In case anyone here doesn’t know, I am also a contributor to Brains a group blog in the philosophy of Mind, Psychology and Cognitive Science…if anyone is interested here are some links to my posts there…
2. The Qualitative Character of Conscious Thoughts
3. Do Horses Sense Their Riders desires?
4. Brain States Vs. States of the Brain
If you have been following the discussion in Plantinga on Free Will and Omiscience you will have seen that I have been struggling to construct a proof of (1), which says that if God knows that I will do some action before I actually do it then it is necessary that I actually do it, from (2), which says that it is necessary that if God knows what I will do some action in advance then I will actually do it.
(1) K(G,R,a) –> []D(R,a)
(2) [](K(G,R,a) –> D(R,a)
So far the two attempts that I have made have both been invalid because of some bonehead mistakes. This has been driving me crazy for the past couple of days, but now I think I got it, in fact it almost seems too simple (which probably means I made another bonehead mistake!)…
I thought that it would be easier if I did not include quantifiers, but I think that is what actually confused me. So, what I really want to prove is (1′), which says that for any action x if God knows that I will do it in advance then it is necessary that I actually do it, from (2′), which you can figure out for yourself.
(1′) (x)(K(G,R,x) –> [](D(R,x))
(2′) (x)[](K(G,R,x) –> D(R,x))
this actually turns out to be quite easy (I *think* 🙂 ).
1. ~(x)(K(G,R,x) –> []D(R,x)) assume as a theorem
2. (Ex)~(K(G,R,x) –> []D(R,x)) 1, by definition
3. (Ex)~~(K(G,R,x) & ~[]D(R,x)) 2, by def
4. (Ex) (K(G,R,x) & ~[]D(R,x)) 3, by def
5. K(G,R,a) & ~[]D(R,a) 4, EI
6. K(G,R,a) 5, CE
7. []K(G,R,a) 6, necessitation
8. ~[]D(R,a) 5, CE
9. (x)[] (K(G,R,x) –> D(R,x)) assumption (2′)
10. [](K(G,R,a) –> D(R,a)) 9, UI.
11. []K(G,R,a) –> []D(R,a) 10, distribution
12. ~[]D(R,a) –> ~[]K(G,R,a) 11, contraposition
13. ~[]K(G,R,a) 8,11 MP
14. []K(G,R,a) & ~[]K(G,R,a) 7,13 CI
15. (x)(K(G,R,x) –> [](D,R,x)) 1-14 reductio
What I didn’t notice before was that since we are assuming 1 as a theorem and we can get K(G,R,a) from that then we can use the rule of necessation, which says that if phi follows from a theorem then phi is necessary, to get []K(G,R,a).
So, free will is incompatible with God’s omniscience…
I just found out via Leiter’s blog that Van Fraassen is going to San Francisco State University…wow, that’s quite a coup for my alma matter! I had thought that after Kent Bach retired the department would be lost, but maybe there’s hope 🙂
I have been preparing for a phil religion class I will be teaching in the Fall and so have been thinking about a lot of these issues. Today I was reading Platinga’s defence of Human free will with God’s foreknowledge of what we will do. He formulates his defense in terms of a scopal difference so, (1) is true but 2 is false (where K(x)=God knows that I will do X in advance and D(x)=I actually do x)
1. [] (K(x) –> D(x))
2. K(x) –> []D(x)
2 is false according to him because there is a possible world (not the actual world) where I do not do X even though God knows that I will do X in the actual world. One thing that worries me is that (1) is equivelent to (1′)
(1′) []K(x) –> []D(x)
and (1′) does seem to entail that I am not free…
He then considers Pike’s modification of this argument which claims that it is an essential trait of God that he is omnicient. Pike’s version of teh arguement is that if God knows at T1 that I will do X at T2 then, if I do not do X at T2 I make the belief that God has a T1 false and this means that God is not omniscient. Plantinga’s response is to point out that to say that I could have done otherwise is to say that there is a world W where I do do otherwise but that this does not mean that God holds a false belief in the actual world.
The problem with this line of argument is that it assumes a view of possible worlds (i.e. Plantinga’s view!) that I find objectionable. To say that I could have done otheriwse is NOT to say that there is a possible world where I do do otherwise and that that world might have been actual! It is to say that I, in this world, might have done otherwise. Adapting Kripke’s humphry objection we can say that it is cold comfort to be told that my being free means that there is someone else who could have done something different than I did. That is nonsense! What it means to be free is that I, myself, could have done otherwise. So if I could have done otherwise in the actual world then God cannot know at T1 what I would do at T2 or if He does then I am not free. So I just don’t see why Plantinga’s response is anything more than question beging…unless I am missing something?
