Sunday, September 12, 2010

The Modal Scope Fallacy

Does divine foreknowledge threaten libertarian free will? Or, to put it another way, is an omniscient agent incompatible with The Garden Of Forking Paths model of free will, the one in which we could have done otherwise?

I think not. But what if somebody says, the fact that god is omniscient means that god infallibly knows that I will eat cornflakes for breakfast tomorrow. God can't fail to know this, being omniscient. The idea then, is that necessarily god knows I will eat cornflakes for breakfast tomorrow. Hence, necessarily, I will eat cornflakes tomorrow and that means it is not possible that I won't eat cornflakes for breakfast tomorrow, and this implies that I can't do otherwise, which refutes libertarian free will.

However, I think this argument fails. What do you think?

47 comments:

Sam said...

God knowing X only implies that X is true. If God knows that tomorrow you'll eat cornflakes, it doesn't mean you can't do otherwise; it only means that you won't do otherwise. I went into more detail about this here.

Psiomniac said...

Yes, I agree with this. Omniscience just means that, necessarily, if tomorrow you'll eat cornflakes then god knows that tomorrow you'll eat cornflakes. In general, where @ means 'necessarily' and Kc(p) means that agent C knows p, then if agent G is omniscient:

@(p => Kg(p))

Whereas the confusion arises because people construe it this way (and # means 'possibly'):

1) @(Kg(p) => p)

2) @Kg(p) => @p (Axiom K on 1)

3) @Kg(p) (Premise, god's knowledge is infallible in the sense that god can't fail to know that p, hence ¬#¬Kg(p) == @Kg(p))

4) @p (Conclusion from modus ponens on 2 & 3)

This appears to torpedo libertarianism. But 3 is false.

Phaedrus said...

I'm afraid I disagree. Free will does not exist in the presence of omniscience. Why? Because Omniscience evokes a determined future. If the future is determined, we both cannot do otherwise and will not do otherwise. Thus you do not have free will.

Accepting just causality, we can still argue for the presence of free will by appealing to that idea that we are active causal agents. But if we introduce an agent that has the power of omniscience, you have introduced a predetermined future for all subjects that agent has knowledge of. Therefore, you have no room for free will because all causal agents are now following the path fated by a deity.

As far as your premise three goes, I believe it's a bit of a strawman if you'll forgive me. The argument isn't "If tomorrow you'll eat corn flakes, then god knows you'll eat cornflakes" That's arguing FOR god's omniscience. But your argument should be demonstrating the presence or absence of free will with god already possessing omniscience: "If god knows you'll eat cornflakes, then you will eat cornflakes." This argues FROM the assumption that god already possesses omniscience, and then you can ask whether or not we have free will. Premise three is questioning god's failure to know something, but the omniscience problem already presumes god HAS omniscience and thus cannot fail to know something.

Anyway, free will is kind of a difficult concept to define. If there is no reason behind your actions, then your actions become sporadic. But if we assume there are reasons behind our actions, those reasons will be causal in nature and thus abandon us to causal determinism. On the other hand if all our actions are not determined from this argument they are sporadic and random, which poses even more problems for free will..

Psiomniac said...

I think we have to be clear about the nature of the omniscient agent. The real problem for the Christian is that given the attributes of their god, it is difficult to see how they avoid predestination as a consequence.

Predestination is inimical to free will, despite Aquinas's attempts to show otherwise. However, omniscience of itself does not entail determinism, let alone predestination. So in my view you are conflating these issues.

The flaw with 3 in my view is that an omniscience condition could reasonably be construed as:

@(p <=> Kg(p))

But 3 basically says that, necessarily, god knows that tomorrow you will eat cornflakes. Which can't be right unless necessarily, tomorrow you will eat cornflakes, which is question begging.

So I am arguing that the logic is flawed and the flaw is in premise 3. You also suspect the argument is flawed, but it seems we don't agree on why.

By the way, when you say:
Premise three is questioning god's failure to know something, but the omniscience problem already presumes god HAS omniscience and thus cannot fail to know something.
I think you have misunderstood. 3 says, necessarily god knows that p, the justification in brackets just points out that god couldn't fail to know p, since this is a condition of omniscience. Questioning doesn't come into it.

I agree with you about the difficulty with defining free will. I'm a compatibilist of a particular kind, so I know what you mean...

Phaedrus said...

