Nicholas Rescher cites this example from Buridan. The proposition is false, but not self-refuting. If every proposition is affirmative, then of course *Every proposition is affirmative* is affirmative. The self-reference seems innocuous, a case of self-instantiation. But *Every proposition is affirmative* has as a logical consequence *No proposition is negative.* This follows by Obversion, assuming that a proposition is negative if and only if it is not affirmative.
Paradoxically, however, the negative proposition, unlike its obverse, is self-refuting. For if no proposition is negative then *No proposition is negative* is not negative. So if it is, it isn't. Plainly it is. Ergo, it isn't.
Rescher leaves the matter here, and I'm not sure I have anything useful to add.
It is strange, though, that here we have two logically equivalent propositions one of which is self-refuting and the other of which is not. The second is necessarily false. If true, then false; if false, then false; ergo, necessarily false. But then the first must also be necessarily false. After all, they are logically equivalent: each entails the other across all logically possible worlds.
What is curious, though, is that the ground of the logical necessity seems different in the two cases. In the second case, the necessity is grounded in logical self-contradiction. In the first case, there does not appear to be any self-contradiction.
It is impossible that every proposition be affirmative. And it is impossible that no proposition be negative. But whereas the impossibility of the second is the impossibility of self-referential inconsistency, the impossibility of the first is not. (That is the 'of' of apposition.)
Can I make an aporetic polyad out of this? Why not?
1. Logically equivalent logically impossible propositions have the same ground of their logical impossibility.
2. The ground of the logical impossibility of *Every proposition is affirmative* is not in self-reference.
3. The ground of the logical impossibility of *No proposition is negative* is in self-reference.
The limbs of this antilogism are individually plausible but collectively inconsistent.
Nicholas Rescher, Paradoxes: Their Roots, Range, and Resolution, Open Court, 2001, pp. 21-22.
G. E. Hughes, John Buridan on Self-Reference, Cambidge UP, 1982, p. 34. Cited by Rescher.
James N. Anderson and Greg Welty have published a paper entitled The Lord of Non-Contradiction: An Argument for God from Logic. Having worked out similar arguments in unpublished manuscripts, I am very sympathetic to the project of arguing from the existence of necessary truths to the necessary existence of divine mind.
Here is a quick sketch of the Anderson-Welty argument as I construe it:
1. There are laws of logic, e.g., the law of non-contradiction.
2. The laws of logic are truths.
3. The laws of logic are necessary truths.
4. A truth is a true proposition, where propositions are the primary truth-bearers or primary vehicles of the truth values.
5. Propositions exist. Argument: there are truths (from 1, 2); a truth is a true proposition (3); if an item has a property such as the property of being true, then it exists. Ergo, propositions exist.
6. Necessarily true propositions necessarily exist. For if a proposition has the property of being true in every possible world, then it exists in every possible world. Remark: in play here are 'Fregean' as opposed to 'Russellian' propositions. See here for an explanation of the distinction as I see it. If the proposition expressed by 'Socrates is Socrates' is Russellian, then it has Socrates himself, warts and all, as a constituent. But then, though the proposition is in some sense necessarily true, being a truth of logic, it is surely not necessarily existent.
7. Propositions are not physical entities. This is because no physical entity such as a string of marks on paper could be a primary truth-bearer. A string of marks, if true, is true only derivatively or secondarily, only insofar as as it expresses a proposition.
8. Propositions are intrinsically intentional. (This is explained in the post which is the warm-up to the present one.)
9. The laws of logic are necessarily existent, nonphysical, intrinsically intentional entities.
10. Thoughts are intrinsically intentional.
The argument now takes a very interesting turn. If propositions are intrinsically intentional, and thoughts are as well, might it be that propositions are thoughts?
The following invalid syllogism must be avoided: "Every proposition is intrinsically intentional; every thought is intrinsically intentional; ergo, every proposition is a thought." This argument is an instance of the fallacy of undistributed middle, and of course the authors argue in no such way. They instead raise the question whether it is parsimonious to admit into our ontology two distinct categories of intrinsically intentional item, one mental, the other non-mental. Their claim is that the principle of parsimony "demands" that propositions be constued as mental items, as thoughts. Therefore
11. Propositions are thoughts.
12. Some propositions (the law of logic among them) are necessarily existent thoughts. (From 8, 9, 10, 11)
13. Necessarily, thoughts are thoughts of a thinker.
14. The laws of logic are the thoughts of a necessarily existent thinker, and "this all men call God." (Aquinas)
A Stab at Critique
Line (11) is the crucial sub-conclusion. The whole argument hinges on it. Changing the metaphor, here is where I insert my critical blade, and take my stab. I count three views.
A. There are propositions and there are thoughts and both are intrinsically intentional.
B. Propositions reduce to thoughts.
C. Thoughts reduce to propositions.
Now do considerations of parsimony speak against (A)? We are enjoined not to multiply entities (or rather types of entity) praeter necessitatem. That is, we ought not posit more types of entity than we need for explanatory purposes. This is not the same as saying that we ought to prefer ontologies with fewer categories. Suppose we are comparing an n category ontology with an n + 1 category ontology. Parsimony does not instruct us to take the n category ontology. It instructs us to take the n category ontology only if it is explanatorily adequate, only if it explains all the relevant data but without the additional posit. Well, do we need propositions in addition to thoughts for explanatory purposes? It is plausible to say yes because there are (infinitely) many propositions that no one has ever thought of or about. Arithmetic alone supplies plenty of examples. Of course, if God exists, there are no unthought propositions. But the existence of God is precisely what is at issue. So we cannot assume it. But if we don't assume it, then we have a pretty good reason to distinguish propositions and thoughts as two different sorts of intrinsically intentional entity given that we already have reason to posit thoughts and propositions.