I was reading this (older) post on the Law of Non-Contradiction over at Philosophy, et cetera. Is it really the case that it is not rational to question LNC? One might think that (P v -P) is an analytic truth. Indeed, I think that it is. But this is true only if one is operating within the confines of a two-valued logic. If one takes a many-valued logic then -(P & -P) is not analytic at all! So then the issue is whether or not classical two-valued logic is The One True Logic or not. How would we know this? I take it that someone like Richard would say that classical logic is what a maximally rational ideal agent would subscribe to. But how could we possibly know what kind of logic such an agent would subscribe to?
In an earlier post (Why Does 1+1=2?) I argued that there is nothing that could possibly decide between whether or not mathematics is an empirical science or an a priori one. The same seems true of logic. The basic laws of logic only seem rational to us because of the kind of experience that we have in this world filled with ‘medium sized dry-goods’ and this means that coherence as a criterion of truth is only valuable because of the world we live in and the kind of experience that we have. So the fact that the LNC seems to us to be denied at our own peril cannot possibly be evidence that it cannot be denied. We have no way of knowing whether it is actually ideally rational or not, since what we can concive of is limited to the kind of experience that we have.
Against my better judgement I have recorded and posted the Empiricist comeback to Prolegomena to Any Future Gangsta Shit…
I invite you to check out my most recent Lame Attempt at Humor
The Philosophical Lexicon defines the verb ‘to quine’ as follows
quine, v. (1) To deny resolutely the existence o[r] importance of something real or significant. “Some philosophers have quined classes, and some have even quined physical objects.” Occasionally used intr., e.g., “You think I quine, sir. I assure you I do not!”
The joke, of course, is that Quine denied the existence of the analytic/synthetic distinction which is both real and important. So is there any reason to think that there is something wrong with this distinction?
Examples of analytic truths are things like ‘bachlors are unmarried males’ and ‘an aniverssary is one year after an event’. Now there are alleged to be counter-examples to these kinds of claims and this is taken to be evidence that there are no alalytic truths. So, to take an excellent example of David Rosenthal’s, consider the following case.
Suppose that I am married (I am not) and that my wife and I decide to get a divorce. We get lawyers and hold meetings and hammer out an agreement. The lawyers draw up the papers and my (soon to be) ex-wife signs the papers on Friday afternoon. I can’t come in on Friday and so arrange with the lawyers to come in first thing Monday morning and sign the papers. Now let us suppose that I go out on Sunday night and meet another woman and let’s further suppose that I somehow get lucky and we end up sleeping together. Now it seems that I cannot be accused of commiting adultry and since only married people can commit adultry there is a sense in which I am not married (and so a bachlor). But technically I am still married (I have not finalized the divorce). So it looks like on Sunday night I am a married bachlor.
Now, people usually resist the conclusion of this scenerio, but let us suppose that it is accurate. Is it a counter-example to the alleged analytic truth that bachlors are unmarried males? I don’t think so. Rather what is at issue here is what counts as being married. Once we settle whether I am really married or not then we will settle whether or not I am a bachlor.
Similarly, consider an alleged counter-example to the anniversay business. Suppose that I get married on Leap year. Then my anniversery will not occur one year later, right? Again, I do not think that this is a counter-example. What is at issue here is ‘what counts as one year?’
So it seems to me that these kinds of cases are not serious threats to the analytic/syntetic distinction and so y’all should stop your quining!
For those that do not know me, I am an agnostic. I do not believe that there is a God, nor do I believe that there isn’t one. In fact I think that both the theist and the atheist make the very same mistake; They each affirm something that there is inadequate evidence for. The agnostic claims that the only intellectually honest answer to ‘is there a God?’ is ‘how the hell am I supposed to know?’ By ‘theist’ I mean someone who believes that there is an all-powerful, all-knowing, all-loving being and by ‘atheist’ I mean someone who denies that. Theism should be distinguished from religion. All existing religions are silly and are obviously the product of Mankind. It is also demostrably true that organized religion has been one of the greatest forces for evil known to man.
Having said that I want to ask the theist a question . Why must we worship God? Closely related to this is the question ‘what is the point of it?’
I suppose that there are three traditional answers to this question.
