stands in real relations to the world grounded in himself, then God is not simple and immutable.
  8. If God possibly stands in real relations to the world which are grounded in himself, then God necessarily stands in real relations to the world which are grounded in himself.
  9. If God necessarily stands in real relations to the world which are grounded in himself then the A-theory is necessarily true.
  10. Therefore, if the A-theory is possibly true, the A-theory is necessarily true.
  11. If the A-theory is not possibly true, then the B-theory is necessarily true.

The reader will have to forgive me for being a little loose as well as slightly enthymematic. I’m not sure this is a good argument. The intuition is supposed to be that God can only be simple and immutable in a B-theory world, that he cannot be simple and immutable in an A-theory world, and that whichever way God is in any possible world (at least with respect to being simple and immutable), that is the way He is in all possible worlds.

Perhaps one will disagree with me that God exists in all logically possible worlds (which is just to say that God does not exist, since, obviously, if a metaphysically necessary being exists in a single possible world it exists in all possible worlds). They will argue that it may seem necessary given theism that whichever theory of time is true of the actual world is true of all logically possible worlds, but that they either reject, or in any case do not accept, theism. It might seem as though we are at a standstill with such a person.

There is, nevertheless, another way to argue that the A-theory is necessarily false (and the B-theory, therefore, necessarily true). Suppose we accept the claims that the (weak-)PSR and the A-theory of time are logically incompatible with each other.[2] Now, take the weak-PSR which says that for any possibly true contingent fact P, P possibly has an explanation. Obviously, if the weak-PSR is true it is a necessary truth. This entails that there is a logically possible world in which P, and the explanation of P, both obtain. Suppose that P is “it is now this particular time.” On the A-theory, this contingent fact does not have an explanation. That means (supposing all we have said so far) that at least one logically possible world is a B-theory world. It follows that there is no logically possible world in which the A-theory is true. However, this reasoning is not likely to be any more compelling than the theistic reasoning explored above.

Can I do any better? Probably not today. (I suppose I could have deployed my argument for thinking that the A-theory is not logically possible because there is no logically possible world in which time flows – an argument I developed a bit in my undergraduate thesis and which, I am beginning to think, may make an appearance in my Master’s thesis – but I’d rather leave it out of this post for the sake of convenience).

[1] Joshua Rasmussen, “Presentists may say goodbye to A-properties,” Analysis 72, no. 2 (2012): 270-276.

[2] For more on this, see

Some Problems With Degreed Existence

It was typical for the Medievals to speak of existence as a degreed concept (i.e., as the kind of thing which comes in greater or lesser degrees). Modern philosophers generally balk at this suggestion, insisting instead that a thing either exists, or does not exist, but that it makes no sense to speak in terms of degrees of existence. It is, of course, possible to adopt that bivalent view with respect to the truth conditions for statements like “x exists”, but also indulge a way of speaking which uses ‘exists’ as a dyadic relation (e.g., “x exists more(/less) than y”). There are several ways in which one can try to make sense of this kind of talk, but I have often thought that the most appealing way was in terms of possible worlds. Suppose we say:

x exists more than y iff x populates more possible worlds than y.

This has seemed, to me, to be satisfying for a number of reasons. Obviously, it allows for the medieval convention, and it also obviously places God at the top of the hierarchy of being (and this without, as of yet, even broaching the topic of one’s theory of existence), which is what the Medievals (and I) ultimately want. At the same time, the modern philosopher is going to be hard-pressed to reject the analytic convention of speaking in terms of possible worlds, and it seems sensible to give ‘existence’ a stipulative qualified definition, for particular purposes, running along these lines. In addition, this modal definition of existence (as a degreed concept) plausibly subsumes several other candidate rationales for this kind of talk, including that ‘degreed existence’ measures immutability, contingency, et cetera.

However, perhaps there are some problems with this which I had previously glossed over. I don’t think much of the objection that existence isn’t a predicate, for a few reasons. First, the way in which the Medievals are using the term, here, is clearly predicatory, and idiosyncratic enough that they can help themselves to a specially stipulated (probably onto-theological) definition. Second, existence isn’t usually considered a first-order predicate, but there isn’t much of a problem considering it a second-order predicate. Third, there are systems on which existence really is a first-order predicate, such as Krypke’s quantified modal logic. These and other reasons incline me to dismiss such a facile (Kantian) objection. Nevertheless, there are some real problems here worth thinking about.

For one thing, the cardinal value of possible worlds with any y, so long as y exists in at least two possible worlds, seems to be ℵ0.[1] It isn’t clear how one thing could exist in more possible worlds than that (I find it hard to imagine the argument for thinking that x exists in ℵn where n>0).