So my first critical point is that the principle of parsimony is too frail a reed with which to support the reduction of propositions to thoughts. Parsimony needs to be beefed-up with other considerations, e.g., an argument to show why an abstract object could not be intrinsically intentional.
My second critical point is this. Why not countenance (C), the reduction of thoughts to propositions? It could be like this. There are all the (Fregean) propostions there might have been, hanging out in Frege's Thrid Reich (Popper's world 3). The thought that 7 + 5 = 12 is not a state of an individul thinker; there are no individual thinkers, so selves, no egos. The thought is just the Fregean proposition's temporary and contingent exemplification of the monadic property, Pre-Personal Awareness or Bewusst-sein. Now I don't have time to develop this suggestion which has elements of Natorp and Butchvarov, and in any case it is not my view.
All I am saying is that (C) needs excluding. Otherwise we don't have a good reason to plump for (B).
My conclusion? The Anderson-Welty argument, though fascinating and competently articulated, is not rationally compelling. Rationally acceptable, but not rationally compelling. Acceptable, because the premises are plausible and the reasoning is correct. Not compelling, because one could resist it without quitting the precincts of reasonableness.
To theists, I say: go on being theists. You are better off being a theist than not being one. Your position is rationally defensible and the alternatives are rationally rejectable. But don't fancy that you can prove the existence of God or the opposite. In the end you must decide how you will live and what you will believe.
Franz Brentano, for whom intentionality is the mark of the mental, is committed to the thesis that all instances of (intrinsic) intentionality are instances of mentality. Propositions and dispositions are apparent counterexamples. For they are nonmental yet intrinsically object-directed. Whether they are also real counterexamples is something we should discuss. This post discusses (Fregean) propositions. Later, dispositions — if I am so disposed.
On one approach, propositions are abstract objects. Since abstracta are categorially barred from being mental, it is clear that if intrinsic intentionality is ascribed to abstract propositions, then the thesis that all instances of intentionality are instances of mentality must be rejected. For specificity, we consider Frege's theory of propositions. He called them Gedanken, thoughts, which is a strangely pyschologistic terminological choice for so anti-psychologistic a logician, but so be it.
A proposition is the sense (Sinn) of a certain sort of sentence in the indicative mood, namely, an indicative sentence from which all indexical elements, if any, such as the tenses of verbs, have been extruded. Consider the following sentence-tokens each of which features a tenseless copula:
1. The sea is blue 2. The sea is blue 3. Die See ist blau 4. Deniz mavidir.
(Since Turkish is an agglutinative language, the copula in the Turkish sentence is the suffix 'dir.')
The (1)-(4) array depicts four sentence-tokens of three sentence-types expressing exactly one proposition. Intuitively, the four sentences say the same thing, or to be precise, can be used by people to say the same thing. That same thing is the proposition they express, or to be precise, that people express by uttering them. The proposition is one to their many. And unlike the sentence-tokens, it is nonphysical, which has the epistemological consequence that it, unlike the sentence-tokens, cannot be seen with the eyes. It is 'seen' (understood) with the mind. Frege is a sort of latter-day Platonist.
So one reason to introduce propositions is to account for the fact that the same meaning-content can be expressed by different people using different sentences of different languages. Another reason to posit propositions is to have a stable entity to serve as vehicle of the truth-values. The idea is that it is the proposition that is primarily either true or false. Given that a proposition is true, then any sentence expressing it is derivatively true.
There is quite a lot to be said for the view that a sentence-token cannot be a primary truth-bearer. For how could a string of marks on paper, or pixels on a screen, be either true or false? Nothing can be either true or false unless it has meaning, but how could mere physical marks (intrinsically) mean anything? Merely physical marks, as such, are meaningless. You can't get blood from a stone, or meaning from meat, no matter how hard you squeeze, and no matter how wondrously organized the meat.
Fregean propositions are especially useful when it comes to the necessary truths expressed by such sentences as '7 is prime.' A necessary truth is true in all possible worlds, including those worlds in which there is nothing physical and so no means of physically expressing truths. If truth is taken to be a property of physical items or any contingent item, then it might be difficult to account for the existence of necessary truths. The Fregean can handle this problem by saying that propositions, as abstract objects, exist in all possible worlds, and that true ones have the property of being true in all possible worlds. The Fregean can also explain how there can be necessary truths in worlds in which there is nothing physical and nothing mental either.
Propositions also function as the accusatives of the so-called 'propositional attitudes' such as belief. To believe is to believe something. One way to construe this is de dicto: to believe is to stand in a relation to a proposition. Thus if I believe that the river Charles is polluted, then the intentional object of the belief is the proposition expressed by 'The river Charles is polluted.' (Of course, there is also a de re way of construing the belief in question: To believe that the Charles is polluted is to believe, of the river Charles, that is is polluted.)
Well, suppose one endorses a theory of propositions such as the one just sketched. You have these necessarily existent Platonic entities called propositions some of which are true and some of which are false. My believing that p is an intentional state directed upon p; but is it not also the case that p is directed upon the world, or upon a truth-making state of affairs in the world in the case in which p is true?
But now it looks as if we have two sorts of intentionality, call them noetic and noematic, to borrow some terminology from Husserl. Noetic intentionality connects a mental state (in Frege's Second Reich) to a proposition (in Frege's Third Reich), and noematic intentionality connects, or purports to connect, a proposition to an object in Frege's First Reich. Frege wouldn't think of this object as a state of affairs or concrete fact, of course, but we might. (The peculiarities of Frege's actual views don't matter for this discussion.)
