The following is the first installment of an article on the philosophy of Gottlob Frege. Students of philosophy may find here something of interest.
I
Among the comic strip faithful it is well known that
(1) Lois believes that Superman is a hero
and that
(2) Superman = Clark Kent.
However, it is just as well known that
(3) Lois believes that Clark Kent is a hero
is false. Indeed, she feels him to be somewhat of a coward. But rather than dismissing the Daily Planet’s best report as an eccentric, readers of the comic find that her beliefs about Superman (i.e. Clark Kent) make the couple’s relationship intriguing.
But how can this be? According to Frege, the reason Lois can have one belief and fail to have the other (and remain sane) is that her two beliefs are about different things. Of course saying this is merely to say what every speaker already knows. But to explain the semantics of it is to do something philosophically important. And the means by which Frege explains the difference is by his celebrated distinction of sense and reference.
The mere distinction of sense and reference is not enough to account for Lois’ doxastic consistency however. For although ‘Superman’ and ‘Clark Kent’ may have different senses, both still refer to Superman. And this being the case, one should be replaceable by the other salva veritate. Frege, of course, understood this problem well and offered a further distinction. Names that occur after a believes-that clause or any other propositional attitude clause do not have their normal sense of reference. Their reference becomes what was the original sense (sense of the name or definite description outside a propositional attitude clauses) and the sense becomes what Frege calls the indirect sense. Thus ‘Superman’ in (1) does not refer to Superman, but the the sense of ‘Superman’.
There are difficulties with Frege’s view however. If we take (1) together with
(4) Superman is a hero,
we can conclude that
(5) Lois believes at least one thing that is true.
Given Frege’s account of indirect sense, though, this inference is cut off. This is due to the fact that ‘Superman’ in the substantival clause of (1) and ‘Superman’ in (4) refer to different things – or, better put, different types of things. The first refers to the normal sense of ‘Superman’ (to use Kaplan’s convention, mSupermanm), the second refers to Superman. (Compare the inference of (5) from (3) and (4) where the same type of non sequitur is committed.) One might propose that we substitute
(6) It is true that Superman is a hero
for (4) and thereby assure a valid inference to (5). Both tokens of ‘Superman’ now refer to the same thing. (Compare the invalid inference of (5) from (3) and (6); the proper names in the substantival clauses now refer to the right type of thing, but not the right thing since mSupermanm is not identical to mClark Kentm. This shows that the inference of (5) from (3) and (4) is doubly in error.) The problem is that Lois’ true belief turns out to be about mSupermanm rather than Superman.
A further problem to the Fregean picture is what to make of propositional attitude clauses embedded within another propositional attitude clause. Take, for example,
(7) John believes that Lois believes that Superman is a hero
or even more gruesome,
(8) Paul believes that John believes that Lois believes that Superman is a hero.
Assuming we can make sense of the indirect reference (and sense) of ‘John’ (i.e. specify conditions of synonymy), what do ‘Lois’ and ‘Superman’ refer to? To carry on Frege’s analysis we would have to say the indirect indirect reference and indirect indirect indirect reference of ‘Lois’ and ‘Superman’ respectively. And concomitant with each stratum of reference is a sense. Indirect senses clutter the world up enough. Now it seems as if we are forced to countenance an indefinite number of types of senses. Surely something has gone awry.
Indirect reference is tolerably clear enough; it is the standard or usual sense of the term. And the indirect sense is what gets at the indirect reference. But this is to put the cart before the horse. Frege’s view is that sense is the conduit to reference. One object can be referred to by multiple senses, but one sense can only refer to one object. As Russell says, “There is no backward road from denotations to meanings.”
These are the standard problems with Frege’s distinction between sense and reference when applied to propositional attitude clauses. In the next section I shall cover the deeper criticism of his view as given by Quine.
First I’ll ask about the part before the discussion of (7) and beyond.
It seems to me that to say “Lois believes at least one thing that is true” means “Lois affirms mpm, and p”. This is not a non sequitor because of the way Frege has set it up. To believe something expressed by the sentence ‘p’ means to assert the sense of ‘p’; to believe at least one true thing means to assert the sense of at least one sentence ‘q’, and q.