– Actually, here is an argument for this: Platonism is true (assumption), and not only natural numbers, but all the reals, are abstract objects. Therefore, there is an non-denumerable infinity of actual things, that infinity’s cardinal value being ℵ1. Further, we can argue that mathematical functions are abstract objects, and since the set of all real functions in the interval 0 < X < 1 is the non-denumerable ℵ2,[2] so too will be the number of actual things (given Platonism). In any case, I digress. –

Perhaps if x existed in all worlds where y existed, and also existed in worlds where y did not exist, we could justify retaining this convention (though we would have to give up Cantor’s notion of equivalence in terms of correspondence or, more precisely, bijection), but then there wouldn’t be a (very?) smooth gradation of being. Dream objects, for instance, would not be less real, or have less existence, than the material objects of the external world (consider that mental states are multi-realizable, so that for any mental state, a whole cacophony of physical states suffices to bring it about, even if, given some particular physical state, the mental state must come about – I assume this, here, just for the sake of argument). I had previously hoped that this problem was roughly analogous to the problem with measuring the ‘closeness’ of possible worlds to each other (when we talk about changing only a little bit of a world’s description, technically we are always talking about changing at least ℵ0 propositions).[3] If the problems were analogous, then their solutions were likely to be analogous, and I was (and remain) supremely confident that there must be a solution to the latter. However, we can apparently solve the latter problem by talking about first-order propositions directly about states of affairs in that world (at least plausibly, there are finitely many of these). That solution doesn’t translate well, as far as I can tell, into a solution for the first problem, so that the problems don’t seem analogous enough to have analogous solutions.

Another problem is that seemingly insignificant beings like atoms are going to be more real (in the sense of having higher/greater existence) than plants, and so human beings have less existence than mosquitoes. The Medievals would not have been thrilled. For them, plausibly, a thing exists to the extent that it succeeds in resembling God.

There is a possible reductio here as well; if some things have more existence than others by the modal measure suggested, then we might wonder whether we can license speech about some things having more unreality than others? Suppose we accept talk of impossible worlds, and suppose we then accept talk of really-impossible worlds. To get an idea what this would look like, refer to Pruss here. Well, then it looks like some things don’t merely not-exist, but some really don’t exist, and they don’t exist even more than other non-existent things.

Not all of these problems are equally troubling, but they are worth taking inventory of regardless. I think the attempted reductio ad absurdum at the end is pretty weak. We can just deny that there are really impossible worlds, or even deny that there really are impossible worlds. In any case, we can just exclude such considerations by fiat, since stipulative definitions can be constrained however we see fit, so we can just constrain the stipulative definition of ‘[degreed] existence’ so as to ignore such puzzles. Still, not all of these are so easy to dismiss. I won’t flesh this out here, but these considerations lead me to suspect that the best way to give an account of ‘degreed existence’ (in the sense the Medievals want to indulge talk about) may be with reference to a well worked out theory of existence after all.

[1] Is this true? Maybe not – maybe there is some y such that y exists only in two (or, in any case, in some finite number of) possible worlds. I have trouble imagining what this would be, but, in any case, for nearly any conceivable y, it will turn out to be true that there are ℵ0 possible worlds containing it.

[2] William Lane Craig, The Kalam Cosmological Argument, (Oregon, Wipf and Stock publishers, 1979), 80.

[3] Technically, we are changing even more propositions than this. It is widely agreed now that there is no set of all true propositions. Taking the power-set 𝔓(W) of all propositions true at possible world W, you can generate infinitely more propositions, and this actually changes the cardinality of the number of true propositions from ℵ0 to ℵ1, the latter of which is a non-denumerable infinity. The process can be repeated indefinitely, leaving us with an indefinitely large set, and there is no way to deal with indefinitely large sets in set theory.

Soundness is Neither Necessary nor Sufficient for Goodness

In this (very) short article, I am going to try to explain what makes an argument valid (comparing two views), what makes an argument sound (again comparing two corresponding views) and then I aim to distinguish ‘good’ arguments from either of these. I will attempt to obviate why validity, on either interpretation, will be a necessary but insufficient condition for soundness (on that respective interpretation). It will turn out that soundness (on either interpretation) will not be a sufficient or a necessary condition for goodness, and that validity (on either interpretation) will be a necessary but insufficient condition of goodness. It will also be shown that goodness is neither a necessary nor sufficient condition of soundness. This article can, perhaps, serve as a useful prolegomenon to introductory deductive logic, though its distinctions are themselves somewhat unorthodox and reach beyond the scope of formal logic.


One definition of validity which is relatively common, easily found in most introductory textbooks on deductive logic, is the following:

An argument is valid if and only if it is not logically possible for the premises to be true and the conclusion false.