The problem for Brentano's thesis above is that propositions — which are abstract objects — seem to display intrinsic aboutness: they are about the concrete world or states of affairs in the world. Thus the proposition expressed by 'The Charles is polluted' is intrinsically about either the river Charles or else about the state of affairs, The Charles River's being polluted.Intrinsically, because the proposition's being about what it is about does not depend on anyone's interpretation.
If this is right, then some instances of intentionality are not only not conscious but not possibly conscious. Does this refute Brentano's thesis? Brentano himself denied that there were such irrealia as propositions and so he would not take propositions as posing any threat to his thesis. But if there are (Fregean) propositions, then I think they would count as counterexamples to Brentano's thesis about intentionality.
Is there a way to uphold Brentano's thesis that only the mental is intrinsically intentional? Yes, if there is a way to identify propositions with thoughts or rather content-laden thinkings. My thinking that 7 is prime is intrinsically intentional. Unfortunately, my thinking is contingent whereas the content of my thinking is necessarily true and hence necessarily existent. To identify propositions with content-laden thinkings one would have to take the thinkings to inhere in a necessarily existent mind such as the mind of God.
So I end on an aporetic note. Intentionality cannot be the mark of the mental if there are Fregean propositions. But given that there are necessary truths and that truth-bearers cannot be physical items, then only way to avoid Fregean propositions is by identifying propositions with divine thoughts, in which case they are Gedanken after all.
1. Here are three temporal platitudes: The wholly past is no longer present; the wholly future is not yet present; the present alone is present. Here are three closely related controversial metaphysical theses: the wholly past, being no longer is not; the wholly future, being not yet, is not; the present alone is. The second trio is one version of presentism. I grant that presentism is appealing, though it would be a mistake to take it to be common sense or immediate fallout from common sense. The platitudes are Moorean; deny them on pain of being an idiot. Not so with the heavy-duty metaphysical theses about time and existence advanced by the presentist. We can reasonably ask what they mean and whether they are true.
2. Now even presentists will admit that the past is not a mere nothing. Last Sunday's hike has some sort of reality that cries out for accommodation. After all it is now true that I hiked eight hours on Sunday. Even if there are no truth-makers, there still must be something that the true past-tensed sentence is about. Here I distinguish between two principles, Truth-Maker and Veritas Sequitur Esse.
3. We should also keep in mind that past times and events do not have the status of the merely possible. When Sunday's hike was over it did not change its modal status from actual to merely possible. It remained an actual event, albeit a past actual event. Soren Kierkegaard WAS engaged to Regine Olsen, but he was never married to her. Intuitively, the engagement belongs to the sphere of the actual whereas the marriage belongs to the sphere of the merely possible, not that it is possible now. Neither event is a mere nothing. Furthermore, the engagement has, intuitively, 'more reality' than the marriage. What was is more real than what might have been. Historians attempt to determine what the actual facts were. They are constrained by the reality of the past, whence it follows that past has some sort of reality. Historians are neither fiction writers nor students of mere possibilia.
4. I take it to be a Moorean datum that past events and times are not nothing and also not merely possible. Hence a theory of time that cannot accommodate these data is worthless. How can the presentist accommodate them? He has to do it in a manner consistent with his claim that past and future items do not exist at all, that only temporally present items exist.
5. One approach is the 'ersatzer' approach: one looks for substitutes for nonpresent times. Let's consider the view that times are maximal propositions. A proposition is maximal just in case it entails every proposition with which it is broadly logically consistent. Accordingly, past and future times are contingently false maximal propositions. But then the present time is the sole true maximal proposition, and temporal presentness is identical to truth.
This scheme seems to allow us to uphold the Moorean data mentioned in #s 2-4 while holding a version of presentism. If each time is a proposition, and propositions exist omnitemporally, then all times are always available to be referred to. Sunday's hike is a wholly past event. Hence, on presentism, it does not exist at all. But the maximal propositions that were true during the hike all exist and exist now. It is just that they are now false. Sunday's hike is not nothing because those maximal propositions are not nothing and each entails *BV hikes,* a proposition that is not nothing. Sunday's hike is not merely possible because those maximal propositions, though now false, were true.
What we have done is to substitute for nonexistent past events and times, existent and present but false propositions.
6. One problem I have with this approach is as follows. If nonpresent times are false maximal propositions, then the present time is the sole true maximal proposition. If the present time is the sole true maximal proposition, then presentness is truth. The concrete universe cannot, however, be said to be true. It follows that the concrete universe cannot be said to be temporally present. But surely this is false: it anythiingis temporally present the concrete universe is. For the presentist, whatever exists, exists at present. The concrete universe exists, ergo, it is present.
Here is a second argument. If a contingent, singular, affirmative proposition is true, then it is made true by an existing non-proposition. If the present time is the sole maximal true proposition, then it has a truth-maker. That truth-maker is the concrete universe in its present state. So the concrete universe must have the property of being temporally present to serve as the truth-maker of the present time. For only the present universe could make true the maximal proposition that alone is presently true.
The ersatzer approach puts Descartes before the whores the cart before the horse: it is the presentness of the concrete universe that explains the present truth of the maximal proposition with which the present time has been identified, and not the other way around. Temporal presentness cannot be truth. It cannot be 'kicked upstairs' to the level of abstracta.
