How Could an Impassible God be Offended or Know Any Contingent Fact?

Earlier (here and here) I asked how an all-good God could sentence a human agent to sempiternal punishment, punishment that has a beginning but no end. If the punishment must fit the crime, and the crimes of finite agents are themselves finite, then it would seem that no one, no matter what his crimes, would deserve sempiternal punishment. To make this a bit more precise we ought to substitute 'sin' for 'crime.' They are different concepts. Sin, but not crime, implies an offense to God. If there is no God then there cannot, strictly speaking, be any sin. But there could still be crime relative to an accepted body of positive law. And if there is no positive law, but there is a God, then there could be sin but no crime. (Positive law is the law posited by human legislators.)

So let us say that the punishment must fit the sin. My claim, then, is that no sin or sins committed by a human agent is such as to merit sempiternal punishment. To put the point more sharply, a God who would condemn a finite human agent to unending misery is a moral monster, and not God. (I am assuming that the agent in question has come to admit the error of his ways and is truly sorry for them. I have no problem with the unending misery of a recalcitrant rebel.)

In response, Leo Mollica said that the offense to God, as an offense to a being of infinite dignity, is itself infinite and so deserves sempiternal punishment. This prompted me to ask how an impassible God could be offended, which is the topic of this post.

Impassibility. To say that God is impassible is to say that nothing external to God can affect God. As Brian Leftow points out in his SEP article, impassibility is not the same as immutability. He gives two reasons, but all we need is one: a God who induces a change in himself is not immutable but still could be impassible. Now if God is impassible, then he cannot be offended by the antics of the Israelites as when they fell to worshipping a golden calf, etc. He cannot be offended by sin. And if he cannot be offended by sin, then he cannot be 'infinitely' offended by it. Or so I maintained.

In response Mollica made a clever move. He pointed out, rightly, that a person could be offended (wronged, slandered, calumniated, etc.) without knowing that he is. Such a person would be offended without being affected. I took the suggestion to be that God too could be offended without being affected. Thus impassibility does not rule out God's being offended.

To this my reply was that God is omniscient. He knows everything there is to know. So although it is true that a finite person could be offended without knowing it, and so not affected by the injury that was done to him, God could not be offended without knowing it. Good Thomist that he is, Mollica came back at me with the notion that God is not affected by what he knows. So when the creature sins, God is offended; but his being offended in no way affects him: he is not affected 'cognitively' by his knowledge that he is being offended, nor is he affected or injured 'morally' by his being offended.

Very interesting, but very problematic, as problematic as the Thomist line on divine knowledge. If God is God, then he must be a metaphysical absolute and the pressure is on to say that he is both impassible and immutable. (An immutable being is one that cannot undergo 'real' as opposed to 'mere Cambridge' change.) After all, a decent absolute is not the sort of thing that could change or be affected by other things. If it underwent change or affection it would be relativized. But how could such an unchanging God know anything contingent? If God is unchanging, then his knowledge is unchanging: it cannot vary over time, or from possible world to possible world. Here is an argument adapted from Hartshorne.

1. If p entails q, and q is contingent, then p is contingent.
2. *Tom sins at time t* is contingent.
3. *God knows that Tom sins at t* entails *Tom sins at t*.
Therefore
4. *God knows that Tom sins at t* is contingent.
Therefore
5. The property of knowing that Tom sins at t is an accidental (not essential) property of God.
6. God has no accidental properties: it is no part of his unchangeable essence that he know any contingent fact, any fact that could have been otherwise.
7. (5) and (6) are contradictories. So one of the premises must be rejected. (6) is the premise most plausibly rejected; but then impassibility and immutability go by the boards.

The challenge for our resident Thomist is to explain how an impassible and immutable God can know any contingent fact.

Posted

May 24, 2011

Aquinas and Thomism, God, Heaven and Hell

Bill Vallicella

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Comments

51 responses to “How Could an Impassible God be Offended or Know Any Contingent Fact?”

Steven

May 24, 2011

I imagine the response will be something along these lines.
God knows his will, and by his will he brings it about that *Tom sins at time t1*. God’s will could have been otherwise, and thus the proposition is contingent; but this is not contrary to divine immutability, since for Aquinas immutability meant that God could not be affected within the actual world, not that he could not be different across possible worlds. (Cf. Eleonore Stump, Aquinas, ch. 3)

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Gian

May 24, 2011

God loves man so how he can be offended?.
Mr Vallicella, you need to decide what kind of God you are considering. A Christian God or a Hindu or Muslim God.

Reply
Bill Vallicella

May 25, 2011

Gian,
I’m sure you’re a nice person, but it is clear that you lack the intellectual equipment, or perhaps the training, to participate in these discussions. You obviously don’t have a clue as to what Mollica and I are discussing.

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Ben Yachov

May 25, 2011

“How can a Classical Theistic God (who on the level of natural philosophical theology is near identical to the Christian, Jewish and Muslim God and maybe some schools of Hinduism) be offended?” is the real question.
But do we mean “offended” in the unequivocal sense or the analogous sense?
Since God in the Classic Sense is not an anthropomorphic entity. It’s not Gian’s he wasn’t first explained the difference between a Classic Deity vs the Theistic Personalist kind.

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Steven

May 25, 2011

Ben Yachov,
“Offended,” in any ordinary understanding of the word, implies a negative response to some event or occurrence that did not occur because of the intentions of the offended agent. It makes no sense to say that x is offended by A when x is unaffected by A in any way, including remaining ignorant of X, and furthermore, it makes no sense to say that x is offended by A if A is something x intended; at least, in a perfectly rational being, that being would not do anything that would offend itself.
Now how exactly is the “offense” of the God of classical theism supposed to be analogous to “offense” in its ordinary sense? What exactly is it that occurs in God that is analogous to this analysis of “offense”? It seems neither of the crucial aspects of “offense” can apply in any form to God.