Let’s explore the dynamics of this definition. It would mean that an argument of the following sort would be considered valid:

  1. All men are human
  2. Socrates is a man
  3. Therefore, Socrates is human.

Clearly, in this argument, it is not logically possible for the premises to (both) be true, and for the conclusion to be false. The same can be said of the following argument:

  1. Bob loves Carroll
  2. If Bob loves Carroll then Carroll loves Joe
  3. Therefore, Carroll loves Joe

This is pretty obviously logically valid. So too, though, is the following argument:

  1. All women are purple.
  2. Socrates is a woman.
  3. Therefore, Socrates is purple.

The reason this argument is valid is that it is not possible for the premises to (both) be true, and for the conclusion to be false. Perhaps the premises and conclusion are all, in fact, false, but in any possible world in which the premises were true, the conclusion would be true. Thus, validity is not concerned with truth so much as truth-preservation. The concern is to ensure that one cannot, in a ‘valid’ argument, move from true premises to a false conclusion. Take the following example as well:

  1. All women are purple.
  2. If all women are purple, then evolution is true.
  3. Therefore, evolution is true.

In this argument, we have a conclusion which is (I presume) true in fact, while the premises are all false. However, the argument is clearly valid as well, since it is not logically possible that the premises be true and the conclusion false. Remember that validity requires nothing more than that it is not possible for both (i) the premises to be true, and (ii) the conclusion to be false.

The difficulty with this account of validity arises when we are confronted with examples of the following variety:

  1. All men are animals.
  2. If all men are animals then Tyrannosaurus Rex makes a good pet.
  3. Therefore, 3+4=7

This argument is logically valid, since it is not logically possible for the premises to be true while the conclusion is false (mostly because it isn’t possible for the conclusion to be false, and it is ‘possible’ for the premises to be true). Such an argument, however, doesn’t have any dialectical appeal. Consider also:

  1. I once drew a square-circle,
  2. If I once drew a square-circle, then I am a married bachelor,
  3. Therefore, I once drew the impossible.

This argument can be tricky; in order to find out whether it is valid we have to ask whether it is possible for both (i) the premises to be true, and (ii) the conclusion false. As it turns out, it is not possible for the premises to be true and the conclusion false, precisely because it is not possible for the premises to be true. Thus, formally speaking, it is a logically valid argument.


The definition of a sound argument is pretty straightforward: an argument is sound if and only if it is (i) logically valid, and (ii) all of its premises are true. For example,

  1. Socrates was mortal.
  2. Everything that was mortal, was once alive.
  3. Therefore, Socrates was once alive.

In this argument, we find that it is not logically possible for the premises to be true while the conclusion is false, and in addition, we find that both premises are clearly true. Thus, we have a sound argument on our hands. Any argument which is logically valid is sound just in case all of its premises are true. Thus, for example, the following argument is sound:

  1. A tautology is a tautology.
  2. 6-2=4
  3. The sentence ‘is this a question‘ expresses a question.

This exemplifies the problem with the formal definitions of validity and soundness. It shows that one can construct sound and vacuous arguments by simply ensuring that the premises and conclusions are all necessary truths, or at least that the conclusions are necessary truths while the premises are true. In the interest of more off-the-cuff examples, take for instance:

  1. I once wrote this sentence.
  2. If I once wrote this sentence, then I have written at least one sentence.
  3. Therefore, 3+4=7

This argument is both logically valid, and sound, and yet it appears to be a very bad argument. Nobody who didn’t already accept the conclusion could be led by it to accept the conclusion. It is a bad argument, even for those of us who accept the conclusion; if this argument were submitted as our reason for believing the conclusion then our mathematical belief that 3+4=7 would literally be unjustified (a necessary self-evident truth in which we believe can, of course, be unjustified). What all this illustrates is, first, that the formal definitions of validity and soundness are concerned only with truth preservation, and not with the persuasive force of an argument at all. As philosophers who specialize in the study of modal logic often make a distinction between ‘broad’ and ‘narrow’ logical possibility (eg. a square-circle is broadly logically impossible, but narrowly logically possible since there isn’t any purely formal way to obviate a contradiction between the predicates ‘square’ and ‘circle’), so too, perhaps, should we make a distinction between broad and narrow validity & soundness. What we have looked at so far would be the purely formal or ‘narrow’ accounts of validity and soundness. Maybe a ‘broad’ view of validity (which I will henceforth write as ‘validity*’) would be something like: an argument is valid* if and only if i) it is not possible for the premises to be true while the conclusion is false, and ii) the conclusion meaningfully follows from the truth of the premises. This definition of validity* says everything the former one did, with the addition that the premises and conclusion have to be semantically related (i.e., meaningfully related; they have to have something to do with one another). We can correspondingly say that an argument is sound* just in case it is valid* and its premises are true.

Now, validity* and soundness* are not appropriate distinctions in an introductory course on deductive logic, and so are somewhat philosophically unorthodox. However, they are rather useful outside of that narrow context, and in the context of doing philosophy. In philosophy, we don’t just want sound arguments, we want sound* arguments!


Speaking of what philosophers want, there is another issue I wish to examine, which is what makes an argument ‘good’ by philosophical standards. It turns out, I will argue, that neither soundness nor soundness* are necessary or sufficient conditions of ‘goodness’.