7. In sum, the presentist must somehow account for the reality of the past since the past is not nothing and not something merely possible. But the above ersatzer approach fails. So what makes it true now that I hiked eight hours on Sunday? If I understood Rhoda's suggestion it is that God's veridical memory of my hiking on Sunday is the truth-maker of 'I hiked last Sunday.' We will have to consider Rhoda's suggestion in a separate post. Deus ex machina?
Earlier, I presented the following, which looks to be an antilogism. An antilogism, by definition, is an inconsistent triad. This post considers whether the triad really is logically inconsistent, and so really is an antilogism.
1. Temporally Unrestricted Excluded Middle: The principle that every declarative sentence is either true, or if not true, then false applies unrestrictedly to all declarative sentences, whatever their tense. 2. Presentism: Only what exists at present exists. 3. Temporally Unrestricted Truth-Maker Principle: Every contingent truth has a truth-maker.
Edward objects: "First, I don't see why the three statements are logically inconsistent. Why can't the truthmaker for a future tense statement exist now, in the present?"
Objection sustained. The triad as it stands is not logically inconsistent.
'Miss Creant will die by lethal injection in five minutes.' Let this be our example. It is a future-tensed contingent declarative. By (1) it is either true or, if not true, then false. By (3), our sample sentence has a truth-maker, an existing truth-maker obviously, if it is true. By (2), the truth-maker exists only at present. Edward is right: there is no inconsistency unless we add something like:
4. If a sentence predicts a contingent event which lies wholly in the future, and the sentence is true, then the truth-maker of the sentence, if it has one, cannot exist at any time prior to the time of the event.
(4) is extremely plausible. Suppose it is true now that Miss Creant will die in five minutes. The only item that could make this true is the event of her dying. But this event does not now exist and cannot exist at any time prior to her dying.
So our antilogism, under Edwardian pummeling, transmogrifies into an aporetic tetrad which, he will agree, is logically inconsistent.
The solution, for Edward, is obvious: Deny the Temporally Unrestricted Truth-Maker Principle as stated in (3). Of course, that is a solution. But can Edward show that it must be preferred to the other three solutions? After all, one could deny Presentism, and many distinguished philosophers do. I would hazard the observation that the majority of the heavy-hitters in the 20th century Anglosphere were B-theorists, and thus deniers of Presentism. Or one could deny Unrestricted LEM, or even (4).
Although I said that (4) is extremely plausible, one could conceivably deny it by maintaining that the truth-makers of future-tensed sentences are tendencies in the present. For example, I say to wifey, "Watch it! The pot is going to boil over!" Assuming that that's a true prediction, one might claim that it is the present tendencies of the agitated pasta-rich water that is the truth-maker.
Please note also that I too could solve the tetrad by denying Unrestricted T-maker. Not by rejecting T-makers tout court in the Edwardian manner, but by restricting T-makers to contingent past- and present-tensed declaratives. I hope Edward appreciates that the above problem does not give aid and comfort to his wholesale rejection of T-makers.
One can always solve an aporetic polyad by denying one of its limbs. Sure. But then you face other daunting tasks. One is to show in a compelling way that your preferred solution should be preferred by all competent practitioners. You have to show that your solution is THE solution and not merely a solution relative to your background assumptions and cognitive values. A school-immanent solution is no final and absolute solution. Another task is to show that your solution can be embedded in a theory that does not itself give rise to insoluble problems.
Do you remember the prediction, made in 1999, that the DOW would reach 36,000 in a few years? Since that didn't happen, I am inclined to say that Glassman and Hasset's prediction was wrong and was wrong at the time the prediction was made. I take that to mean that the content of their prediction was false at the time the prediction was made. Subsequent events merely made it evident that the content of the prediction was false; said events did not first bring it about that the content of the prediction have a truth-value.
And so I am not inclined to say that the content of their irrationally exuberant prediction was neither true nor false at the time of the prediction. It had a truth-value at the time of the prediction; it was simply not evident at that time what that truth-value was. By 'the content of the prediction' I mean the proposition expressed by 'The DOW will reach 36,000 in a few years.'
I am also inclined to say that the contents of some predictions are true at the time the predictions are made, and thus true in advance of the events predicted. I am not inclined to say that these predictions were neither true nor false at the time they were made. Suppose I predict some event E and E comes to pass. You might say to me, "You were right to predict the occurrence of E." You would not say to me, "Although the content of your prediction was neither true nor false at the time of your prediction, said content has now acquired the truth-value, true."
It is worth noting that the expression 'come true' is ambiguous. It could mean 'come to be known to be true' or it could mean 'come to have the truth-value, true.' I am inclined to read it the first way. Accordingly, when a prediction 'comes true,' what that means is that the prediction which all along was true, and thus true in advance of the contingent event predicted, is now known to be true.
So far, then, I am inclined to say that the Law of Excluded Middle applies to future-tensed sentences. If we assume Bivalence (that there are exactly two truth-values), then the Law of Excluded Middle (LEM)can be formulated as follows. For any proposition p, either p is true or p is false. Now consider a future-tensed sentence that refers to some event that is neither impossible nor necessary. An example is the DOW sentence above or 'Tom will get tenure in 2014.' Someone who assertively utters a sentence such as this makes a prediction. What I am currently puzzling over is whether any predictions, at the time that they are made, have a truth-value, i.e., (assuming Bivalence), are either true or false.
Why should I be puzzling over this? Well, despite the strong linguistic inclinations recorded above, there is something strange in regarding a contingent proposition about a future event as either true or false in advance of the event's occurrence or nonoccurrence. How could a contingent proposition be true before the event occurs that alone could make it true?