I guess my response is, how does omniscience NOT entail a determined future? Foreknowledge, it seems to me, necessitates a future that is determined (because knowledge requires an objective truth condition (e.g. this future condition is true or false)), if not set by nature, then by the being that has foresight itself. Just as a matter of logic, even if the future is determined by the omniscient being minutes in advance, it's foreknowledge requires that the causal agent in question lacks free will as a result (that it couldn't have done otherwise than what the foreknowledge of the omniscient being dictates).

Psiomniac said...

Ok, I think there are three aspects to this whose interaction make this difficult to think about: the temporal, the causal, and the epistemic.

So I think you have the strong intuition that an agent can only have foreknowledge if the future is causally determined.

But as Sam points out above, although by the definition of knowledge, if an agent knows that p then p is true (your objective truth condition), this says precisely nothing about how p became true or how the agent acquired the knowledge. In particular it entails no causal relation from the knowledge of p to the truth of p (although vice versa is a different matter).

If we also move to a B-theoretic model where propositions are made true in reference to tenseless facts and bear in mind that the Christian god is often construed as atemporal, we can see that G knowing in advance is a red herring. For an atemporal agent (whatever that could mean!) there is no 'advance' or 'retrospect', they are equivalent. But if an agent knows what you did in retrospect, does that compromise your ability to have done otherwise?

So suppose there is a possible world, let's call it L in which, when you decide to have breakfast, you have a choice. You choose cornflakes but you could have done otherwise. Now, suppose I say that L also contains an omniscient agent, G. Your argument seems to be that this state of affairs is inconsistent, but I can't see how. G's knowledge that you had cornflakes is contingent on the fact that you had cornflakes. If you'd decided on waffles, then G would have known that fact instead. L remains causally indeterministic since G's knowledge did not determine your choice, and finally G knows every p in the set of true propositions relating to world L regardless of when their truth value is fixed by events in L.

So it seems to me that an omniscient agent does not preclude libertarian free will either on logical or causal grounds.

Phaedrus said...

Foreknowledge is not a red herring. A red herring is an irrelevant topic to the argument. While an atemporal being may not think in terms of past, present, and future, WE DO. This demands that foreknowledge be addressed relative to agents in the present (the argument isn't whether god "feels" time, but that WE do, and that creates a problem when we say that god has knowledge of our future). Time being infinite, and a being who is atemporal doesn't really help your argument. As long as omniscience contains knowledge of the future relative to the our present, we have a determined future (which doesn't need to be causal to present the logical problem at hand).

Now all you're doing to fix the argument is playing with the definition of omniscience and removing the concept of foreknowledge from the problem. If omniscience is only perfect knowledge of what HAS happened and what IS happening, then it does not require a determined future. So I agree with this. BUT, omniscience for the Abrahamic religions is often presented as knowledge of the future and what will be. Once you do this, you have a determined future relative to the agents that being has foreknowledge of (Whether the deity thinks in this manner or not - that's not the logical problem).

By your argument, the knowledge is known in advanced from our perspective (the present), while God is atemporal knows all present, past, and future. Just because god transcends time doesn't mean this solves the problem. God cannot both exist and not exist at the same time. He couldn't create a rock so heavy he couldn't lift it, and then fail to lift it (omnipotence). He is still constrained by logic in all possible worlds (You seem to agree with Lewis, so there you go). This means that perspective necessitates the concept of time. Foreknowledge from humanity's perspective of the present, requires a determined future for all beings living in that present.

So to solve the problem you would have to argue that god does not have foreknowledge. But if you do this, you are saying God has no knowledge of the future (only the present and past, because the future has not happened). This is fine, but most followers of the Abrahamic religion would disagree with this conclusion.

Phaedrus said...

Putting it in logical form:

(1) If God has foreknowledge that S will do A, then it is necessary that S will do A.

(2) If it is necessary that S will do A, then S is not free with respect to doing A.

Therefore,

(3) If God has foreknowledge that S will do A, then S is not free with respect to doing A.

The solution is that god does not have foreknowledge, but then god is not really ALL knowing in the traditional sense.

You can also take Pike's more powerful argument and make the previous argument even stronger:

(4) A proposition reporting an event in the past is forever afterwards “fixed” or “unalterable” or accidentally necessary.

(5) A contingent proposition that is entailed by an accidentally necessary proposition is itself accidentally necessary (accidental necessity is closed under entailment).