I submit that the goodness of an argument consists in two things: i) that the argument is logically valid*, ii) that the accumulated uncertainty of the premises to the argument’s intended audience sets a reasonably high lower bound on the probability of the conclusion. This second criterion is specially crafted to avoid the common mistakes which have, in the past, been made even by some relatively good philosophers like William Lane Craig; namely, the mistake of thinking that premises in a valid argument need be merely each more plausible than their respective negations for the conclusion to follow forcefully. Indeed, the (probability of the) premises of an argument merely set a lower bound on the probability of the conclusion.[1] If that lower bound on the probability of the conclusion is less than or equal to 0.5 then the argument is not compelling. Whether an argument is persuasive or not to some subject is going to depend on their appraisal of the premises, of course, but a good argument will consist of premises which are not merely more plausible than not, but also highly plausible – plausible enough, at least, that the conclusion will also seem highly plausible. This definition obviously subjectivizes ‘goodness,’ making it dependent upon an audience’s appraisal, but that shouldn’t bother us very much because plausibility has to figure into the goodness of an argument in some way, and ‘plausibility’ is already a term of epistemic appraisal.

Consider the following two arguments, both of which are valid and at least one of which is sound. First, the modal ontological argument, which we can roughly reconstruct as:

  1. God possibly exists (i.e., God exists in at least one logically possible world).
  2. If God exists in one logically possible world then God exists in all logically possible worlds.
  3. If God exists in all logically possible worlds then God exists.
  4. Therefore, God exists.

This argument is sound just in case the conclusion is true. However, that doesn’t make it a very good argument in my sense. Indeed, consider its parody:

  1. God possibly does not exist (i.e., there is at least one logically possible world in which God does not exist).
  2. If there is at least one logically possible world in which God does not exist, then there is no logically possible world in which God exists.
  3. If God exists in no logically possible worlds then God does not exist.
  4. Therefore, God does not exist.

At least one of these two arguments is valid, valid*, sound and sound*, but it is arguable that neither of them are good. Goodness, then, consists in more than just soundness*. So, given the way I’ve just outlined things, we can imagine any number of arguments which are good without being sound, sound without being good, valid* without being sound, sound* without being good, but none which are good without being valid*. The goodness of an argument, it seems, is largely in the eye of the beholder; the goodness of a valid* argument is entirely in the eye of the beholder.


[1] See:

Pope Pius XII and the Holocaust

The Catholic Church certainly doesn’t have an immaculate history; from the Spanish inquisition to the atrocities committed during the crusades, history has borne witness to myriad spectacles of moral failure on the part of Catholics. This point, I take it, is beyond reasonable contest. However, having acknowledged that, I have to say that I have grown aggravated by the mindless tendency to sensationalize and exaggerate these failures, as well as to fabricate some of them wholesale. Enough is enough, and the nonsense has to be called out. Nowhere is this trend more irritating to me than in the case of the wild accusation that Pope Pius XII (one of my favorite popes of all time) was a Nazi sympathizer. So, I will break with my usual habit of blogging about strictly philosophical and/or theological issues and write a little bit in defense of venerable Pope Pius XII.

The late Christopher Hitchens, one of the famed ‘four horsemen’ of the new atheism, wrote:

“None of the Protestant churches, however, went as far as the Catholic hierarchy in ordering an annual celebration for Hitler’s birthday on April 20. On this auspicious date, on papal instructions, the cardinal of Berlin regularly transmitted “warmest congratulations to the führer in the name of the bishops and dioceses in Germany,” these plaudits to be accompanied by “the fervent prayers which the Catholics of Germany are sending to heaven on their altars.” The order was obeyed, and faithfully carried out.

To be fair, this disgraceful tradition was not inaugurated until 1939, in which year there was a change of papacy. And to be fair again, Pope Pius XI had always harbored the most profound misgivings about the Hitler system and its evident capacity for radical evil. (During Hitler’s first visit to Rome, for example, the Holy Father rather ostentatiously took himself out of town to the papal retreat at Castelgandolfo.) However, this ailing and weak pope was continually outpointed, throughout the 1930s, by his secretary of state, Eugenio Pacelli. We have good reason to think that at least one papal encyclical, expressing at least a modicum of concern about the maltreatment of Europe’s Jews, was readied by His Holiness but suppressed by Pacelli, who had another strategy in mind. We now know Pacelli as Pope Pius XII, who succeeded to the office after the death of his former superior in February 1939. Four days after his election by the College of Cardinals, His Holiness composed the following letter to Berlin:

To the Illustrious Herr Adolf Hitler, Fuhrer and Chancellor of the German Reich! Here at the beginning of Our Pontificate We wish to assure you that We remain devoted to the spiritual welfare of the German people entrusted to your leadership. […] During the many years We spent in Germany, we did all in Our power to establish harmonious relations between Church and State. Now that the responsibilities of Our pastoral function have increased Our opportunities, how much more ardently do We pray to reach that goal. May the prosperity of the German people and their progress in every domain come, with God’s help, to fruition!