Our problem can be set forth as an antilogism or aporetic triad:
1. U-LEM: LEM applies unrestrictedly to all declarative sentences, whatever their tense. 2. Presentism: Only what exists at present exists. 3. Truth-Maker Principle: Every contingent truth has a truth-maker.
Each limb of the triad is plausible. But they can't all be true. The conjunction of any two entails the negation of the third. Corresponding to our (inconsistent) antilogism there are three (valid) syllogisms each of which is an argument to the negation of one of the limbs from the other two limbs.
If there is no compelling reason to adopt one ofthese syllogisms over the other two, then I would say that the problem is a genuine aporia, an insoluble problem.
People don't like to admit that there are insolubilia. That may merely reflect their dogmatism and overpowering need for doxastic security. Man is a proud critter loathe to confess the infirmity of reason.
Your most recent post (for which many thanks) inspired the below-expressed argument, and I was curious as to your opinion of it . . . . I think it has something behind it, but right now I feel uncertain about my examples in (2).
0. There is something curious about the relation between a proposition or declarative sentence and the terms or words that compose it: the list L ("Christ," "Judas," "betrays") clearly differs, at the very least in not having a truth value, from the sentence "Judas betrays Christ," yet nothing immediately presents itself as the ground G of this difference. One plausible candidate for G is some kind of union or togetherness amongst the members of L present in "Judas betrays Christ" and not in L itself, but this proposal is open to a serious challenge.
1. Suppose we accept Barry Miller's thesis, from "Logically Simple Propositions," that some declarative sentences have only one semantic element. His favorite such sentence is the Romanian "Fulgura," whose only constituent word translates (if I remember aright) the English "brightens," and which is interesting in requiring no actual or implied subject to form a complete sentence (like "It's raining" in English, but without the dummy subject).
2. Now, the lone word in "Fulgura" seemingly can occur outside any proposition. If, for example, someone were to ask me to recite my favorite Romanian word, or to translate "brightens" into Romanian, it would be strange to take me as telling them something false, or to have them respond "No, it isn't," upon my replying with "fulgura." There would, however, be nothing strange about the sentence "Fulgura" being false and someone telling me as much. [. . .]
3. Even in such simple sentences, therefore, there is a distinction between the sentence and the words contained therein, for one can be had without the other. But the ground of this distinction cannot be any union or togetherness among the words that enter into the sentence for the simple reason that no union or togetherness amongst items can be had without distinct items to unify or bind together. It can, therefore, be at least plausibly argued that the general ground of the difference between a sentence and its constituent words is no kind of union or togetherness.
I take Mr Mollica's basic argument to be this:
a. If there are logically simple sentences/propositions, then the problem of the unity of the sentence/proposition is not one that arises for every sentence/proposition. b. There are logically simple sentences/propositions. Therefore
c. The problem of the unity of the proposition is not one that arises for every sentence/proposition.
My response is to reject (b) while granting (a). I discussed the question of logically simple sentences/propositions with Barry Miller back in the '90s in the pages of Faith and Philosophy. My "Divine Simplicity: A New Defense (Faith and Philosophy, vol. 9, no. 4, October 1992, pp. 508-525) has an appendix entitled "Divine Simplicity and Logically Simple Propositions." Miller responded and I counter-responded in the July 1994 issue, pp. 474-481. It is with pleasure that I take another look at this issue. I will borrow freely from what I have published. (Whether this counts as plagairism, depends, I suppose, on one's views on diachronic personal identity.)
A. A logically simple proposition (LSP) is one that lacks not only propositional components, but also sub-propositional components.Thus atomic propositions are not logically simple in Miller's sense, since they contain sub-propositional parts. A proposition of the form a is F, though atomic, exhibits subject-predicate complexity.
B. Miller's examples of LSPs are inconclusive. Consider the German Es regnet ('It is raining'). As Miller correctly notes, the es is grammatical filler, and so the sentence can be pared down to Regnet, which is no doubt grammatically simple. He then argues:
Now there is no question of Regnet being a predicate; for as a proposition it has a complete sense, whereas as a predicate it could have only incomplete sense. Hence, Regnet and propositions like it seem logically simple. (Barry Miller, "Logically Simple Propositions," Analysis, vol. 34, no. 4, March 1974, p. 125.)
I find it hard to avoid the conclusion that Miller is confusing propositions with the sentences used to express them. Regnet and fulgura are grammatically simple. But it scarcely follows that the propositions they express are logically simple. What makes them one-word sentences is the fact that they express propositions; otherwise, they would be mere words. So we need a sentence-proposition distinction. But once that distinction is in place then it becomes clear that grammatical simplicity of sentence does not entail logical simplicity of the corresponding proposition.
C. It is also unclear how any intellect like ours could grasp a proposition devoid of logical parts, let alone believe or know such a proposition. To believe that it is snowing, for example, is to believe something logically complex, albeit unified, something formulatable by some such sentence as 'Snow is falling.' So even if there were logically simple propositions, they could not be accusatives of minds like ours. And if propositions are defined as the possible accusatives of propositional attitudes such as belief and knowledge, then the point is stronger still: there cannot be any logically sinple propositions.
D. So it seems to me that 'the problem of the list' or the problem of the unity of the sentence/proposition is one that pertains to every sentence/proposition. It is a problem as ancient as it is tough, and, I suspect, absolutely intractable. For a glimpse into the state of the art, I shamelessly recommend my June 2010 Dialectica article, "Gaskin on the Unity of the Proposition."
I know you're in a bit of a mereology phase at the moment, but I figured I'd shoot this by you.