(6) If a proposition is accidentally necessary at a time, no one is able at any later time to make it false.

If god is infallible under this argument then his belief in P makes any contingent proposition that follows in the future, entailed by P. If S cannot do otherwise than A because it is contingent upon P, then S is not free.

So even if God has only infallible beliefs of present and past action, this determines a future entailed by those actions. Unless you just abandon causality altogether.

Sources:

http://plato.stanford.edu/entries/omniscience/#ForHumFreAct

http://plato.stanford.edu/entries/free-will-foreknowledge/

Psiomniac said...

Ok, sorry, 'red herring' was the wrong way to put it, since clearly a lot of the literature deals with issues relating to foreknowledge.

What I was trying to get across was expressed in the second of your sources this way:
"The necessity of the past has the advantage of being deeply imbedded in our ordinary intuitions about time; there are no ordinary intuitions about the realm of timelessness. Perhaps, then, the view that God is timeless puts the theological fatalist on the defensive."

I think you have helped yourself to these intuitions in your argument, and although you could argue that your sources countered my Boethian take on this, I don't think you did. Just because we think in terms of past present and future, you cannot just assume that the propositions with temporal indexicals will transfer meaningfully to a timeless agent. You could have made the point that the notion of a timeless agent is incoherent, and I don't think I could defend against that.

The argument that you put in logical form is the one that commits the modal scope fallacy in the title of this blog entry. This is pointed out in your first source, which notes that Aquinas had spotted it:
"Subsequent philosophers, however, beginning at least as early as Aquinas, identified a flaw in the argument. According to Aquinas (Summa contra Gentiles, I, 67, 10), the first premiss is ambiguous between the “necessity of the consequence” and the “necessity of the consequent.”

Phaedrus said...

Well I didn't mean to offend you or anything. Just trying to figure out why your argument helps free will, or at least why you think it does.

Why is premise three false, and how does that help? So god CAN fail to know something? Then he is not omniscient. And Sam's can't-won't argument isn't compelling. It's stating that if god has future knowledge of an action, the agent responsible will always choose that action. Even if the choice is genuinely from the agent and not god, this still describes a static reality that cannot travel outside the path of god's foreknowledge (which if you are talking about eating cornflakes tomorrow, we are talking about foreknowledge from the perspective of the agent who exists within time, and has a point of view from the present). It describes a world where every action you will ever commit is fated and you're left with nihilism. The logical problem has to be addressed from the perspective of humanity, not from the ambiguous perspective of god. It is the perspective of humanity who want a free relationship with god that is causing the problem. Which is why you can't just take time out of the equation. You have to address knowledge over past, present, and future. Because those are the concepts that would effect human free will in this problem.

Psiomniac said...

I'm not offended, in fact I thought your sources were interesting and I learned something from reading them, so thanks. Why did you think I might be offended?

I think 3) is false and this would mean the argument is unsound, which helps in the sense that it removes one objection to the compatibility of an omniscient agent and libertarian free will.

However the falsity of 3 does not entail that god can fail to know something in my view. 3 says the equivalent of: necessarily, god knows you will eat cornflakes. That can't be the case because at possible world w' you choose waffles, so at w' it is false that god knows you will eat cornflakes. So even though you will eat cornflakes and god knows it, the correct way to construe the necessity of god knowing this is:
necessarily( if you will eat cornflakes then god knows this).

On your point that we need to argue this from the perspective of humanity, in order to do that you would have to show that it is true at t0 that god knows that p at t1. How can you do that if god is atemporal?

Phaedrus said...

I agree with your assessment of premise three.

I guess I would argue that if a deity has some kind of relationship that has significant influence on temporal beings, then god cannot be completely independent of time. If god IS completely independent of time, then it would be fairly easy to write an argument that easily dismisses divine intervention in virtually all forms.


My other concern is that, if god has logical consequences on temporal beings, and the concern is a specific logical consequence on temporal beings (free will or not), then the argument has to address the logical consequence from the point of view of the agent who is being affected by that consequence. If the solution is that god is independent of time, it still doesn't have much affect if the temporal being has a perspective of god's temporal knowledge of the future. Because humanity has a perspective of past, present, and future, a being independent of time (from the perspective of the temporal being) still has knowledge of all three time spectrums which still creates a logical consequence for the temporal being. So.. This is what my intuition is having problems with.