Within six years of this evil and fatuous message, the once prosperous and civilized people of Germany could gaze around themselves and see hardly one brick piled upon another, as the godless Red Army swept toward Berlin. But I mention this conjuncture for another reason. Believers are supposed to hold that the pope is the vicar of Christ on earth, and the keeper of the keys of Saint Peter. They are of course free to believe this, and to believe that god decides when to end the tenure of one pope or (more important) to inaugurate the tenure of another. This would involve believing in the death of an anti-Nazi pope, and the accession of a pro-Nazi one, as a matter of divine will, a few months before Hitler’s invasion of Poland and the opening of the Second World War.”[1]

This is as naïve an analysis of Catholic theology, as well as of history, as it is possible to find.

Specialists on this issue, such as Ronald J. Rychlak,[2] had challenged Hitchens to debate the issue publicly, but Hitchens never accepted (for whatever reason), and lest one imagine that Rychlak, being Catholic, is unfairly biased, I can direct the reader just as easily to X-Catholic atheists, such as Mark Riebling (who, it just so happens, has done an interview on the topic with another one of the horsemen of the new atheism, Sam Harris).[3] It is worth noting, for a start, that Eugenio Maria Giuseppe Giovanni Pacelli (better known as Pope Pius XII) ascended to the papacy as a successor to Pius XI, whose legacy of opposition to the Nazi’s is as clear as is his encyclical Mit brennender Sorge (1937), in which he denounced and condemned them unequivocally. One source reads:

“When Pius XI died in 1939, the Nazis abhorred the prospect that Pacelli might be elected his successor.
Dr. Joseph Lichten, a Polish Jew who served as a diplomat and later an official of the Jewish Anti-Defamation League of B’nai B’rith, writes: “Pacelli had obviously established his position clearly, for the Fascist governments of both Italy and Germany spoke out vigorously against the possibility of his election to succeed Pius XI in March of 1939, though the cardinal secretary of state had served as papal nuncio in Germany from 1917 to 1929. . . . The day after his election, the Berlin Morgenpost said: ‘The election of cardinal Pacelli is not accepted with favor in Germany because he was always opposed to Nazism and practically determined the policies of the Vatican under his predecessor.’ “[4]
Former Israeli diplomat and now Orthodox Jewish Rabbi Pinchas Lapide states that Pius XI “had good reason to make Pacelli the architect of his anti-Nazi policy. Of the forty-four speeches which the Nuncio Pacelli had made on German soil between 1917 and 1929, at least forty contained attacks on Nazism or condemnations of Hitler’s doctrines. . . . Pacelli, who never met the Führer, called it ‘neo-Paganism.’ “[5]””[4]

For example, in April of 1935 Pacelli delivered a speech at Lourdes, France, stating before an audience of no less than 250,000 pilgrims that “[Nazi’s] are in reality only miserable plagiarists who dress up old errors with new tinsel. It does not make any difference whether they flock to the banners of social revolution, whether they are guided by a false concept of the world and of life, or whether they are possessed by the superstition of a race and blood cult.”””[5] When he finally ascended to the papacy, Pius XII confirmed every worry the German elites had about him when he continued to write scathing speeches against Nazism. Not only did he remain vigilant, but he alerted the world to the philosophical horrors of Nazism long before the discovery of the death camps, particularly in one Christmas address so clear it became a cry heard around the world.

“”The New York Times at the time observed of Pius XII’s Christmas address, “This Christmas more than ever he is a lonely voice crying out in the silence of a continent.” Pius XII’s message was carefully analyzed by Reinhard Heydrich’s branch of the SS, which saw the pope’s message as an attack on the Nazi regime and its anti-Semitism. Calling the Christmas address “a masterpiece of clerical falsification,” the SS reported that the “Pope has repudiated the National Socialist New European Order” and noted his assertion that “all peoples and races are worthy of the same consideration.” “Here,” they argued, “he is clearly speaking of the Jews.”””[6]

How are we to believe that this man was Hitler’s Pope? This is the same man who helped write the first draft of Mit brennender Sorge,[7] who orchestrated the secret rescue of as many as 800,000 Jews,[8] who was consulted in the (unsuccessful) plot to oust Hitler from power,[9] who sanctioned the plot to assassinate Hitler,[10] and the same man whom Hitler allegedly[11] plotted to forcefully enter the Vatican and detain.[12] This was the man upon whose death in 1958 Israel’s Foreign Minister at the time, Golda Meir, issued the following statement by way of condolence communicated to the Vatican:

“When fearful martyrdom came to our people in the decade of Nazi terror, the voice of the Pope was raised for the victims. The life of our times was enriched by a voice speaking out on the great moral truths above the tumult of daily conflict. We mourn a great servant of peace.””[13]