Mereology is the theory of parts and wholes. Now propositions, whether Fregean or Russellian, are wholes of parts. So mereology is not irrelevant to questions about the nature and existence of propositions. The relevance, though, appears to be negative: propositions are unmereological compositions, unmereological wholes. That is to say, wholes that cannot be understood in terms of classical mereology. They cannot be understood in these terms because of the problem of the unity of the proposition. The problem is to specify what it is about a proposition that distinguishes it from a mere aggregate of its constituents and enables it to be either true or false. No constituent of an atomic proposition is either true or false, and neither the mathematical set, nor the mereological sum, of the constituents of any such proposition is true or false; so what is it that makes a proposition a truth-bearer? If you say that a special unifying constituent within propositions does the job,then you ignite Bradley's regress. Whether or not it is vicious is a further question. Richard Gaskin maintains the surprising view that Bradley's regress is "the metaphysical ground of the unity of the proposition." Far from being vicious, Bradley's regress is precisely that which "guarantees our ability to say anything at all."
For more on this topic, see my "Gaskin on the Unity of the Proposition," Dialectica vol. 64, no. 2 (June 2010), 265-277. It is part of a five article symposium on the topic.
I am not sure if you believe in Fregean propositions or not. As for myself, I don't look favorably upon the idea of Fregean propositions because of the problem of Bradley's regress. (I am assuming propositions would be composite structured entities, built out of ontologically more basic parts, maybe the senses of the individual terms of the sentences that expresses it, so that the proposition expressed by "Minerva is irate" is a structured entity composed of the senses of "Minvera", "irate", etc.)
I provisionally accept, but ultimately reject, Fregean propositions. What the devil does that mean? It means that I think the arguments for them are quite powerful, but that if our system contains an absolute mind, then we can and must reduce Fregean propositions to contents or accuusatives of said mind. Doing so allows us to solve the problem of the unity of the proposition.
By the way, what you say in parentheses is accurate and lucid.
In your book, you offer a theistic strategy for solving the problem of Bradley's regress as applied to facts. I don't know that a theistic solution to the problem as applied to propositions works as smoothly because of the queer sort of things senses of individual terms of sentences are supposed to be. The building blocks of facts are universals, which are somewhat familiar entities; but the building blocks of propositions are senses like "Minerva" which are murky and mysterious things indeed. What the hell kind of a thing is a sense anyway?
A sense is a semantic intermediary, an abstract 'third-world' object neither in the mind nor in the realm of concreta, posited to explain certain linguistic phenomena. One is the phenomenon of informative identity statements. How are they possible? 'George Orwell is Eric Blair' is an informative identity statement, unlike 'George Orwell is George Orwell.' How can the first be informative, how can it have what Frege calls cognitive value (Erkenntniswert), when it appears to be of the form a = b, a form all of the substitution-instances of which are false? Long story short, Frege distinguishes between the sense and the referent of expressions. Accordingly, 'George Orwell' and 'Eric Blair' differ in sense but have the same referent. The difference in sense explains the informativeness of the identity statement while the sameness of referent explains its truth.
Further, propositions are supposed to be necessarily existent; hence the individual building blocks of the propositions must also exist necessarily. But how could the senses expressed by "Minerva" or "Heidegger's wife", for instance, exist when those individuals do not? (This is the same sort of argument you give against haecceity properties conceived of as non-qualitative thisnesses.)
If proper names such as 'Heidegger' have irreducibly singular Fregean senses, then, as you well appreciate, my arguments against haecceity properties (nonqualitative thisnesses) kick in. It is particularly difficult to understand how a proper name could express an irreducibly singular Fregean sense when the name in question lacks a referent. For if irreducibly singular, then the sense is not constructible from general senses by an analog of propositional conjunction. So one is forced to say that the sense of 'Minerva' is the property of being identical to Minerva. But since there is no such individual, there is no such property. Identity-with-Minerva collapses into Identity-with- . . . nothing! Pace Plantinga, of course.
In the case of identity-with-Heidegger, surely this property, if it exists at all, exists iff Heidegger does. Given that Heidegger is a contingent being, his haecceity is as well. And that conflicts with the notion that propositions are necessary beings. Well, I suppose one could try the idea the some propositions are contingent beings.
Are there any solutions to the former problem (which you've blogged and written about before!) you think are promising? Further, what do you think of the second problem?
Perhaps you think the second problem can be sidestepped by saying that "Heidegger's wife" is just shorthand for some longer description, e.g. "the woman who was married to the man who wrote a book that began with the sentence '...'". I don't know that it is so easy, because that sentence itself makes reference to things that are contingently existent (women, men, books, sentences, marriage...).
Yes,all those things are contingent. But that by itself does not cause a problem. The problem is with the notion that proper names are definite descriptions in disguise. If the very sense of 'Ben Franklin' is supplied by 'the inventor of bifocals' (to use Kripke's example), then the true 'Ben Franklin might not have invented bifocals' boils down to the necessarily false 'The inventor of bifocals might not have invented bifocals.' (But note the ambiguity of the preceding sentence; I mean the definite description to be taken attributively not referentially.)
The current issue of Dialectica (vol. 64, no. 2, June 2010) includes a symposium on Richard Gaskin, The Unity of the Proposition (Oxford 2008). Gaskin's precis of his work is followed by critical evaluations by William F. Vallicella ("Gaskin on the Unity of the Proposition"), Manuel Garcia-Carpintero ("Gaskin's Ideal Unity"), and Benjamin Schnieder ("Propositions United: Gaskin on Bradley's Regress and the Unity of the Proposition"). The symposium concludes with Gaskin's replies ("The Unity of the Proposition: Replies to Vallicella, Schnieder, and Garcia-Carpintero").