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Marius Manci

May 25, 2011

Let’s suppose that God shares the following properties:
– immutability
– impassibility
-omniscience
-omnipresence
The first two properties (namely immutability & impassibility) render a God who is not affected by anything external. The third property entails that God knows/is aware of everything; now as you suggested, regardless of Its knowledge with regards to the external sphere(our world) God is not/or at least should not be affected/nor offended.
However the fourth property seems to indicate the problematic area: if God is omnipresent then evidently God’s nature encompasses this world as well as every possible world; thus the dichotomy ‘God vs external sphere’ does not seem as a valid one anymore. The world/’external sphere’ is immanent in God’s nature and no longer outside Its nature. If so, then God indeed could be offended (not moved) by things that God knows from within.
Certainly this raises a whole new conundrum: if the contingent nature of this world is immanent in God’s nature, doesn’t that entail that God’s nature is contingent? We certainly know that such thing cannot be, but then we are still left to decipher how God interacts with this world. The immediate analogy that comes to mind is for an individual to have a stomachache. The stomachache is temporary and slowly fades away whereas the individual persists beyond the stomachache. In this case the stomachache represents a contingent fact whereas the individual symbolizes God. (I hope I haven’t fallen into the category of anthropomorphizing God, but perhaps at times we need contingent models to make sense of that which is above).

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Ben Yachov

May 25, 2011

>it makes no sense to say that x is offended by A if A is something x intended; at least, in a perfectly rational being, that being would not do anything that would offend itself.
I deny God is a being alongside other beings. No such “God” exists as far as I am concerned. Thus your question makes no sense to me.
God is Being Itself and not an Anthropomorphic entity. I wonder if these questions presuppose a Theistic Personalist deity?

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Marius Manci

May 25, 2011

Ben-notice Mollica (see above) maintains this:’God too could be offended without being affected..’
If so, Mollica seems to describe a deity akin to “Personalist deity’.
“it makes no sense to say that x is offended by A if A is something x intended; at least, in a perfectly rational being, that being would not do anything that would offend itself.I deny God is a being alongside other beings. No such “God” exists as far as I am concerned. Thus your question makes no sense to me”.
I concur! However given the above properties (the aforementioned 4 properties) this is the odd conclusion that such properties lead us to(as I’ve explained). Given such odd conclusion, illogical even, then perhaps we need to identify what sort of properties God could possibly have in order for such a conclusion to be avoided. Indeed perhaps we need to either (a) get rid of the property Omnipresent altogether or (b) redefine Omnipresence in such a way as to avoid the immanence notion.

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Steven

May 25, 2011

>> I deny God is a being alongside other beings. No such “God” exists
>> as far as I am concerned. Thus your question makes no sense to me.
>> God is Being Itself and not an Anthropomorphic entity. I wonder if
>> these questions presuppose a Theistic Personalist deity?
I know you think God is being itself. My point was that there is no sense in saying that being itself could possibly be offended by anything — “offense” makes no sense to attribute to being itself.
When the Bible says God is offended, and you say God is being itself and that the Bible is speaking metaphorically or analogically, what exactly is going on? For, to repeat my original argument, neither of the two elements of “offense” seem to be in any way applicable to being itself.

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Ben Yachov

May 25, 2011

Steven,
When the Bible says God will enfold us in His wings I don’t for a second believe God is a giant meta-Chicken.
I’m not certain what it means to be metaphorically or analogously offended since I would have look up what Aquinas said. But I do know “offended” is not to be understood unequivocally here anymore than God can be said to literally have wings.
That is the necessary starting point to answer this question. I’m just pointing it out there.

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Ben Yachov

May 25, 2011

>>I know you think God is being itself.
But your original comment (a perfectly rational being) suggests you are only familiar with a Theistic Personalist concept of God.
Do you really know the difference?

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Ben Yachov

May 25, 2011

The concept of “offended” is not clearly defined. Are we saying God “feels outrage” when His Will is transgressed by Free Will beings he created? How can that be? God has no emotions.
I lack the philosophical sophistication to express it but my gut tells me this is on the same level as Stephen Law’s evil God challenge.
We have questions being asked here about an Anthropomorphic personalist deity in the tradition of Plantinga or Swinburne. But such questions might be incoherent when applied to a Classic Deity.
Offended likely doesn’t mean God feels slighted when analogously applied to Him.

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Leo Carton Mollica

May 25, 2011

Goodness, am I flattered! I do hope that I can continue to meet the high expectations that accompany being your “resident Thomist.” 🙂
A first thought upon reading this post was that I could not see that your argument succeeded in establishing the desired conclusion, and that on two grounds. First, we cannot infer from (3) as it stands that (God knows that Tom sins at t) is contingent, for it is not the case that CKCpqKMqMNqKMpMNp (hooray for Polish notation!). Proof: from a contradiction, anything follows; moreover, any contradiction is necessarily false and thus not contingent. Therefore, while it is contingently true that Leo blogs, and while Leo’s blogging follows from Bill Vallicella both blogging and not blogging, it is not contingent that Bill Vallicella both blogs and does not blog. So we must either qualify (3) so as to make the inference valid (say by making God’s knowing that Tom sins at t and Tom’s sinning at t logically equivalent) or import some further premise.
A second possible objection is that (5) and (6) equivocate on “property”: it may mean either the “Cambridge” or “real” variety. Since only on the “real” construal am I obliged to accept (6), (5) must, if the argument is to succeed, be given a “real” construal as well, and that such an interpretation is the correct one has not been established by the argument. Nevertheless, it is a rather plausible principle that knowledge of p is always a real property, so the burden is on me to explain how God can know something contingent without having that knowledge constitute a real Divine property.
Briefly and tentatively, my position is something like follows: God has a complete understanding of Himself (I won’t go into my reasons for this here, but I will if you press me), and in understanding Himself understands any creature to the extent that it falls within the scope of the Divine power to effect, has its proper perfection as preexisting in the Divine Essence, and participates in the Divine actuality. For if God did not understand them thus, He would not fully understand His power, Essence, or actuality. But all three are identical, by the Divine Simplicity, with God Himself; therefore, on the supposition that God understands none of them completely, He fails to understand Himself completely, which I have already rejected. Note, though, that none of this commits me to saying that God takes on creatures as intentional objects: the only intentional object in this act of understanding is God Himself.
An analogy inspired by Barry Miller: suppose that I will to walk to my local church along a stretch of sidewalk with squares A, B, C… Y, and Z. In a way, I really do intend to walk over A, B, C, etc. Someone could truthfully say of me, “he means to walk over Y.” Now suppose that, as I am walking, Y miraculously vanishes. In that case, I no longer mean to walk over Y, it is no longer part of my intention to do so, since it is no longer on the path to my church. But surely, as I am on my way, my volitional state does not (really) change: it is the same as it was before, even though it has ceased to extend to walking over Y. Since I only ever willed to walk over Y qua falling under the scope of my intention to walk to church, and since God only ever understands a contingent entity qua participating in His actuality, a change in Y or in creatures need not signal a change in God’s cognitional state.
Tell me if this all makes sense.
A further point: I don’t see that, in order for God to know all things, He must know, for any proposition p, that p. This seems to imply that God’s cognition is propositional, which it need not be (God could know through intuition or understanding, the way we know the meaning of a term, which precedes our use of the term in assent to propositions) and indeed seems repugnant to the Divine simplicity (since propositional knowledge requires distinct understandings of all the terms used in a proposition). For Aquinas’ treatment of the matter, see here.