Now Aquinas got this idea from Boethius as you pointed out, and it states that god's grasp of all temporal events in temporal reality are before god's mind all at once. Aquinas likens this to a circle analogy in which "a timeless God is present to each and every moment of time is compared to the way in which the center of a circle is present to each and every point on its circumference" (SCG I, 66).

But the Boethian solution does create another problem structurally parallel to this one according to Linda Zagzebski.

"If God is not in time, the key issue would not be the necessity of the past, but the necessity of the timeless realm. So the first three steps of the argument would be reformulated as follows:
(1t) God timelessly knows T. 
(2t) If E is in the timeless realm, then it is now-necessary that E. 
(3t) It is now-necessary that T.
"Perhaps it is inappropriate to say that timeless events such as God's timeless knowing are now-necessary, yet we have no more reason to think we can do anything about God's timeless knowing than about God's past knowing. The timeless realm is as much out of our reach as the past. So the point of (3t) is that we cannot now do anything about the fact that God timelessly knows T. The rest of the steps in the timeless dilemma argument are parallel to the basic argument. Step (5t) says that if there is nothing we can do about a timeless state, there is nothing we can do about what such a state entails. It follows that we cannot do anything about the future."

Pasted from


Check out some of the other solutions at the above link. Zagzebski summarizes them beautifully. ;)

Phaedrus said...
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Phaedrus said...
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Phaedrus said...

Sorry, having posting issues. Here is the source I was referring too:

http://plato.stanford.edu/entries/free-will-foreknowledge/#2.1

Psiomniac said...

Yes, on your first two paragraphs, the reasons I said I couldn't defend against an argument that the concept of an atemporal agent is incoherent is that I think that is the case and can't think of any counters.

On the further problem of the inaccessibility of the timeless realm, I'm not so sure. You will have noticed that I quoted the paragraph after the one you did, and I still think that our intuitions about the past do not carry over in terms of necessity per accidens. If I choose waffles then for all time god knows I chose waffles. If I choose cornflakes, then for all time god knows I chose cornflakes. This seems contradictory from our temporal perspective, but I'm not convinced that there is a contradiction that is not subsumed under the primary difficulty of an atemporal being's interface with a temporal universe.

Still let's face it, it's all bonkers.

Bx4 said...

Why 'divine' and why 'foreknowledge''

Wouldn't an omniscient observer with a B-theoretic perceptual and cognitive stucture sit better as it would


(a)Avoids the theological baggage

(b) Avoids issues of the propositional status of future conditionals

Psiomniac said...

Yes probably.

If you have read the comments above you'll realise that I don't think the problem is solved by recasting this in the terms you suggest though.

I'm happy to tackle it in those terms, but so far we have been unable to resolve our differences in the other place even when we discussed it in a B-theoretic context.

Bx4 said...

Agreed

But I think we can start from epistemic axiom T

(a) @(KcP=>P)

and (from alethic axiom K)

(b) @KcP=>@P


and look at a B-theoretic model where tenseless facts are the referents of tensed sentences.

From this we might manage an agreed notion of an omniscient observer and see where it goes from there.

Quite happy to look at this in the other place but it seemed to hit the buffer with the mereology of the Worm People

Psiomniac said...

I'm happy to attempt that here, I agree on your (a) and (b) above and I think that my arguments work in a B-theoretic context.

My concern is that we failed to agree some basics in the other place. For example we couldn't even agree on what @p means, so how do we avoid reaching the same impasse here?

Bx4 said...

My aim is to proceed by 'baby steps' so that we can avoid any 'disagreements' that are a consequence of mere amphiboly and so identify genuine points of disagreement.

For @P

I take '@'to be a notation for the modal primitive*** 'it is necessary that' or alternatively 'necessarily'

I take 'p' to be /some/ proposition which has as a referent /some/ fact in the world F

Here I have deliberately avoided 'any arbitrary proposition P' since this might be seen as implying that agent c is omniscient.

This is not my intent agent c may know P but this does not entail that he knows some other prposition.

***While we could alternatively treat 'possibly'(#)or 'it is possible that' as the primitive, I suggest in this instance we treat '@' as the primitive such that #P is defined as ¬@¬P

going off piste for a bit

Bx4 said...

My aim is to proceed by 'baby steps' so that we can avoid any 'disagreements' that are a consequence of mere amphiboly and so identify genuine points of disagreement.

