Clutch

There are a bunch of different modal logics. Roughly speaking, it is typically thought that S5 does a good job of expressing logical possibility. Other logics (esp. S4) are more suited for capturing epistemic notions. Mixing epistemic with logical notions of possibility is a wash, though.

For example, if the view known as logicism is correct, then numbers exist necessarily. Now, is logicism correct? Well, the jury is out on that. Some say yes, some say no. Some people are nominalists and claim that there are no numbers at all.

Now, can we conceive that the logicists are right? Sure. In this sense, then, it's possible that the numbers are necessary. For all we know they are. So let's use the Philip-Tercel slingshot to launch ourselves into the necessity of the numbers: It's possible that the numbers exist necessarily; therefore the numbers really do exist necessarily. Hey, the jury isn't out after all! Someone tell those nominalists that they are necessarily wrong!

Yuck.

By the same token, if we start by asking whether someone will grant that it's at least *possible* that God exists, we have to be clear about what exactly is being granted. If all that's being granted is the bare possibility that, hey, for all we know something might come along that would make it reasonable for people to say, "there's a god", whatever definition that would receive -- well, that's a merely epistemic possibility. And "it is epistemically possible that it's logically necessary that P" does *not* imply "it is logically necessary that P" -- no more here than in the case of the numbers.

Finally, I would be careful about receiving formal logical instruction from Philip Osbourne. He recently formalized the following "inference" for me: If p then q; if q then r; therefore, r. Philip called this "modus ponens". Caveat emptor!

Philip Osborne

"Finally, I would be careful about receiving formal logical instruction from Philip Osbourne. He recently formalized the following "inference" for me: If p then q; if q then r; therefore, r. Philip called this "modus ponens". Caveat emptor!"

Yes, I admit that that was a sloppy inference by me (I skipped a few steps). Although in my defense, the argument I presented there was ultimately valid, which you demonstrated with your reformulation. Also, I would be careful about receiving spelling instruction from Clutch, who writes my name as "Osbourne" when "Osborne" is plainly visible in the author description!

Nowhere in my post did I indicate that the epistemic possibility of God's existence implies that God's existence is logically possible, so it is an incorrect characterization to say that I claimed otherwise. In order for the S5 argument of Hartshorne and Plantinga to be sound (or at least for us to know that it is sound), there must be some sort of demonstration that the existence of God is logically possible, which goes beyond the mere intuition that His existence is possible.

[ July 25, 2002: Message edited by: Philip Osborne ]

[ July 25, 2002: Message edited by: Philip Osborne ]</p>

Clutch

Philip, my apologies for mangling your name! It's that darned Canadian/British 'ou' thing.
Fine. Nowhere in my post did I indicate that you said this. What I showed is that failing to make this distinction clear, moving incautiously from unqualified natural language terms like "possible" and "necessary" to the logical operators of S5, is a recipe for magical and fallacious misproofs. By the same token, nowhere did you note this ambiguity and caution against it. So I did.

That, I think, is what the atheists or agnostic were bridling at, in their reaction to the claim that "possibly necessarily P" implies "necessarily p". Namely, that merely by not ruling out dogmatically the possibility of evidence or some hitherto unimagined argument for a god's necessary existence, they could be committed to such a god's necessary existence, simpliciter. That was the flavour of the disbelieving reactions -- and, hence, their disbelief was entirely correct.

Philip Osborne

"Fine. Nowhere in my post did I indicate that you said this."

I read this characterization in from your quote, "So let's use the Philip-Tercel slingshot to launch ourselves into the necessity of the numbers: It's possible that the numbers exist necessarily; therefore the numbers really do exist necessarily." My response was that I said nothing to advocate this "slingshot," so it shouldn't be called mine. Perhaps I was wrong in my interpretation; I'm simply pointing out how I was lead to it.