Is the problem, how to deduce “Lois believes at least one thing that is true” in a symbolic syllogism?
I intend to reread this post as it’s been awhile since I studied Frege. While reading it I couldn’t help but remember a bit of confusion I was running into some time ago with the law of Transitivity, Leibniz’s Indispensability of Identicals and sense and reference concerning the Trinity. The law of Transitivity:
a=b
c=b
therefore a=c
Jesus is God
The Holy Spirit is God
therefore Jesus is the Holy Spirit etc.
Wherever Jesus is so is the Holy Spirit and the Father, for neither of them are a part of God such that they can be separated metaphysically, each are fully God. So in a sense, in reference to God’s unity Jesus is the Father etc. Moreover is God not logical, or beyond logic, or perhaps the law of logic known as transitivity is in error? Leibniz’ principle of the Indiscernibility of Identicals seemingly applies and does not apply here. How am I to understand this?
Subsequent to this confusion of mine is the problem of God’s omnipresence. If God is truly everywhere then how is it possible for him to create anything other than or separate from Himself? The answer I’ve heard to this is that God is immaterial and thus distinct — an angel example is generally offered. However regarding angels, created beings who are one place at a time and thus not omnipresent such an example doesn’t seem to marry. When we talk about God being everywhere certainly this is a metaphysical claim in which case either he is or is not everywhere. Does God however, an immaterial being, have locatability and thus extension? The other answer given is that God is sovereignly omnipresent. Is this what is meant by omnipresence in which case He isn’t actually everywhere for to be somewhere necessitates locatability? I look forward to your reply.
Mo — While we’re waiting for MB to re-emerge, I’ll chime in. God being non-spatial essentially, if he creates objects that relate spatially, he fully inheres and wraps around those, so that he is fully present at every point equally. Of course, even that way of saying it is to employ spatial metaphors. We can’t avoid that, as finite creatures that relate to each other and other things spatially. Even so, most people seem to have an intuitive comfort with God being fully present at every point, more so than, say, some do with the temporal analogue.
The real mystery is: how can God create at all, or rather: what is the difference between God thinking about x, and x existing? This is why Berkeley’s idealism still has attraction. I feel your pain. And those that think what it means to create ex nihilo has obvious meaning haven’t wrestled deeply enough I think.
We can maybe take Berkeley as a starting point and then back out of the idealism. I know that I am different than “God thinking about Tim” because I can say “I”. Thoughts do not reflect on themselves. I also know that I am not God. But if it is possible for God to create other persons that in some sense have subsistence that is not God’s own thought, then a fortiori it must be possible for him to do so with the lesser creatures, i.e. things.
What does it mean for God to create an electron, that is different than him thinking about an electron? Well, it means something analogous to what he did to create Mo and Tim — somehow, to decree continuity of presence that allows it a kind of selfness that makes it a true Gegenstand even to God himself.
God does not become spatial by creating spatially-related objects. Space is the manifold that allows objects to subsist simultaneously as parts of a world in distinction from other parts. It is a relative and relational concept. It is not a thing. It can only be described transcendentally.
Perhaps we could say that space is the physical analogue to the “space” of the persons in the Trinity — that which is the implied substratum of one Person having an I-thou relation, so that the I does not disappear into the Thou.
There is no brute “substratum” for God. The substratum is itself an aspect of God, or perhaps just how we must think of him. If it were “brute,” then we would not yet have found the true God.
As van Til observed, every doctrine is ultimately mysterious from the creature’s point of view. We can make analogies.
To your question in #2, we must distinguish whether the “is” in “Jesus is God” is the “is” of identity or attribution. From the logical standpoint, take as a starting point that it is the “is” of attribution: Jesus is God-ness if you will. Thus you can no more say that “Jesus is the Holy Spirit” than you can “Mo is Tim” because each is human.
Now with God, attribution is not contingent; so “Jesus is Godness” and “Jesus is God” coalesce. This just means that we must guard our predication from absurdity when we cross the Creator/creature divide.