As for '@P'

I take '@'to be a notation for the modal primitive*** 'it is necessary that' or, alternatively, 'necessarily'

I take 'P' to be /some/ proposition which has as a referent /some/ fact (state of affairs) in the world 'F'

Here I have deliberately avoided 'any arbitrary proposition P' since this might be seen as implying that agent c is omniscient.

This is not my intent, agent c may know P but this does not entail that he knows some other proposition Q.

***While we could, alternatively, treat 'possibly'(#)or 'it is possible that' as the primitive, I suggest in this instance we treat '@' as the primitive such that #P is defined as ¬@¬P

going off piste for a bit

Bx4 said...

Oops! appear to have posted twice. Please disregard the first post.

Psiomniac said...

I don't have any problem with any of that so far. I think the reason we ground to a halt last time was that we couldn't agree on what @p means even after we translate '@' in exactly the way you suggest above.

We could try again, let's suppose p stands for something like 'it is raining at (x,y,z,t)'.

Then suppose I say:

1) p (premise).

then I'm taking as my premise that it is in fact raining at (x,y,z,t). What I'm not doing is saying that either it is or it isn't raining at (x,y,z,t).

Now suppose I had said:

1) @p (premise).

then I'm taking as my premise that necessarily it is raining at (x,y,z,t). What I'm not doing is saying that necessarily either it is or it isn't raining at (x,y,z,t) since I take that as a given in the form of the law of the excluded middle.

Now, quibbles aside, unless we can agree something like the above, I can't see how to make progress.

Bx4 said...

Perhaps the nub of our disagreement centres not so much on the proposition P but rather its referent, F, the relevant state of affairs (F) in the world, that is:

F(it is raining at x,y,z,t) is the referent of P('it is raining at x,y,z,t')

Specfically a difference as to whether F can be contigent or not.

Note: the '' round P are not meant indicate a specific utterance of P but are simply intended as a way of distinguishing the proposition P from the fact F.

Bx4 said...
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Bx4 said...

As to your specific point:

(a)p (premise):it is in fact raining at (x,y,z,t).

(b) @p (premise: necessarily it is raining at (x,y,z,t)

I am quite happy to go along with both. I'm not really clear why you would imagine I would do otherwise.

'I take that as a given in the form of the law of the excluded middle.'

I think it was stephenlawrence in the other place who didn't take it as a given though, as I recall, he was arguing erroneously from the LNC rather than the LEM

Psiomniac said...

Specfically a difference as to whether F can be contigent or not.
What do you think? What does it mean to say that what is actual possibly isn't? It is easy to suppose that p is contingent because we can imagine that F is different than what is actual without logical contradiction. But to suppose F itself can be contingent seems to lead to a contradiction, namely that it is possible that actual states of affairs do not obtain. Maybe I'll have to think some more on that.

Psiomniac said...

I am quite happy to go along with both. I'm not really clear why you would imagine I would do otherwise.
Specifically, it's because you said this:

"I have just had a speed read of of your 557. The crux of your argument seems to be that Ramsey's Ladder /entails/ that if necessarily P then necessarily P is true.

Of course it doesn't as you can see if you substitute ¬P for P which would make ¬P necessarily true and P necessarily false.

Moreover:

'Many philosophers divide the class of propositions into two mutually exclusive and exhaustive subclasses: namely, propositions that are contingent (that is, those that are neither necessarily-true nor necessarily-false) and those that are noncontingent (that is, those that are necessarily-true or necessarily-false).'
('Truth', Internet Encyclopedia of Philosophy)

Which seems to contradict your claim that a necessary proposition /must/ be a necessarily-true


But the IEP quote doesn't mean that the same p can be necessarily true or false, it means that there is a set of propositions, some of which are necessarily true and some necessarily false. So I accept that you can have @¬q which is taken to mean that, necessarily q is false.

All I was trying to get you to agree in #581 on that thread was that if we say:

1) @p

then we mean that necessarily p, which is equivalent to saying that necessarily p is true.

If you now agree this, as you seem to, we can move on.

Bx4 said...

Sorry for delay. Want to read environs of 557 before I reply and I have not had time to do so yet.

One point though on IEP extract:

'Many philosophers divide the class of propositions into two mutually exclusive and exhaustive subclasses: namely, propositions that are contingent'

Note 'many' not 'all'. I'm with those who don't. Can't see how propositions with referent facts can be contingent.

Psiomniac said...