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Leo Carton Mollica

May 25, 2011

Hm… I’m not entirely satisfied with that comment. Please tell me where you’d like me to clarify.

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Steven

May 25, 2011

>> But your original comment (a perfectly rational being) suggests you
>> are only familiar with a Theistic Personalist concept of God.
>> Do you really know the difference?
Trust me when I tell you, I am aware of the difference.
>>The concept of “offended” is not clearly defined. Are we saying God
>> “feels outrage” when His Will is transgressed by Free Will beings
>> he created? How can that be? God has no emotions.
>> I lack the philosophical sophistication to express it but my gut
>> tells me this is on the same level as Stephen Law’s evil God
>> challenge.
>> We have questions being asked here about an Anthropomorphic
>> personalist deity in the tradition of Plantinga or Swinburne. But
>> such questions might be incoherent when applied to a Classic
>> Deity.
>> Offended likely doesn’t mean God feels slighted when analogously
>> applied to Him.
The question then remains, what could it possibly mean? Is it nonsense altogether, in which case the Bible is evidently mistaken and metaphysically inadequate; or is it some kind of analogous statement, in which case, how on Earth could it possibly be analogous? If there is not anything like being slighted, not anything like a reaction, then how could it be anything like being offended?

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Ben Yachov

May 25, 2011

Are we discussing the Bible or Natural Theology? Plus whose interpretation of the Bible? Some neo-Evangelical Theistic Personalist interpretation or the correct interpretation of the Catholic Church?
>Trust me when I tell you, I am aware of the difference.
I don’t doubt your sincerity but at this point I am skeptical you understand the difference.
>Is it nonsense altogether, in which case the Bible is evidently mistaken and metaphysically inadequate; or is it some kind of analogous statement, in which case, how on Earth could it possibly be analogous?
Might I suggest studying Aquinas’ doctrine of analogy?
>If there is not anything like being slighted, not anything like a reaction, then how could it be anything like being offended?
Well I do know God’s “anger” is really nothing more than His Will to Justice. It’s not the literal unequivocal emotion you might feel when you learn someone willfully ran over you cat.
So God is only “Offended” in an analogous sense. Thus Bible verse that talk of His being offended should not be understood to say God is feeling a literal emotion. Anymore than God is a giant Chicken because it speaks of God’s “wings”.
It’s not hard. Go look up the Summa Contra Gentiles on how God doesn’t hate anything for a further explanation.

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peterlupu

May 25, 2011

An *offense* can be said to have occurred against a person or against a law. It seems most of this discussion steered toward assuming that a sin is a direct offense against God as a person. But why can’t the solution be that a sin is only a direct offense against a law. One might think of this as follows.
God established a moral order expressed by means of laws which humans are required to follow on pain of a pre-established punishment. Thus, offense against the laws commanded by God (i.e., a sin) carries a punishment (either finite or infinite) that has been determined in advance. A sin, therefore, is a direct offense against the laws and is not a direct offense against God. One might then view an offense against the laws as affecting the pre-established moral order commanded by God. But a violation of this pre-established order is not a direct offense against God and, therefore, it does not violate the impassibility doctrine.
What about Bill’s problem of an *infinite* punishment for a *finite* offense against God’s laws?
First, let us remember that we must distinguish the finite/infinite categories within time and outside of time. So it is not clear that a *finite* sin that occurs within time is commensurable or not commensurable with an *infinite* punishment that takes place outside the boundaries of time. (I am assuming that if punishment occurs, it occurs to the soul which transcends beyond the temporal world). Thus, the measure of a *finite* sin may very well be isomorphic in some way to *some* infinite ordinal outside of time.
Second, and related, as you all know there are different kinds of infinity: e.g., while the set of even numbers is infinite, it is contained within the set of natural numbers. So in some sense the later is *larger* than the former. And then of course there is a significant difference between alpha-zero infinity (i.e., the cardinality of the natural numbers) and the cardinality of the power set of the natural numbers. So there could be an infinite punishment that is isomorphic to the (lets say) the even numbers, but it is not isomorphic to the infinity of the natural numbers or their power set. Thus, if you will, we can say that the punishment is infinite but it does not last *forever*, where ‘forever’ is a metaphor that means that while the soul endures an infinite amount of time in punishment, it exists an even larger infinite amount of time w/o punishment.

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arash

May 26, 2011

I think Steve made a good point in his first post: “mutability” has to do with time within the actual world and not with modality across possible worlds. Bill could you please clarify a bit more on this?