In 1955 the Israeli Philharmonic Orchestra, in an act permeated with symbolism, gave a special performance at the Vatican in honour of the Pope. No less eminent a scholar than Rabbi David G. Dalin observes:

“on May 26, 1955, the Israeli Philharmonic Orchestra flew to Rome to give a special performance of Beethoven’s Seventh Symphony, at the Vatican’s Consistory Hall, to express the State of Israel’s enduring gratitude for the help that the Pope and the Catholic Church had given to the Jewish people persecuted by the Nazis during the Holocaust. That the Israeli Philharmonic Orchestra so joined the rest of the Jewish world in warmly honoring the achievements and legacy of Pope Pius XII is of more than passing significance. As a matter of state policy, the Israeli Philharmonic has never played the music of the nineteenth century composer Richard Wagner because of Wagner’s well-known reputation as an anti-Semite and as Hitler’s “favorite composer,” and as one of the cultural patron saints of the Third Reich, whose music was played at Nazi party functions and ceremonies. Despite requests from music lovers and specialists, the official state ban on the Israeli Philharmonic’s playing Wagner’s music has never been lifted.”[14]

This is the man whose example of Christian charity, virtue and faith was so great that, in the absence of intellectual argument (of which, I note in passing, he was eminently capable), he managed, by example alone, to convert the chief Rabbi of Rome (who also happened to be a doctor of philosophy) Israel Zolli, who, upon conversion to and reception into the Catholic Church in February of 1945, took as his baptismal name ‘Eugenio Maria Zolli,’ in clear homage to the pope.[15] Pius XII actually agreed to Zolli’s request to become his godfather. This conversion, it is worth underscoring, was sincere, as Zolli stresses in his book originally titled “Before the Dawn” and later released under the title “Why I Became a Catholic.”[16] It came about as an indirect result of Zolli observing the actions of Pius XII throughout the second world war, which included housing Zolli in the Vatican, as well as making the Apostolic Palace of Castel Gandolfo a refuge for a significant number of Jews, even allowing his own bed to be used at least 17 times for Jewish mothers to give birth within the safety of the Apostolic Palace.[17]

To claim in the face of such evidence that Pope Pius XII was, in any way, sympathetic to Hitler or Nazism is flatly incredible. Whence, then, this impression of him as Hitler’s Pope? The answer may surprise you. It comes primarily from a piece of propaganda in the form of a play popularized in Germany, written by Rolf Hochhuth in 1963, titled Der Stellvertreter (which is usually translated as “The Deputy” but may be better translated as “The Vicar”).[18] This eight-hour long piece of… egregious historical revisionism was used by the Soviet Union to promote communism in Germany. It was, however, only after this play was performed on Broadway that the caricature of Pope Pius XII as Hitler’s Pope gained notoriety in the West.[19] It catalyzed a slew of literature in the English-speaking world, among the most influential fruits of which we find John Cornwell’s book “Hitler’s Pope: The Secret History of Pius XII,” published in 1999.[20] Since then it has shoved its way into the collective subconscious of misinformed westerners everywhere. Misinformation, it seems, travels faster than the speed of thought.

To be fair, while the play is undoubtedly the primary source for the popular perception, the impression is at least partly promoted by some criticisms of Pius XII suggesting that he could have done more. The Encyclopedia Britannica has an entry an excerpt of which reads as follows:

“Pius XII… played a much more controversial role during the war, [and] has been criticized for failing to speak out more forcefully against the genocidal policies of the Nazis. His strongest statement against genocide was regarded as inadequate by the Allies, though in Germany he was regarded as an Allied sympathizer who had violated his own policy of neutrality. Pius also approved efforts to help the Jews and ordered that the Jews of Rome be given refuge in the city’s religious houses. After the war, the Vatican was involved in extensive humanitarian efforts. Pius, however, was criticized for not having done more. A cautious and experienced diplomat who feared that bold actions would cause more harm than good, he was not a prophet at a time when the world may have needed one.”[21]

This criticism is slightly uncharitable, and it fails to appreciate some of the complexities inherent in negotiating the political and religious terrain with which Pius XII was presented. It is true that Pius XII urged the allied forces to seek alternative solutions to war (see Summi Pontificatus). It is also true that Eugenio Pacelli, acting as the Vatican’s secretary of state, negotiated and agreed to the Reichskonkordat in 1933, a concordat between the Holy See and the German Reich.[22] It is fair to say that Pius XII also attenuated his tone during the second world war, particularly when he saw the Nazi’s target for imprisonment and death Catholic laity, nuns, and clergy by the hundreds in response to his own rhetoric. Hitler’s Nazi Germany showed itself to be incorrigible in the face of criticism, and Pius XII readjusted himself accordingly, focusing his energy on the ‘underground network’ he used to save hundreds of thousands of lives.