I don't really understand your view on this. Perhaps your thinking on the ontological status of 'possibilia' leads you to conclude that the actual is necessary. If so, I don't agree.

Bx4 said...

'I don't really understand your view on this. Perhaps your thinking on the ontological status of 'possibilia' leads you to conclude that the actual is necessary. If so, I don't agree.'

I was a much narrower polnt about how a proposition like P('it is raining at x,y,z.t') which has a referent the fact F(Rain at x,y,z,t) is contigent.

This does not presuppose that a failure to demonstate that the actual is can be contigentof the actual, validates the notion of the actual as necessary.

Quite the opposite since I find the notion of contingent facts and necessary facts incoherent not to say absolutely daft

Bx4 said...
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Bx4 said...

'I don't really understand your view on this. Perhaps your thinking on the ontological status of 'possibilia' leads you to conclude that the actual is necessary. If so, I don't agree.'

It was nothing to do with 'pssibilia' which seen abit of a movable feast rather a much narrower polnt about how a proposition like P('it is raining at x,y,z.t') which has a referent the fact F(Rain at x,y,z,t) can be contigent.

This does not presuppose that a failure to demonstate that the actual can be contigent, validates the notion of the actual as necessary.

Quite the opposite since I find the notion of contingent facts and necessary facts not just incoherent but absurd.

Bx4 said...

double posting again probles with the word veification 'feature. ignore first of pair

Psiomniac said...

Ok, so I don't understand your view on this. I don't see why a proposition cannot be contingent just because it has F as its referent, even if F is not contingent or necessary. Perhaps you could explain this.

Bx4 said...

Perhaps you could begin by defining what you mean by contingent?

I don't understand the difficulty you have with my argument but I'll try again.

Assume B-theoretic spacetime continuum with the fact F(Rain at x,y,z,t) and with the referring proposition P('It is raining at time x,y,z,t').

Then what feature of the above warrants the labelling of P as 'contigent' or, alternatively, as 'necessary'?

Psiomniac said...

'Contingent' just means not necessarily true nor necessarily false doesn't it?

P is contingent on F. It is not logically necessary.

An example of a necessary proposition is Q, where:

Q==Pv¬P

Bx4 said...
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Bx4 said...

'Contingent' just means not necessarily true nor necessarily false doesn't it?'

I don't see that this gets us anywhere since all you have done is defined one problematic state 'contingent' in terms of the other problematic state 'necessary'

Moreover, this does not explain why you hold that either state is relevant to PrF where 'r' is the relationship 'has as a referent'.

P is contingent on F. It is not logically necessary.

This seems have the same problem as the above except insofar as you have added the qualifier 'logical' to the modality 'necessary' but not to the modality contigent.

This seems a much more limited claim. Is the antithesis of 'logically necessary', contigent or logically contingent?

If the latter, in what sense is logically contingent different from contingent?

'An example of a necessary proposition is Q, where:

Q==Pv¬P'

I'm not quite clear as to what work '==' is doing here and what the definition of a contingent proposition would be. Perhaps you would clarify?

Psiomniac said...

Sorry, but I don't understand your view at all. I have given a definition of 'contingent' as you asked.

You have not confirmed whether you now agree on the meaning of @p. Please could you address this.

A few comments ago I asked you to explain your view, please could you give your objection to the idea of contingent propositions clearly, or at least an exposition of your view.

Your objections to my definition of 'contingent' can be fixed. Replace '==' with '='; I accept that '==' was unnecessary, and remove 'logical' to give:

P is contingent on F. It is not necessary.

An example of a necessary proposition is Q, where:

Q=Pv¬P

I don't see why this is problematic. A necessary proposition is true under all valuations. Above, Q is true for all possible truth values of P.

I hope that clarifies.

Psiomniac said...

One refinement I need to make is to say that a necessary proposition is a proposition which is true under every possible valuation.

It might help to consider the following:

1) Kc(p) => p

where '=>' is material implication.

If Kc(p)= T and p = F then the above is false. If this is not a possible valuation of 1) then this proposition is necessary and we can say;

@(Kc(p) => p)

In fact in defining Kc(p) we have to take Kc(p) => p as an axiom, in other words by the definition of 'knowledge' it is not possible to know something that is not the case.

Bx4 said...