About the source of the non-theists' disbelief over the argument, I think you are correct. That's why I accept the need for "big words," that is, analytic philosophy should use unusual words (words not used in everyday language) because it deals with unusual concepts. If analytic philosophy used everyday words, people would confuse their meanings with the everyday meanings, resulting in confusions similar to the one we observe with the S5 argument.

Sincerely,

Philip

Clutch

Philip, you're quite right. And even though you did not caution that the formal argument you gave could not simply be read back "in English" without crucial qualifications, Tercel did go out of his way to note that the relevant sense of possibility was not epistemic.

So read "the Philip-Tercel slingshot" as "the inviting S5 inference". Either way, it's a fallacy on the reading that seems to make it work so cheaply.

Automaton

Starting from the law of universal possibility, I can prove the law of universal necessity.
1. &lt;&gt;~p -&gt; []&lt;&gt;~p (law of universal possibility.)
2. ~[]&lt;&gt;~p -&gt; ~&lt;&gt;~p (MT reversal.)
3. ~[]&lt;&gt;~p -&gt; []p (solving ~&lt;&gt;~ to [].)
4. ~[]~[]~~p -&gt; []p (solving &lt;&gt; to ~[]~.)
5. ~[]~[]p -&gt; []p (double negation.)
6. &lt;&gt;[]p -&gt; []p (solving ~[]~ to &lt;&gt;.)

[ July 25, 2002: Message edited by: Automaton ]</p>

Automaton

Whatever do you mean? The system of S5 is just system S4 with the addition of axiom 5. By different modal logics, I think you don't mean systems of axioms in straight modal logic, but other logics entirely, such as deontic or doxastic. These types are indeed epistemic, but they are still considered "modal" as they talk of the modality of epistemic states, however they have nothing to do with straight modal logic or any of its systems or axioms.

Clutch

Hmm. Well, I mean what is usually meant by the plural "logics". As in, classical and intuitionistic logics are different -- even though classical is just intuitionistic plus LEM. Just as there different substructural logics as well.

Just as, yes, S5 is S4 plus (B). So what? S4 is just K plus (T) and the 4-principle. G is K plus W. And K4.3 is K plus 4 plus L. Hooray, are we accomplishing something? I have no idea what you're taking exception to, really. These are different logics in the rather obvious sense that they do not share all the same axioms, beyond K. Inferences permissible in one are impermissible in another. So, different.

Are you disagreeing that S4 has been held to be a good candidate for an epistemic logic? The 4-principle amounts to KK, which was long considered plausible, but has come into disrepute with the rise of justification externalism. T amounts to the factivity of knowledge. The epistemic reading of S4 is familiar.

Your claim about deontic and doxastic logics I do not understand either. K4 is sometimes advanced as a doxastic logic, and KD is recommended occasionally as a deontic logic. If by "straight" modal logic you mean the shared element of normal modal logics, then that's just K. And all of these logics share K, so it is odd -- meaning, plain wrong -- to claim that these "have nothing to do with straight modal logic or any of its systems or axioms".

If none of that is what you mean, though, maybe you could explain yourself more clearly. Thanks.

[ July 25, 2002: Message edited by: Clutch ]</p>

Kenny

Automaton,

No; at least not in accordance with what I understand unlimited to mean: a being that possess all the positive qualities of being to their maximal degree. In this sense, there is only one maximum – only one possible being to be described which holds this attribute.

But, according the Christian conception of God, at least, God freely chose to create the universe. “Having created the universe” is an accidental rather than essential quality of God’s being.

Granted, there are numerous parodies of the ontological argument you can construct. The simplest one, and the one the atheist could most plausibly claim intuitive warrant for, would probably be Plantinga’s argument in reverse:

[quote] Here, the key premise of this “atheistic ontological argument” is (1) and all else follows modally from (1) and the definitions. However, if a person, such as myself, has intuitive reason to accept the key premise of the theistic ontological argument “there is a possible world in which maximal greatness is instantiated,” then that person has every reason to reject (1) in the above argument.