If this criticism, with all the advantage of hindsight and the luxury of idealism, is all there is to say against Pope Pius XII, then even if we conceded it without qualification it would go no considerable distance toward justifying the moniker ‘Hitler’s Pope.’ Once we clear away the debris of misinformation and bring into focus all the evidences which bear on his actions, his attitude and his general character, we can see with stunning clarity just how astounding, even scandalizing, it is to refer to this Pope as a Nazi sympathizer. Almost literally, nothing could be further from the truth. As far as asking people in the Church to pray for Hitler, that is not only standard (the Bible in 1 Timothy 2:1-4 commands Christians to pray for their political leaders, however awful they may be – and all the more the more awful they are), but to do the contrary would have been to send a very strong condescending message from the Vatican to Nazi Germany, and the Vatican had to be meticulously diplomatic in its actions (and inactions) to prevent or mitigate the complete political turmoil in Germany. As I indicated above (and others have made the point more competently than I have), the Pope could only vocally oppose Hitler to an extent before it would lead to more casualties, and Pius XII took it as his priority to save lives rather than to save face.

Allow me now, briefly, to anticipate one possible objection to this conclusion on which I insist. Perhaps it occurs to the reader that I, being a Catholic, have a vested interest in defending the Pope, in shielding the Pope from criticism, and as such I turn out to be (even if through no fault of my own) as unreliable as any inordinately biased source. Two responses come to mind. In the first place, if you think that I am guilty of misrepresenting the historical portrait, then I sincerely invite you to peruse and explore the literature on this topic and see for yourself what you make of the matter. Second, perhaps it is worth clarifying that Catholics believe in papal infallibility, but not in papal impeccability. We believe that Popes are guarded by the Holy Spirit against teaching error through the exercise of their papal authority. We do not hesitate to believe that many popes have been astonishingly and spectacularly sinful. Let us suppose, for the sake of argument, that Pius XII was actually horrendously evil, that he was Hitler’s pope, that he had horns growing out of his head, et cetera. What consequences would follow from this for the credibility of the Catholic worldview? Precisely none. Nothing of relevance follows about the truth or falsity of the Catholic worldview as a whole, or about any doctrine in particular. Infallibility does not entail impeccability, and Catholics regard the Pope as infallible only when, under very specific conditions, he invokes his papal authority. Nowhere does Pius XII teach anything (positive) about Hitler’s ideals, or his national socialism, so there is simply nothing here for me to defend out of any misguided sense of Catholic propriety.

The reason I defend this Pope is that I have grown to have a warm affection for both his character and his intellect. Of the veritable library of encyclicals he managed to produce during his pontificate, Humani Generis, Mystici corporis Christi, Orientales omnes Ecclesias, Sempiternus Rex Christus, Musicae sacrae, Ad Apostolorum principis, and Divino afflante Spiritu stand out as being among the most beautiful and (for me) intellectually formative encyclicals I have ever read. Pope Pius XII was a towering intellect with a solid commitment to the exploration of the beauty, truth and goodness of his faith. He also happened to have the moral fortitude and heroism of a saint. This is the reason I rush to his defense.

[1] Hitchens, Christopher. God is Not Great: How Religion Poisons Everything. New York: Atlantic Books, 2008.

[2] See some of his extended interviews here:







[9] Peter Hoffmann, History of the German Resistance, 1933-1945. (McGill-Queen’s University Press: 1996) 161, 294.


[11] This is hotly disputed, and may be propaganda from British and allied forces.

[12] Owen Chadwick, Britain and the Vatican During the Second World War, Cambridge University Press: 1988. And Dan Kurzman, “Hitler’s Plan to Kidnap the Pope,” June 26, 2007, accessed November 25, 2016. Additionally, note the oddity of the British using this as pro-allied forces propaganda if Pius XII really was in league with Hitler. Thus, even if this was originally propaganda, it is propaganda which provides evidence that Pius was not a Nazi sympathizer.

[13] Rabbi David G. Dalin, “A Righteous Gentile: Pope Pius XII and the Jews,”

[14] Rabbi David G. Dalin, “A Righteous Gentile: Pope Pius XII and the Jews,”…/a-righteous-gentile…



[17] (29 minutes in).



[20] Cornwell, John. Hitler’s Pope: The Secret History of Pius XII. Penguin, 2000.


[22] Which can be found here, but only in Italian and German:

Is Presentism true(-making apt)?

Here’s an argument against presentism from the intuitively plausible principle that for any truth, there must be a truth-maker which makes a difference. Although I’m assuming a correspondence theory of truth, I don’t mind flirting with the idea that other theories of truth could adopt some truth-making principle and carry on with my argument keeping everything else the same. What I mean, here, by making a difference is something like this: if there is a possible world W1, in which T1 is true, and M1 is T1‘s truthmaker, then there is no possible world W2 which is maximally close to W1 in all respects save for that M1 (or its equivalent M2)[1] is unavailable (so, similar mutatis mutandis), at which T1 (or its equivalent T2) is true. I will bracket concerns about whether truths are multiply-realizable in the sense that any particular truth Tn might have any of a set of realizers {M1, M2, M3… Mn}, and I will, therefore, dodge questions about over-determinated truth-values and related concerns; I only note in passing that I don’t think much of these concerns, but I want to avoid them because I also haven’t thought much about these concerns.