1. One of the entailments of the doctrine of divine simplicity (DDS) is that God is identical to: God's omniscience, God's omnipotence, and in general God's X-ness, where 'X' ranges over the divine attributes. And it is easy to see that if God = God's F-ness, and God = God's G-ness, then (by transitivity of identity) God's F-ness = God's G-ness. I suggest that we use 'divine attribute' to refer to those properties of God that are both essential and intrinsic. The problem, of course, is to make sense of these identities given the fact that, prima facie, they do not make sense. The pattern is the same as with Trinity and Incarnation. These doctrines imply identities which, on the face of it, beggar understanding. It thus falls to the philosopher of religion to try to render coherent that which, on the face of it, is incoherent.
2. One of the questions that arise when we try to make sense of DDS concerns which category of entity such phrases as 'God's omniscience' pick out. One possibility is that such phrases pick out properties, whether universal (multiply exemplifiable) properties or particular (not multiply exemplifiable) properties, also known as tropes. But this leads to trouble as Brower points out. For if God is identical either to omniscience or to his omniscience, then God is identical to a property -- which sounds absurd: how can God, a person, be a property? Properties are predicable entities, but God is an individual and so not predicable. Properties are exemplifiable entities (whether multiply or non-multiply); but God is an individual and so not exemplifiable. Properties are abstract (causally inert) whereas God is concrete (causally active/passive). No property is a person, but God is a person. No property creates or knows or loves. These are some hastily sketched reasons for thinking that God cannot be identical to his properties.
3. Jeffrey E. Brower forwards an interesting proposal. He suggests that such phrases as 'God's nature,' 'God's goodness' and 'God's power' refer to "entities of a broadly functional type -- namely, truthmakers." (Simplicity and Aseity, sec. 2) The idea is that 'God's omniscience' refers to the trruthmaker of 'God is omniscient' or perhaps to the truthmaker of the proposition expressed by 'God is omniscient.' If (Fregean) propositions are the primary truthbearers, then (tokenings of) declarative sentences that express such propositions can be said to be secondary truthbearers. I trust that it is clear that truthbearers and truthmakers are not to be confused. One key difference is that while some truthbearers are are false, no truthmaker is false. Truth and falsity are properties of certain representations (propositions, declarative sentences, beliefs, judgments, etc.) whereas truthmakers are the ontological grounds of some true truthbearers. If I understand Brower's view, it is not only that truthmakers are neither true nor false -- every TM theorist will hold this -- but also that truthmakers are not at all proposition-like. By contrast, I follow D. M. Arstrong in holding that truthmakers must have a proposition-like structure. But more on this in a moment.
4. Roughly, a truthmaker is whatever plays a certain role or performs a certain function; it is whatever makes true a true truthbearer. The 'truthmaker intuition' -- which I share with Brower -- is that a sentence such as 'Tom is blogging' cannot just be true; there is need of some worldly entity to 'make' it true, to serve as the ontological ground of its truth, to 'verify' it in an ontological, not epistemological, sense of this term. To say that some or all truthbearers need truthmakers is not yet to specify which sort of entity plays the truthmaker role. Among philosophers who accept the need for truthmakers there is disagreement about the ontological category to which they belong.
Brower says rather incautiously that the functional characterization of truthmakers "places no restriction on the specific nature or ontological category to which a truthmaker can belong." (sec 2.1) That can't be right. Surely there are some restrictions. For one thing, a truthmaker cannot be a Fregean proposition for the simple reason that such items are among the items made true by truthmakers. And the same goes for declarative sentences, beliefs, and judgments. My belief that the cat is asleep is either true or false and as such is a truthbearer. It is in need of a truthmaker but is not itself one. Of course, the fact of my believing that the cat is asleep can serve as truthmaker for the sentence ' BV now believes that the cat is asleep' if concrete facts are admitted as truthmakers -- but that is something else again. So not just anything can be a truthmaker. Charitably interpreted, what Brower is telling us is that TM theorists are allowed some ontological latitude when it comes to specifying which category of entity is fit to play the truthmaker role.
5. Let us note that if a true Fregean proposition p entails a Fregean proposition q, then one could say that the first 'makes true' the second. And so one could speak of the first as a 'truthmaker' of the second. But this is not what is meant by 'truthmaking' in these discussions despite the fact that p broadly logically necessitates q. What is intended is a relation of broadly logical necessitation that connects a nonpropositional entity (but on some theories a proposition-like entity) to a propositional entity, or more precisely, to an entity that can serves as the bearer or vehicle of a truth-value. As I see it, the entailment relation and the truthmaking relation are species of broadly logical necessitation; but truthmaking is not entailment. Entailment will never get you 'outside the circle of propositions'; but that is exactly what truthmaking is supposed to do. A truthmaker is an ontological, not propositional or representational truth-ground. Philosophers who are attracted to truthmakers typically have a realist sense that certain of our representations need to be anchored in reality.
Brower sees it a little differently. He would agree with me that entailment and truthmaking cannot be identical, but he thinks of it as "a form of broadly logical necessitation or entailment" and says that entailment is necessary but not sufficient for truthmaking. (Sec. 2.1) So Brower seems to be maintaining that while there is more to truthmaking than entailment, every truthmaker entails the truth it makes true. But this makes little or no sense. Entailment is a relation defined on propositions. If x entails y, then you can be sure that x and y are propositions or at least proposition-like entities, whether these be sentences or judgments or beliefs or even concrete states of affairs such as the fact of (not the fact that) Peter's being tired, which concrete fact contains Peter himself as constituent, warts and all. But for Brower, as we will see in a moment, concrete individuals such as Socrates, entities that are neither propositions nor proposition-like, can serve as truthmakers. As far as I can see, it makes no sense to say that Socrates entails a proposition. It makes no sense because entailment is defined in terms of truth, and no individual can be true or false. To say that p entails q is to say that it is impossible that p be true and q false. Since it makes no sense to say of an individual that it is true, it makes no sense to say of an individual that it entails a proposition. So truthmaking cannot be a type or species of entailment if individuals are truthmakers.