Clearly, “exact same reasoning” needs some fleshing out here. Any valid argument can be parodied by plugging different premises into the same logical structure. But, surely it is not irrational to accept one argument because the premises seem intuitive to you and reject another because its premises do not.

The proper epistemic attitude towards whether a particular logical proposition is logically possible no doubt varies from proposition to proposition. In some cases, we may hold with certainty that some logical proposition is logically possible – truths such as “2+2=4,” for instance or certain basic metaphysical truths such as “something exists” (and actually, I believe that “God exists” is a basic metaphysical truth that can properly be held to be true and therefore logically possible, with certainty, as well, but I’m trying to generate non-controversial examples at the moment). Other sorts of propositions are more properly regarded with agnosticism concerning their logical possibility – propositions such as “Goldbauch’s Conjecture is correct,” for instance. Other sorts of propositions, logical contradictions for example, can be known with certainty to be impossible. Still other sorts of propositions, even though we cannot prove that they are logical impossibilities, seem intuitively absurd enough that we can safely regard them as such. Consider the property of “maximal-Barney-ness” the property of being a stupid annoying purple dinosaur in all possible worlds. I think it is safe to say that there are no possible worlds where maximal-Barney-ness is instantiated.

Actually, the last example is, I think, informative, because here we recognize an example of a property which can’t be proven to be logically impossible but is still intuitively recognized as such. Here it seems perfectly rational, indeed warranted, to regard maximal-Barney-ness as a logical impossibility on intuitive grounds. On the flip side, it seems reasonable to me that there might be propositions whose logical possibility may be rationally affirmed on intuitive grounds.

No, for several reasons. First, it is possible that two rational people might have differing intuitions or rank certain intuitions higher than others. Numerous controversies in philosophy and mathematics are fed by this fact. Second, it is possible for someone to suffer from a cognitive malfunction in a particular area without being irrational or insane. Third, some have more attuned intuition in certain areas than others. For a mathematical prodigy a certain complex theorem may be recognized intuitively in such a way as to be warranted for that individual while another may struggle just to comprehend the meaning of the theorem let alone intuit it’s truth value. This suggests that intuition may serve as a source of warrant for some regarding the truth of a particular proposition but not for others. Finally, there are certain arguments that can only be settled by an appeal to intuition. If someone expressed skepticism toward the proposition “2+2=4,” for instance, or toward the principle of induction, or the existence of other minds, there is no other way to settle the matter than an appeal to intuition.

Well, all of mathematics traces itself back, eventually, to basic rational intuitions. Those propositions which are regarded as “certain” in mathematics are based on intuitive premises that seem so obvious to everyone that anyone who denied them would be considered either foolish or insane. There are mathematical controversies, however, largely due to the fact that people have varying intuitions or they rank conflicting intuitions with differing priorities. Of course, it’s best to try and argue from premises that everyone finds intuitive, but this is not always possible.

Of course not. Intuition is fallible and, like most other sources of warrant, is subject to potential defeaters and overridders form other sources of warrant. But, intuition is a source of warrant. It is rational, all things being equal, to trust it, and some if not most of the things we know about the world depend directly or indirectly upon it.

I agree that the OA is not very useful for convincing non-believers, but that does not mean it isn’t sound or that it’s question begging or that it isn’t a good argument or that a rational person could not receive warrant towards her belief in God from it.

God Bless,
Kenny

Kenny

Synaesthesia,

But, as far as I can see, you have failed to demonstrate that the argument does beg the question. How does it do so, exactly? The only argument you have produced to that effect thus far is that the conjunction of its premises are logically equivalent to the conclusion. But, that’s true of any valid logical argument and it would be very strange indeed to say that all valid logical arguments beg the question. Plantinga’s OA has one key premise, that “maximal greatness is logically possible.” This premise is accepted on intuitive grounds. The rest follows modally from the definitions. Where is the question being begged?

God Bless,
Kenny