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arash

May 26, 2011

Peter you said “So it is not clear that a *finite* sin that occurs within time is commensurable or not commensurable with an *infinite* punishment that takes place outside the boundaries of time.”
While Bill’s assumption was: “If the punishment must fit the crime, and the crimes of finite agents are themselves finite, then it would seem that no one, no matter what his crimes, would deserve sempiternal punishment.”

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peterlupu

May 26, 2011

arash,
I thought that my statement which you quoted was an answer to Bill’s problem which you quoted.

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Bill Vallicella

May 26, 2011

Peter,
Sin by definition is an offense against God. One cannot sin against an abstract moral principle or a positive law. That is what both Mollica and I are assuming and it is part of the problem. The problem is to explain how a God who is assumed to be impassible can also be offended. My point was that if God is offended, then he is affected, which violates impassibility. Mollica’s point is that talk of God’s being offended, and also talk of God’s being aware that he is offended, can be upheld without violation of impassibility.
That and nothing else is the issue under discussion.
This is distinct from the earlier question of how an all-good God could condemn a human agent to sempiternal punishment.
Let’s drop ‘finite’ and ‘infinite’ to avoid vagueness and confusion. Stalin murdered millions. Do you think he deserves sempiternal post-mortem punishment?

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peterlupu

May 26, 2011

Bill,
“Sin by definition is an offense against God.”
First, if a definition leads to an inconsistency or contradicts some other doctrine (e.g., impassibility), then perhaps one should consider the possibility that it is an inadequate definition and propose to change it.
Second, you say: “One cannot sin against an abstract moral principle or a positive law.”
But surely a violation of one of the ten commandments is a sin. Yet the ten commandments are neither “abstract moral principle(s)” nor are they “positive law(s)”. Since they are laws commanded by God they are not mere “positive law”, where the later is understood as based upon social conventions. And since the ten commandments were delivered to Moses in a very specific form (at least according to the Old Testament), they are not mere abstractions. They are specific and concrete divine commands based upon the authority of God.
Thus, I suggest that there cannot be a sin without a violation of divine command. Divine command in turn rests upon divine authority. Hence, a sin is an offense against God’s divine authority. But, surely, no one suggests that an offense against divine authority somehow alters or in any way diminishes such authority. And if it does not, then there is no basis to claim that a sin causes any change in God or any of his attributes. I have not seen an argument to the contrary.
Third, the term ‘offense’ is ambiguous between: (a) insult; (b) violation of a command or law. Surely, you do not mean (a) in the present context. Hence, it can only mean (b). But, then, to say that a sin offends against God just means what I have outlined above. What else could it mean?

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Bill Vallicella

May 26, 2011

Peter,
I’m afraid you are missing the point. Mollica takes sin to imply an offense against God. I am granting that to him and then asking him how an offense against God is consistent with divine impassibility.

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Bill Vallicella

May 26, 2011

Arash writes, >>I think Steve made a good point in his first post: “mutability” has to do with time within the actual world and not with modality across possible worlds. Bill could you please clarify a bit more on this?<< Properly speaking, change or mutation is within the actual world, not across possible worlds. But I'm not sure Steven understood the argument. The question is whether there is any contingency in God. God knows that elephants exist. 'God knows that elephants exist' entails 'Elephants exist.' But 'Elephants exist' is contingent. So 'God knows that elephants exist' is also contingent. Now what is the truth-maker in God of 'God knows that elephants exist'? It must be something contingent and intrinsic to God. But then God has accidental properties, which contradicts his identity with his nature.

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Bill Vallicella

May 26, 2011

Leo,
I’m not following you. Are you questioning the validity of this subargument:
1. If p entails q, and q is contingent, then p is contingent.
2. *Tom sins at time t* is contingent.
3. *God knows that Tom sins at t* entails *Tom sins at t*.
Therefore
4. *God knows that Tom sins at t* is contingent.
I hope not!

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peterlupu

May 26, 2011

Bill,
” Mollica takes sin to imply an offense against God”
Well, then, his concept of ‘sin’ requires explanation, for I do not understand what that means other than what I have stated in my posts.

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Steven

May 26, 2011

Bill,
>> The question is whether there is any contingency in God. God knows
>> that elephants exist. ‘God knows that elephants exist’ entails
>> ‘Elephants exist.’ But ‘Elephants exist’ is contingent. So ‘God
>> knows that elephants exist’ is also contingent. Now what is the
>> truth-maker in God of ‘God knows that elephants exist’? It must be
>> something contingent and intrinsic to God. But then God has
>> accidental properties, which contradicts his identity with his
>> nature.
I pointed out that some (e.g., Stump, op. cit.) have interpreted Aquinas to allow that God have contingent aspects to his nature, because for Aquinas, an accident is not merely a feature of a thing that it has contingently (in our language of possible worlds), but some aspect or feature of him that has incomplete or imperfect being. If that is contrary to God’s identity with his nature, or whatever, that is another question; your question was how would Leo the Thomist respond to the problem of contingent aspects of God’s being, and I pointed out a Thomist who allows for contingent aspects of God’s being.
Peter Laughlin in his “Divine Necessity and Created Contingence in Thomas Aquinas,” The Heythrop Journal (2009), 648-657 interprets Aquinas the same way. He says:
>> Since God is eternal, divine knowledge has the characteristic of
>> eternality and therefore God apprehends each successive temporal event
>> in the eternal now. In such a case all contingent events are fully known
>> by God because God sees them all at one and the same time. It must be
>> pointed out though that God’s knowledge of these events, while immutable
>> in the sense that it cannot change over time, does not inevitably
>> include the requirement to be immutable across all possible worlds. This
>> simply means that if things in the world had been different, then God’s
>> knowledge of them would have been different as well; hence in a
>> different possible world, God would know something different from what
>> God knows in this world. Thus there is no need in this view of God’s
>> knowledge to require that creatures do not have the ability to do other
>> than they do in every possible world (p. 653).
If all this is incompatible with God’s being identical to his act, then that is a problem with divine simplicity, not immutability/impassibility.