6. But setting aside for the moment the above worry, if it makes sense to say that God is the truthmaker of 'God is omniscient,' and if 'God's omniscience' refers to this truthmaker, then it will be clear how God can be identical to God's omniscience. For then 'God is identical to his omniscience' is no more problematic than 'God is God.' It will also be clear how God's omniscience can be identical to God's omnipotence.
7. But can it really be this easy to show that DDS is coherent? Although I agree with Brower that some truthbearers need truthmakers, I don't see how truthmakers could be ontologically structureless individuals or 'blobs' as opposed to 'layer-cakes' in Armstrong's terminology. By 'ontologically structureless' I mean lacking in propositional or proposition-like structure. Consider the following true intrinsic essential predicative sentences: 'Socrates is human,' 'Socrates is an animal,' Socrates is a material object,' 'Socrates exists,' and 'Socrates is self-identical.' (It is not obvious that 'Socrates exists' is an essential predication inasmuch as Socrates exists contingently, but let's not enter into this thorny thicket just now.)
Brower's claim is that in each of these cases (which parallel the true intrinsic essential predications of divine attributes) the truthmaker is the concrete individual Socrates himself. Thus Socrates is the truthmaker of 'Socrates is human' just as God is the truthmaker of 'God is omniscient.' Unfortunately, no individual lacking propositional or proposition-like structure can serve as a truthmaker as I argued in #5 above. Just as it makes no sense to say that Socrates is true, it makes no sense to say that Socrates entails the proposition expressed by 'Socrates is human.'
There is more to say, but tomorrow's another day. Time to punch the clock.
In an earlier post, I provided a rough characterization of eliminative materialism (EM). Here is a more technical exposition for the stout of heart. If EM is true, then there are no beliefs. But what about the belief that EM is true, a belief that one would expect eliminative materialists to hold? If we exfoliate this question will we find an objection to EM? Let's see.
1. 'Every generalization is false' is self-referential: because it itself is a generalization, it refers to itself or comes under its own scope. Hence it refutes itself. If true, then false; if false, then false; so, necessarily false. But 'There are no beliefs' is not self-referential. Neither this sentence, nor the proposition it expresses is a belief. So we must abandon hope of a quick knock-out along self-referential lines.
In his SEP entry on propositions, Matthew McGrath presents what he calls the 'Metaphysics 101' argument for propositions. Rather than quote him, I will put the argument in my own more detailed way.
1. With respect to any occurrent (as opposed to dispositional) belief, there is a distinction between the mental act of believing and the content believed. Since believing is 'intentional' as philosophers use this term, i.e., necessarily object-directed, there cannot be an act of believing that is not directed upon some object or content. To believe is to believe something, that the door has been left ajar, for example. Nevertheless, the believing and the believed are distinct.
2. The contents of believings have properties that belief-states lack. For one thing, belief-contents are sharable. That the door has been left ajar, that Frege died in 1925, that both 2 and -2 are roots of 4, are contents to which more than one mind has access. But the psychological state that I am in when I believe that the door is ajar is not sharable in the same sense. Second, the belief-contents can be accepted, rejected, entertained, etc., which is not the case for the corresponding believings, disbelievings, and entertainings unless of course these believings, etc. become the objects of higher order beliefs. Third, belief contents are either true or false, which cannot be said in the same sense of believings, etc.
3. There are occurrent beliefs.
4. There are propositions.
To understand this argument, one must understand that no particular theory of propositions is being argued for. (It even allows for such wacky theories of propositions as that propositions are sets of possible worlds. That penetrating minds have championed such theories shows that such minds can descend into wackiness under various materialist and extensionalist pressures.) The argument is to the conclusion that something or other must play the roles of truth-bearer, object of such attitudes as knowing and believing, and ground of the possibility of two or more minds' coming to believe or know the same thing. It is an argument for the existence of propositions that leaves open their exact nature. (Analogy to be explored: in the way Aquinas' God-arguments leave open the exact , and indeed largely unknowable, nature of God.)
Perhaps the argument could be strengthened by restricting it to de dicto as opposed to de re beliefs. Compare 'S believes of some black that he is articulate' with 'S believes that some black is articulate.' The first is de re, the second de dicto. The first does not entail the second. Suppose S is a redneck who believes that no black is articulate. He hears a man on the radio speaking in an articulate manner, a man who, unbeknownst to S is black. It follows that S believes of some black man that he is articulate without believing that some black man is articulate.
Be this as it may. Like any argument, the Metaphysics 101 argument for propositions can be countered in several ways. Alan Rhoda discusses one way in his post, Propositions and Make-Believe. My own view is that the argument is more credible than any of its attempted counterings. More later.
Franz Brentano, for whom intentionality is the mark of the mental, is committed to the thesis that all instances of (intrinsic) intentionality are instances of mentality. The last post in this series considered apparent counterexamples to this thesis. But there are others. Joseph Jedwab usefully pointed out in a comment on my old blog that propositions and dispositions are apparent counterexamples. Whether they are also real counterexamples is something we should discuss. This post discusses (Fregean) propositions. Later, dispositions — if I am so disposed.