Another way to think about it might be helpful. You cannot say, “The Son is the triune God.” Unpacking what that means leads to a series of propositions (say, as stated in Nicene) that are true but which must be “regulated” by the proper distinctions, such as I allude to above.
Tim thanks for your response. I actually assumed that you wrote the article.
Regarding the law of Transitivity, I recall that it concerns Identity rather than Predication, in which case it seems that one could say Jesus is the Triune God so long as the reference is God’s unity over against His diversity, after all Jesus is fully God and God is triune. Am I understanding your analysis correctly?
With respect to the second question about God’s omnipresence, what exactly does it mean to say that God “fully inheres and wraps around those, so that he is fully present at every point equally”? For space is indeed vast, it would seem that this merely relates to His wrapping around the vastness of space en total instead of space’s many individual constituents after all what’s true of the whole isn’t necessarily true of the parts. If I were to point to a thing say my car and say God is fully wrapped around my car, my car is still well within the created order so how does God not exist in the actual physical atmosphere but somehow exist around my car? And this lends to questions about say the indwelling of the Holy Spirit who is both everywhere, although not everywhere but rather wrapping around creation, and yet “in” some people while not in others.
As per your bit about God creating ex nihilo, I hear ya, quite the mystery. Van Til’s discussion of the seeming contradiction of Him being fully contained and absolute and yet creating for the intension of receiving more glory as well as being eternal and yet having historical relations and concerns has well bruised my brain.
Mo — on the 1st question, no, you aren’t understanding my analysis correctly. “Jesus is the unity of the triune God” is not a proper identity.
On the 2nd question, I plan to do more on the questions of space and time in the coming months. One last thought experiment until then: Let all the objects of the universe be “decoupled” from space. Then you can set them all on top of each other as it were. Now let the parts of each object do the same. The whole universe is sitting there as a non-spatial point. Since God is non-spatial, that is one model I use to imagine omnipresence.
I’m wondering if the spatial question is just an intellectual curiosity for you, or an existential one. Most people intuitively have no problem saying, “I can pray to God right here,” then walk to the next room and say, “I can also pray here equally well.” It seems to be part of the sensus divinitatis. Most moderns balk at the omni-presence of God in time, i.e. his eternity, and not at spatial omnipresence.
TJH – Are there any resources you would recommend that discuss omnipresence, creation ex nihilo, sovereignty, etc. in relation to space/time (analyzing some of the philosophical ramifications of such beliefs as you did)? I haven’t found this discussed in depth from a Christian perspective. But it doesn’t need to be from a Christian perspective, just one that tackles some of the more interesting issues. But until then, a couple of questions:
1) “The real mystery is: how can God create at all, or rather: what is the difference between God thinking about x, and x existing? This is why Berkeley’s idealism still has attraction. I feel your pain. And those that think what it means to create ex nihilo has obvious meaning haven’t wrestled deeply enough I think.”
Could you elaborate on this point? I have always found Berkley’s idealism attractive for many reasons myself and would like to hear your thoughts as to why, scripturally speaking, we would need to back out of idealism after using it as a starting point. If there is biblical warrant for that, how exactly could it be used and then backed out of?
2) “On the 2nd question, I plan to do more on the questions of space and time in the coming months. One last thought experiment until then: Let all the objects of the universe be decoupled from space. Then you can set them all on top of each other as it were. Now let the parts of each object do the same. The whole universe is sitting there as a non-spatial point. Since God is non-spatial, that is one model I use to imagine omnipresence.”
This thought experiment is giving me some trouble due to all the spatial references. It could be just my inability to get around these references to understand what you’re getting at but if you could elaborate more here it would be of interest.
I hope to see more articles from you on this subject soon.
And I think that’s how we have to leave it until then. Otherwise, it’s going to keep distracting MB from answering #1 in reference to Frege, which we are getting pretty far away from. In the meantime, Bavinck (vol 2, pp. 164-170) is a good reference, as I’m sure Turretin too is tho’ I didn’t have time to check latter before hitting road this morning.