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peterlupu

May 26, 2011

Bill,
It seems to me that the following is false:
“1. If p entails q, and q is contingent, then p is contingent.”
Consider the following counterexample. Let ‘p’ be ‘Bill=Bill’ and ‘q’ be ‘(Ex)(x=Bill)’.
(Bill=Bill) entails ((Ex) x = Bill).
Now, ‘(Ex) x = Bill’ is contingent and it is entailed by ‘Bill-Bill’. But the later is not contingent, but necessary. Therefore, (1) has a counterexample.

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Steven

May 26, 2011

Peter,
I don’t think that is right, unless *Pegasus = Pegasus* entails *(∃x)(x = Pegasus)*.
Indeed, if p entails q, that just means that p could not be true if q is false. So how could p be necessary, and hence always true, and q contingent, and hence sometimes false?

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Bill Vallicella

May 26, 2011

Peter,
Very interesting! I understand ‘entails’ as follows:
p entails q =df there is no broadly logical possible world in which p is true and q is false.
Your counterexample requires that ‘Bill’ be a nonvacuous name, one that has an existing referent. But then ‘Bill = Bill’ is short for ‘Bill = Bill & (Ex)(x = Bill)’ which is contingent.
Or else, as Steven points out, you are committed to saying that the self-identity of Pegasus entails the existence of Pegasus.
(1) is a well-known principle of modal logic, so I’d be very surprised if it has a counterexample.

Reply
Leo Carton Mollica

May 26, 2011

Dr. Vallicella,
Like Mr. Lupu, I take issue with (1), since it seems to run afoul of the following argument:
1. Necessarily, it is false that p & ~p.
2. If necessarily, it is false that q, then it is not contingent that q.
3. From a contradiction, anything follows.
4. Let r be a contingently true proposition.
5. If p & ~p, then r. (3, 4)
6. That p & ~p entails a contingently true proposition. (4, 5)
7. That p & ~p is not contingent. (1, 2)
8. p & ~p entails a contingently true proposition and is not contingently true. (6, 7)
If I’m committing a fallacy somewhere, I can’t see it and would appreciate your pointing it out. (I overlooked (1) the on the first read-through of your argument and thought you were just tacitly assuming it. Sorry for the carelessness.)
Mr. Lupu:
“Well, then, his concept of ‘sin’ requires explanation, for I do not understand what that means other than what I have stated in my posts.”
Roughly, I mean some act or omission that violates, or affronts, or otherwise offends against God’s dignity, i.e. His worthiness of respect and honour. Examples of ordinary, non-supernatural such offences would include slander, libel, contempt, etc. against someone who deserves to be respected. Does that help?

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Jan

May 26, 2011

Leo,
Your counterexample is correct. It is easy to amend 1.:
1*. If p entails q, and q is contingent, then p is either contingent or impossible.
This does not however substantially change the argument. Logically, God’s knowledge of the existence of elephants is either contingent or nonexistent. The latter option is rejected for obvious reasons.

Reply
Bill Vallicella

May 26, 2011

Leo,
You’re a smart guy! That is a valid argument. Well done. But as Jan — another smart guy — points out, (1) is easily amended. His (1*) should now be above all possible reproach.

Reply
peterlupu

May 26, 2011

Bill,
I see your point. But still the assumption that ‘Bill’ is non-vacuous cannot render ‘Bill = Bill’ contingent. If all singular identities of the form ‘a = a’ (when ‘a’ is referential) are contingent, then Frege’s puzzle evaporates, for then there is no difference in the content of ‘a=a’ and ‘a=b’, when the later is true.
Moreover, to say that “‘Bill’ is non-vacuous” is equivalent to (Ex)(‘Bill’ refers to x), not to (Ex)(Bill=x). While the former is a meta-linguistic statement, the later is an object language statement.
Steven,
Regarding your Pegasus example, existential generalization in first-order classical logic assumes that the terms affected by the generalization are non-vacuous and the quantifiers are objectual (this assumption may not be in force in Free-Logic or in systems that include substitutional quantification). Therefore, these assumptions rule out your Pegasus example.

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Bill Vallicella

May 26, 2011

Steven,
Thanks for the Loughlin quotation which helps. He speaks of God’s knowledge as not being immutable across possible worlds. But surely God’s nature is immutable across possible worlds. So if God = God’s nature, and God’s knowledge is part of his nature (because everything is as he wills it), then how is contingency in the world possible?

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Jan

May 27, 2011

Peter,
Your counterexample purports to show there is a necessary proposition that implies a contingent one. First, note that the counterexample would be invariant on which possible world is the actual world. This is because the modal status of a proposition is invariant across the possible worlds. But there is a modal symmetry between Pegasus and Bill in the sense that there is a possible world in which B exists and P does not, and a possible world in which P exists and B does not. From this it follows that if the Bill counterexample works, then the Pegasus one, which you sensibly reject, works too.
Both arguments are I think question begging. You rightly say: “existential generalization in first-order classical logic assumes that the terms affected by the generalization are non-vacuous and the quantifiers are objectual”. If your argument is to be construed as a modal one, this must be true across all the possible worlds, and not only in the actual world. In other words, (Ex)(x = Bill) must be necessary.
Dr. Vallicella,
(1*) is certainly beyond reproach logically. Contingency of q means there’s a possible world in which q is false. But p => q, therefore p must be false in this world too. That is, p is either false in all worlds (impossible) or only in some worlds (contingent).