This is a reply to your:

http://psiomniac.blogspot.com/2010/09/modal-scope-fallacy.html?showComment=1296862149252#c9082794691043198787

In your 557 you explicitly say:

(1'@p means necessarily p, which is short for 'necessarily p is the case, ie p is true, recall Ramsay's Ladder

Asserting Ramsey's ladder assupporting your case is a bit odd. It was first enunciated by Simon Blackburn in 'Ruling Passions'(Oxford: Clarendon Press, 1998, pp. 78, 295-6)

A.W. Moore in 'Quasi-realism and Relativism (Philosophy and Phenomenological Research, Vol. LXV, No. 1, July 2002,150-156) ) decribes it thus:

This is a series of propositions each of which, bar the first, looks as if it is on a higher level than its predecessor (in the sense of being substantially
about its predecessor) though in fact they all have the same content; as Blackburm puts it, ‘Ramsey’s ladder is horizontal'

or as Blackburn puts it himself:

'We can see why this is so if we put it in terms of what we can call Ramsey’s ladder. This takes us from p to it is true that p, to it is really true that p, to it is really a fact that it is true that p, and if we like to it is really a fact about the independent order of things ordained by objective Platonic normative structures with which we resonate in harmony that it is true that p...Ramsey’s ladder is horizontal. The view from the top is just the same as the view from the bottom, and the view is p.'
(Review of Thomas Nagel, The Last Word)

http://consc.net/pics/expressivism.html

So in the end as far as its originator, Blackburn, is concerned the Ramsey Ladder reduces to no more than position p. Which seems closer to my stance on PrF than yours which seems to hold that the additional state 'contingent' C(PrF) or, alternatively, the additional state 'necessary N(PrF), where 'r' stands for 'has the referent'

'But the IEP quote doesn't mean that the same p can be necessarily true or false.'

Since I have never claimed this the point seems of little relevance.

The substantive point at issue as far as I was concerned was that the modality of a proposition was distinct from its truth-value.
.

As I say later in my 580 from which you take the above quote

'A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement' [my emphasis].
('Modal Logic, SEP)

'All I was trying to get you to agree in #581 on that thread was that if we say:

1) @p

then we mean that necessarily p, which is equivalent to saying that necessarily p is true.'


But clearly by my quoting SEP above I don't agree to that. Nor given modal axiom T

@p->p (wherein p the truth-value of p the modality @)

am I clear why you would think that.

'If you now agree this, as you seem to, we can move on.'

I don't see why you think I have changed my position. Surely, it is you who should agree that the truth-value of any arbitrary proposition p is independent of its modality?

Bx4 said...

Corrigendum

@p->p (wherein p the truth-value of p the modality @)

should read

@p->p (wherein p the truth-value of p is independent ofthe modality @)

Psiomniac said...

I don't see why you think I have changed my position.
That's simple, I made the argument that @p means necessarily p, and that in turn this means that necessarily p is true, (not that it can be true or false), with two points about premises a few posts ago. You responded:
I am quite happy to go along with both. I'm not really clear why you would imagine I would do otherwise.

Asserting Ramsey's ladder assupporting your case is a bit odd.
Why? The quote from Blacburn you give supports my idea that to assert that p is true is equivalent to asserting p. The ladder is horizontal. My point is that if I say:
1) p

then that is the same as saying

2) p is true

or

3) it is true that p is true

and so on.

Since I have never claimed this the point seems of little relevance.
Then the original quote has no relevance to my argument, so I'm unclear as to why you brought it up. Some propositions are necessarily true, we symbolise this by saying, for example @p. If we want to say a proposition, q for example, is necessarily false, we say @¬q.

The substantive point at issue as far as I was concerned was that the modality of a proposition was distinct from its truth-value.
If I say that necessarily it is raining(x,y,z,t), then I am qualifying the truth of that proposition, I agree. But all I'm doing is saying that not only is it true (it is the case that it is raining(x,y,z,t)), I'm qualifying that by saying that it is not possible for it to be false.

But clearly by my quoting SEP above I don't agree to that.
I don't understand your point here. I agree that 'necessarily' is used to qualify the truth of a judgement. In the case of @p it qualifies 'p is true' to become 'necessarily p is true'. If you wanted to qualify the judgement that something is false you'd say something like @¬q.

Nor given modal axiom T
Again, I can't see your point.

Consider axiom T:

@p->p

Now you say that the truth-value of any arbitrary proposition p is independent of its modality. Well, in a sense that's true. Suppose p is true, it might also be necessarily true or not. Suppose p is false, it might be necessarily false or not.