Suffice it to say that by T1 having a truth-maker in M1, I mean that M1 is the reason T1 is true.[2] Now, consider the world as it looks through the eyes of a presentist. The presentist believes that the set of all things which exist, and the set of all things which exists now, are identical. There is no thing which both exists, and does not exist presently. Only the sum of all truths which are true ‘right now’ are true at all (this may be thought to be an unfair characterization, since the presentist may still believe that necessary truths have timeless entities, such as abstract objects, as their truth-makers, but I think this is contrary to the letter, if not the spirit, of presentism; for the strict presentist, only that which is present exists).

Now, what, on presentism, can account for the fact that we can make true statements about the past (let alone the future)? There is, presumably, some truth-making ingredient which presently exists which can make true statements about the past true. However, consider the classical problem in epistemology of the unverifiability of the reality of the past. As Bertrand Russell put it in his famous Problems of Philosophy, our knowledge of the past is based not on sense-experience (which would make it empirical in the strictest sense), but on our acquaintance with our own memory. We must, he insists, be able to have knowledge by acquaintance with things other than sense-experience, or else we would not be able to know that the past was real:

“But if [sense-data] were the sole example [of the things with which we are acquainted], our knowledge would be very much more restricted than it is. We should only know what is now present to our senses: we could not know anything about the past–not even that there was a past…
This immediate knowledge by memory is the source of all our knowledge concerning the past: without it, there could be no knowledge of the past by inference, since we should never know that there was anything past to be inferred.”[3]

The point here is that skepticism about the reliability of our memory will lead to skepticism about the very reality of the past, a worry which no amount of empirical investigation can alleviate. Suppose, for the sake of argument, that the whole world popped into existence moments ago with the appearance of age (e.g., light travelling to your retinas with the appearance of having come from stars (light-years away), memories of the first half of the conversation you may now be in, memories of having read the opening paragraph of this post, etc.). How would the world look any different from how it would have looked if it had had a past (and, let’s assume, precisely that past in which the evidence leads us to believe)? There seems to be no difference between the two. The worlds look empirically identical.

You might (quite rightly) think that these possible worlds could be metaphysically differentiated, but how could we articulate the metaphysical distinction on presentism? We cannot just say that only one of the worlds has the property of having a past, for whatever that amounts to on presentism will, it seems, be metaphysically indistinguishable from the property of having the appearance of having a past! Where, on the present ‘slice’ of the universe (whatever shape that takes), cosmos, and/or noumenal world can we locate a truth-maker for past-tense truths which would not have been there if the world had merely popped into existence moments ago preloaded with all the appearances of age? If there is no way to articulate a difference, then we might have on hand a good reason to be skeptical of presentism (or else, I suppose, skeptical of truth-making accounts of truth, but I take it as nearly incontestable that presentism is less intuitively secure than the generic truth-making account of truth). Maybe I’m mistaken, but I am under the spell of a powerful suspicion that the metaphysics of presentism makes no room for the kind of truth-maker I’m looking for.

But: perhaps there is a problem with the question itself. The presentist might insist that they take issue with the grammar of this objection, since it seems as though it assumes the reality of the past. The presentist may insist that on presentism there is no metaphysical difference between the possible world ‘with a real past’ and the possible world ‘with an apparent past’ precisely because there is no difference (i.e., simpliciter). The question becomes a pseudo-question, and the presentist follows the dance-moves of the positivist around the issue. This, however, seems to me to be an at least equally damning flaw in presentism as the lack of a truth-maker would be; if the presentist cannot make room for the meaningfulness of a distinction we all know very well to be meaningful then we should treat presentism with the same[4] disdain with which we treat logical positivism. If they do not make room for the semantic difference then they will either be violating the law of excluded middle, or they will be denying the meaningfulness of propositions we all know to be perfectly intelligible.

[1] I’m not sure if this comment, along with the one shortly to follow, is entirely appropriate here. I suspect that it may depend on one’s theory of reference across possible worlds. Nevertheless, I think my meaning is clear enough for the purposes of this post.

[2] Depending on how we cash out ‘reason’ here, this might be enough to avoid the difficulties I gestured towards above.

[3] Bertrand Russell, The Problems of Philosophy, (OUP: Oxford, 2001), 21.

[4] If not the same, on account of logical positivism’s being self-referentially incoherent (a flaw which we have yet to show presentism to have earned for itself), then at least a similar disdain. One might even say, a disdain so similar that the difference cannot be verified.