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peterlupu

May 27, 2011

Jan,
Good talking to you again.
“…there is a modal symmetry between Pegasus and Bill in the sense that there is a possible world in which B exists and P does not, and a possible world in which P exists and B does not.”
First, I deny that there is a symmetry between Steven’s Pegasus case and the case of Bill. In this I follow Kripke who maintains that there is no possible world in which Pegasus exists, whereas there are some possible worlds in which Bill exists and others in which he does not.
Second, consider another counterexample to both Bill’s (1) as well as your (1*). I=I entails (Ex)(x=I). Yet while ‘I=I’ is necessary, (Ex)(x=I) is contingent. Hence, both (1) as well as (1*) are false. Incidentally, the same goes for ‘You’, other indexical expressions, and identities involving rigid terms.
I suppose one could save (1*) by simply exempting identities from its scope.
Bill, Jan,
Going back to Bill’s original claim. Let P be any contingent proposition and w* the actual world. Bill’s original argument was this:
(a) God knows that P entails P.
Since P is contingent, so must be God knows that P by a modified (1*). But since propositions of the form ‘God knows that …’ are necessary regardless of what proposition is inserted in the ‘…’, we have a problem.
The problem I suspect is with the formulation of (a). Consider the following alternative formulation of (a):
(a*) God knows that P-is-true-in-w* entails that P is true in w*.
But the proposition ‘P is true in w*’ is true in every possible world. Or to put it in other words: if ‘P is true in w*’ then ‘possible-P’ is true in every possible world. Hence ‘P is true in w*’ entails: necessarily it is possible that P (at least in S5.)
So the solution to Bill’s problem is that we simply cannot say that God knows a proposition without indexing the proposition to the world in which it is true. Once the proposition is so relativized, then what God knows is that some proposition is possible. And this entails that it is necessarily possible (in S5). So far as I can see this would solve Bill’s problem (unless I made a mistake in my modal logic).

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peterlupu

May 27, 2011

Leo,
(Peter will do.)
Consider a simple case where a person A insults, libels, slanders, or has contempt for B. We are assuming that ‘libel’ and ‘slander’ are not considered here as legal terms. The question is this: Does A’s insulting (slandering, etc.,) B causes a change in B? Not necessarily.
If such insult causes a change, then such a change can only be of two kinds: (a) B’s social status changes (e.g., his reputation is diminished, etc.,); or (b) B undergoes a psychological change (e.g., he gets angry, irritated, hurt, offended, slighted, etc.)
However, suppose that no one who hears A’s insult cares about it. Then no social change occurs. Moreover suppose that B himself is immune to insults: i.e., he simply does not care. Then B’s psychological states do not change at all. Hence, an insult etc., need not cause any change in the one insulted.
Now, if B is God, then the case against an insult causing a change is considerably strengthened. First, clearly a change in the social status of God, even if an insult causes such a change, is not a change in God. Therefore, cases of the type (a) do not apply.
Secondly, if anyone can be psychologically immune to such things as insults, God can; and I maintain God must be immune. Therefore, insults do not cause any change of type (b) in God either. The same holds for slander, libel, contempt and other such *feeble-sins*. Therefore, I do not see what sort of change such *feeble-sins* are supposed to cause in God. So unless you come up with an alleged change that is not already included in (a) or (b), I do not see how any of the action types under consideration can cause a change in God.
Moreover, as I pointed out in previous posts, a sin that means a moral violation of a command is not a violation of God (whatever that might mean) and, hence, is not a change in God. Rather it is a violation of a law commanded by God, which does not imply a violation of God and, hence, a change in him.

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Jan

May 27, 2011

Peter,
Good talking to you too! I claim to have proved (1*) in the last paragraph of my previous comment (the implicit definition of implication being ‘p implies q iff in every possible world in which p is true q is true also’). If you’d rather avoid the semi-formal language of possible worlds, here’s a proof using axioms of modal logic:
A1 (Distribution Axiom): ( Nec(p => q) ) => ( Nec(p) => Nec(q) )
T1: ( Nec(p => q) ) => ( ¬Nec(q) => ¬Nec(p) )
T2: ( Nec(p => q) ) => ( Pos(¬q) => Pos(¬p) )
T2 is exactly (1*). Do you agree with this?
I also think I gave a reason as to why your argument is not in fact a counterargument to (1*). For the argument to be a modal one, the antecedent must have meaning across all the possible worlds. That is, ‘Bill = Bill’ must be meaningful in all the possible worlds, which is equivalent to ‘Bill exists in every possible world’. A very similar argument was already given by BV.

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peterlupu

May 27, 2011

Jan,
I do not challenge the argument for (1*). I only point out that it has counterexamples involving necessary identities. Therefore, the best remedy is to exclude from the scope of (1*) such identities.
“That is, ‘Bill = Bill’ must be meaningful in all the possible worlds, which is equivalent to ‘Bill exists in every possible world’.”
‘Bill=Bill’ is *meaningful* in every possible world. Moreover, it is even true in every possible world in which Bill exists. And so is ‘I=I’, and so on for other indexicals and rigid designators.
Consider the following axiom of identity. (x)(x=x). Clearly this is necessary. But then so is every logical consequence of this axiom for every referring term. Thus, if ‘a’ is a referring term, then ‘a=a’ is necessary in every possible world in which a exists. Hence, so is (Ex)(x=a). The provision that ‘a’ refer is not a problem, for such a provision will hold in one form or another for every category of terms. The only remedy I can see is to exclude identities from (1*). O/w so far as I can see it has counterexamples and it is false.

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Leo Carton Mollica

May 27, 2011

Peter,
I am somewhat confused by your comment: I have never claimed that offence against God induces a real change in Him; indeed, my denial of this position sparked this post! It is, however, by my lights trivially true that if I at t do not offend against God and at a later time t* do so offend, I have induced a Divine Cambridge change: God has acquired the property of being-offended-against-by-Leo.
Dr. Vallicella and Jan,
I agree that, pace Peter, 1* is logically sound. Nevertheless, we cannot derive Dr. Vallicella’s desired contradiction unless we introduce some further premise, say
1.1. It is possible that God knows that Tom sins at t, or more strongly
1.2. God knows that Tom sins at t.
Both premises, however, I deny on the grounds that, as far as I can see, they require that God (possibly) know propositionally, which I deny on the grounds that propositional knowledge introduces propositions into the intellect, that propositions are complex entities (as you yourself admit), and thus that their introduction into the Divine intellect is repugnant to the Divine simplicity.