Let's again suppose that p = it is raining at (x,y,z,t). What does axiom T (or M) say? It says that if, necessarily it is raining at (x,y,z,t) then it is raining at (x,y,z,t). That would still be so, even if it turns out that it is not the case that it is raining at (x,y,z,t). We would just conclude that the antecedent is also false.

What I'm trying to get you to agree is the meaning of asserting p and asserting @p.

Maybe the point you haven't taken on board is that the meaning is distinct from the truth value. So:

a) it is raining at (x,y,z,t)

means the same as saying

b) it is true that it is raining at (x,y,z,t)

regardless of whether it is true that it is raining at (x,y,z,t).

Bx4 said...

psomniac:

'That's simple, I made the argument that @p means necessarily p, and that in turn this means that necessarily p is true, (not that it can be true or false), with two points about premises a few posts ago. You responded:

I am quite happy to go along with both. I'm not really clear why you would imagine I would do otherwise.


I really wish you would stop misrepresenting what I say.

My comment above was simply an agreement to:


your specific point:

(a)p (premise):it is in fact raining at (x,y,z,t).

(b) @p (premise: necessarily it is raining at (x,y,z,t)



which clearly has nothing to do with what follows your ' That's simple'

'Why? The quote from Blacburn you give supports my idea that to assert that p is true is equivalent to asserting p. The ladder is horizontal.'

Strange then that in your 557 you neglect to mention Blackburn, or the horizontality of the ladder or his minimalist conclusion.
Instead presenting it as an upward, almost vertical, progession that supported a conclusion of the type Blackburn was satirising.

There seems to be a considerable amount of revisionism in play here.

'Then the original quote has no relevance to my argument, so I'm unclear as to why you brought it up.'

The original quote began:

"I have just had a speed read ...your 557...

This was you quoting me rather than the reverse.

If it has 'no relevance to your argument' then your introduction of it is, to say the least, rather odd.

However, as I said to you before my preference is for dianoetic rather than competitive debate. This is clearly degenerating into the latter.

I only came on here because of your last post in hootoo. I see no point in continuing.

So once again, adieu not au revoir.

Psiomniac said...

That's a shame Bx4 since I was not seeking a competitive debate, rather I was doing my best to understand your view, and failing. If you change your mind and want to try to sort it out you'll be most welcome.

I really wish you would stop misrepresenting what I say.
I was trying my best to understand, sorry.

My comment above was simply an agreement to:


your specific point:

(a)p (premise):it is in fact raining at (x,y,z,t).

(b) @p (premise: necessarily it is raining at (x,y,z,t)


which clearly has nothing to do with what follows your ' That's simple'

Well there doesn't seem to be anything in the above that warrants your agreement or not, so I naturally assumed you meant the substantive argument of which the above was a part. Sorry I got that wrong.

Strange then that in your 557 you neglect to mention Blackburn, or the horizontality of the ladder or his minimalist conclusion.
Not really, I thought you'd remembered that I've read Blackburn and I thought you'd get that I meant the ladder was horizontal because that was the point I was making. Why you think I was using it any other way is just baffling to me; I just don't understand why you think necessity or contingency had anything to do with the Ramsey's ladder part of my argument. I just thought I might get you to see that @p means necessarily p is true from seeing first that 'p is true' is equivalent to 'p'. Hence the Ramsey reference.

There seems to be a considerable amount of revisionism in play here.
There isn't and I think it is a shame that you would make such an accusation.

This was you quoting me rather than the reverse.
I'm afraid we've got very tangled here. You brought up something, I made my best attempt at an interpretation that I thought would be relevant, you responded by saying that wasn't the point you were making. Therefore I still can't see the relevance of your quote.

I used Ramsey's ladder in a way I'll illustrate with brackets:

@[p]==@[p is true] (by Ramsey's ladder.

hence @p means necessarily p is true.
Seems clear to me.

However, as I said to you before my preference is for dianoetic rather than competitive debate. This is clearly degenerating into the latter.
I'm sure you don't mean to imply that I'm solely to blame for that :-)

So once again, adieu not au revoir.
That might be for the best. Although we have had some interesting debates I've concluded that we basically don't 'get' each other, and this leads to miscommunication which is inimical to progress or satisfactory resolution. I wish you well though, and as I said the door is open.