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Leo Carton Mollica

May 27, 2011

Peter,
Another point: I have in the course of this discussion made no use of Divine commands. I do not think we need have recourse to them if we are to provide a general account of sin.

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peterlupu

May 27, 2011

Leo,
“I have never claimed that offence against God induces a real change in Him; indeed, my denial of this position sparked this post!”
Great! Then I do not see how a sin can violate impassibility; i.e., violate the principle of no change in God. For if a sin is an offense and an offense only induces so-called Cambridge-change, which is not a real change, then we do not have a problem at all.
“I have in the course of this discussion made no use of Divine commands. I do not think we need have recourse to them if we are to provide a general account of sin.”
I do not see how an account of sin; meaning a moral violation, can avoid making use of divine commands. Perhaps, you simply mean something else by ‘sin’. So, perhaps, you can elaborate on this point.

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Jan

May 27, 2011

Peter,
If I understand you correctly, you’re saying that while the proof of (1*) is correct, it still admits counterexamples. Such a thing is not possible in the category of mathematics (to which the proof belongs). Either there is a mistake in the proof, or the counterexample is only apparent. Please note that the proof did not exclude identity statements from its scope.
The following are the only options:
1. ‘Bill=Bill’ is not meaningful in some possible world.
In this case, your argument fails as I argued before. You have already rejected (1).
2. ‘Bill=Bill’ is meaningful in every possible world.
In this case, your argument needs to be amended lest it falls to Pegasus-like counterexamples, as I argued in one of my previous posts. The valid implication is I think:
C*: (O=O) entails ( Pos ((Ex) x = O) ).
That is, the conclusion is not that there is O, but that there is a possible world w in which there is O. This argument is immune to Pegasus-style counterexamples, at the cost of making the consequent a necessary proposition. Note that for the P-s counterexample to work it suffices that one object exists in some possible world w but does not exist in the actual world w*. Do you deny there is such an object?
“‘Bill=Bill’ is *meaningful* in every possible world. Moreover, it is even true in every possible world in which Bill exists.” Do you imply it is false in worlds in which Bill does not exist? If so, you’ve conceded that the antecedent is not necessary. Or is ‘Bill=Bill’ true in a world where Bill does not exist? In that case, the antecedent is true, but the consequent false and the implication fails to hold. I rest my case.
Leo,
I spoke too hastily indeed when I said “[the impossibility of God knowing p] is rejected for obvious reasons”. In fact, there is a very good argument to the effect that one cannot quantify over (true) propositions, which in turn makes the definition of omniscience as knowledge of all true propositions incoherent.

Reply
Leo Carton Mollica

May 27, 2011

“Great! Then I do not see how a sin can violate impassibility; i.e., violate the principle of no change in God. For if a sin is an offense and an offense only induces so-called Cambridge-change, which is not a real change, then we do not have a problem at all.”
Neither do I, but Dr. Vallicella thought plausible arguments could be given against such a view, so he wrote this post asking that I respond to it. I’m glad to know that we agree 🙂
I do not see how an account of sin; meaning a moral violation, can avoid making use of divine commands. Perhaps, you simply mean something else by ‘sin’. So, perhaps, you can elaborate on this point.
I do mean by “sin” a moral violation, or at perhaps such a violation insofar as it is contrary to our proper relation to God, and I don’t see why we need Divine commands to make sense of it. Even on the supposition that my upright, hard-working, benevolent father has never commanded that I do not viciously mock, slander, and defame him in the company of my friends (indeed, even on the supposition that nobody has commanded this of me), so acting is a wrong against my father. It is contrary to his dignity.
So, why would Divine commands be necessary?

Reply
peterlupu

May 27, 2011

Jan,
I have given three counterexamples against (1*) (We are now assuming that your (1*) replaced Bill’s original (1)):
(a) Bill=Bill;
(b) I=I; for the indexical ‘I’,
(c) (x)(x=x).
CE (a) had to do with proper names; CE (b) with indexicals; and CE (c) with a universal statement. I could have given one with rigid natural kind terms a la` Kripke, e.g.,
(d) water=H2O; which if, true, is necessarily true. Yet it entails the contingent proposition ‘there exists a substance X such that X is identical to water’.
And here is another one:
(e) God=God.
CEs (a), (b), and (e) follow from the necessary proposition (c) by instantiation. Do you deny this? I don’t think you can. If you do not, then in each case a necessary proposition entails a contingent one. This is a clear refutation of (1*).
Re: Your argument: “If I understand you correctly, you’re saying that while the proof of (1*) is correct, it still admits counterexamples. Such a thing is not possible in the category of mathematics (to which the proof belongs). Either there is a mistake in the proof, or the counterexample is only apparent. Please note that the proof did not exclude identity statements from its scope.”
Indeed! However, your proof belongs to propositional modal logic and not to quantified modal logic plus identity. Surely, you admit that the scope of quantified modal logics plus identity is broader than propositional modal logic. Thus, your proof is not sensitive to the subtleties of logic once identity and quantification is taken into account.
For instance, let Fa=P and (Ex)(Fx)=Q. From the point of view of propositional logic alone, P does not entail Q. From the point of view of quantification theory, P (i.e., ‘Fa’) does entail Q (i.e., ‘(Ex)(Fx)’). Are we to say that we have here a contradiction? We certainly do not say that. So my point is that (1*) is correct only for propositional modal logic and not for quantified modal logic plus identity.
Moreover, if even one item on the list (a)-(e) holds, then you got a counterexample to (1*). Since all items on the list involve identity the only solution I can think of is to maintain that (1*) holds *only* for propositional modal logic and it fails to hold for quantification modal logic plus identity.
“1. ‘Bill=Bill’ is not meaningful in some possible world.
In this case, your argument fails as I argued before. You have already rejected (1).
2. ‘Bill=Bill’ is meaningful in every possible world.
In this case, your argument needs to be amended lest it falls to Pegasus-like counterexamples, as I argued in one of my previous posts.”
There is a third option. It is that if Bill fails to exist in some world w*, and hence ‘Bill’ fails to refer in w* to anything, then ‘Bill=Bill’ is undefined for w* and, thus, is not a wff. And if it is not a wff, then it has no truth-value in w*. Such a policy is more or less equivalent to the typical provision added in such cases; namely, “provided the object exists in the world in question”.
A fourth option is to force the name ‘Bill’ to refer to any arbitrarily selected object that does exist in w*. Then the proposition ‘Bill=Bill’ would still be true. Note that this option is available in every possible world in which there is at least one object, be that God or the number two.
The Pegasus case is not a problem, provided we require that the terms flanking the identity sign refer. Moreover, as I stated, I hold that it is not possible for Pegasus to exist in any possible world.
Re: Your (C*): (O=O) entails (Pos ((Ex) (x=O)).
C* is of course correct, but only because the antecedent entails (Ex)(x=O) by existential generalization which in turn entails the consequent of C* because if something is true then it is possible. Your proposal seems to suggest to skip existential generalization altogether and go from the necessity of (O=O) directly to the proposition that it is possible that O exists. I do not see how such *skipping* would work.
(You say regarding C*: “This argument is immune to Pegasus-style counterexamples, at the cost of making the consequent a necessary proposition.” Did you mean to say a “necessary proposition” or a modal proposition? Strictly speaking, the consequent of C* is not a necessary proposition, although it entails a necessary proposition: i.e., Nec(Pos ((Ex) (x=O))) in S5.)
Regarding your last paragraph, I have answered the objections there above.

Reply
peterlupu

May 28, 2011

Leo,
“why would Divine commands be necessary?”
The present question is specifically whether sin against God must involve a violation of a divine command. The concept of ‘sin’ as a moral wrongdoing independently from God need not involve any commands.
Your father example shows at most that you may have some moral obligations towards your father even in the absence of any commands from *him*. However, I wish to remind you of the fifth Commandment which says: “Honor thy father and they mother;” So even in your father example there is a divine command to avoid dishonoring your father. Doing so would be a sin against God, if you think the ten commandments were indeed issued by God.
And of course there are other examples of moral obligations that do not arise from commands: e.g., you ought to keep your promises, all else being equal, even if there is no specific command to do so.
The deeper point is this. In order for there to be a moral violation there has to be a moral principle that is violated. The question is about the source of the authority of moral principles. According to the Divine Command Theory this authority ultimately stems from God’s commands. So even if some moral principle is not directly commanded by God, it must be in some way subsumed under another moral principles which itself is either directly commanded by God or it is subsumed under another moral principles which is directly commanded by God, and so on.
Now, either you maintain that the authority of moral principles ultimately rests with God’s commands or you maintain that there is at least one moral principle the authority of which does not rest with God’s commands. If you opt for the former, then a sin is a moral violation of a moral principle the authority of which rests with God’s commands. If you opt for the later, then you abandon the view that the ultimate source of morality rests with God’s commands. These are your choices.

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Leo Carton Mollica

May 28, 2011

“Now, either you maintain that the authority of moral principles ultimately rests with God’s commands or you maintain that there is at least one moral principle the authority of which does not rest with God’s commands. If you opt for the former, then a sin is a moral violation of a moral principle the authority of which rests with God’s commands. If you opt for the later, then you abandon the view that the ultimate source of morality rests with God’s commands. These are your choices.”
I opt for the latter. Why should this be problematic?

Reply
peterlupu

May 28, 2011

Leo,
It is not so far as it goes. However, those who think that morality must rest somehow upon God’s authority question whether opting for the later provides any foundation for morality. But, this, of course is a different story altogether. So it seems to me we have come to agree on most of the issues currently under discussion.

Reply
Alexander R Pruss

May 30, 2011

Dr Vallicella:
In your little Hartshornish argument at the end, 5 doesn’t follow from 4 without the assumption:
(*) There is a property of knowing that Tom sins which, necessarily, is had by all and only the entities that know that Tom sins.
After all, 1-4 say nothing about properties, while 5 starts talking about “the” property. A nominalist, thus, can deny 5 while accepting 1-4. So can a sparse property theorist. A sparse property theorist denies that every predicate corresponds to a property, and so he might deny that the predicate “knows that Tom sins” corresponds to a property. A final way of denying (*) would be to say something like this: “There is a property of knowing that Tom sins, and it is had by anything that knows that Tom sins. But it is possible to know that Tom sins without having that property, namely if you are God. In the case of creatures, predication of ‘knows that Tom sins’ attributes a property, but in the case of God, predication of ‘knows that Tom sins’ doesn’t attribute a property. And that’s what we’d expect given the theory of analogy.”
Furthermore, the simplicity doctrine does not seem to require 6. It seems to only require: “God has no accidental intrinsic properties”. God obviously has accidental Cambridge properties, like being loved by Francis.
And so you need a premise that says that knowledge is an intrinsic property. But it’s not. In one world I know that my car is in my garage. In another world I am exactly alike internally, but the car has been quietly stolen, so it is false that I know that my car is in my garage.
So, rather than working with knowledge, you should work with belief. It’s more controversial to claim that there can be Cambridge differences in respect of belief, but semantic externalism says there can, and the arguments for semantic externalism are pretty good.
Leo:
Yeah, there is that logical gap in the original argument, but it can be fixed by adding the premise that God knows that Tom sins at t, since one can infer that q is contingent from the assumptions (a) p entails q; (b) q is contingent; and (c) p is true.

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peterlupu

June 1, 2011

Alex,
“…,since one can infer that q is contingent from the assumptions (a) p entails q; (b) q is contingent; and (c) p is true.”
You must mean that one can infer that p is contingent. For otherwise what you say is trivial: of course you can infer that q is contingent from the assumption that q is contingent; i.e., (b).

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