1. Because God is all-powerful!!! He could destroy you in a micro-second or banish you to an eternity of pain and torture…so you had better worship Him or you’re screwed!!
This might be a reason that it is in my best interest to worship God, but it does not seem like the kind of reason that I am looking for. This answer makes God out to be a petty tyrant and that is incompatible with the description of Him as all-knowing and all-loving.
2. Because God deserves it! He created this Universe just for us. Think of a beatuiful sunset, or any natural beauty, don’t you think that it would be nice to thank the Creator of that beauty? We worship God to show our appreciation for the gifts that He has given us.
This answer has always kind of bothered me. In the first place why am I obligated to be grateful for a gift that I did not ask for? But let us wave this consideration. The more pressing problem is whether God really deserves to be worshiped. The problem of evil in the world seems to me to be reason to think that He may not deserve it after all and as far as I can see there is no really good answer to this problem.
3. We should worship God because he commands us to do so!
If this answer is to be different from (1) then the reason that we should follow the command cannot be because of fear of the consequences or desire for reward. It seems that there must be some reason that grounds God’s command, but so far we have not found one…but let us leave that aside. The more pressing concern is ‘what kind of God would command us to worship him?’ This seems sort of needy and insecure, something that I take to be at odds with the characterization of God as all-knowing, all-loving, and all-powerful.
A related question that has always bothered me is what is the point of prayer? It seems contradictory to hold that an all-loving, all-loving being would require that I ask for something that I need before He would give it to me. What kind of a person would i be if I knew what my girlfriend wanted and I could give it to her, and I claimed to really love her, yet I refuse to give it to her simply because she did not ask me for it?!?!?!?!
So it seems to me that even if God exists there is no reason that it is obligatory that I worship Him or pray to him, nor do I think that He cares if I do or not. So it is contradictory to hold that there is an all-powerful, all-loving, all-knowing being who will punish me if I do not pick the right religion.
I was reading this post in the latest edition of the Philosophers’ Carnival on conditionals and free will…I don’t have anything to say about the main topic of the post so I thought I would comment here…
What caught my eye was someone in the comment section who said that material implication ‘–>’ is not meant to capture ‘if…then’ in English rather it is merely a “convient way to combine negation and disjunction”…It is true that material implication is defined in terms of negation and disjunction but so is ‘&’ and in fact all of the truth functional connectives but that doesn’t mean that they do not attempt to capture the meaning of the English words. The truth conditions for ‘–>’ are meant to capture at least on of the things that we mean when we say ‘if…then’. Consider,
(1) if Santa is fat then Santa is jolly
The truth table definition of material implication says that this sentence is true when both antecedant and consequent are true and also when they are both false as well as wehn the atecedant is false and the consequent is true. The only time the sentence is false is when the antecedant is true and the consequent is false. So the claim is that these truth-conditions do not capture ‘if…then’ in English. Even the author of the post expresses some suprise that these turn out to be the truth-conditions for ‘if…then’.
But, what we mean when we say (1), and the reason why people intuitively accept Modus Ponens as a valid argument form, is that if it is true that santa is fat then it will also be true that Santa is jolly. The natural way to see if this sentence is true is by finding out whether Santa is fat or not and whether he is jolly or not. Now suppose that Santa in fact turns out to be neither fat nor jolly, does common sense expect (1) to be false? I don’t think so. (1) says that on the condition that Santa is fat he will be jolly as well, so if he is not in fact fat the condition doesn’t hold, but (1) could still be true because it might be true that if Santa were fat then he would be jolly. So the falsity of ‘Santa is fat’ is compatible with what the sentence says still being true counter-factually. But suppose that Santa turned out to be in fact fat but decidely NOT jolly. Then the sentence would be false because the relation that it asserts is shown not to hold. So it seems to me that the truth-table meaning of ‘–>’ does capture the meaning of ‘if…then’ in English.
It seems to me that the reason why the truth-conditons are suprising to people who see them for the first time is that it makes them realize that some sentence’s truth conditions depend on how the sentence behaves modally in opposition to the naive view that all sentences simply depend on how the world actually is for their truth. To put it a bit technically it forces them to realize that the sentence is made true in this world because it is true at some other possible world. It is NOT because these truth-conditions clash with what we take the meaning of ‘if…then’ to be…This, incidently, seems to me to be more evidence that there is something wrong with Williamson’s argument against the distinction.
These truth-conditions capture one of the meanings listed for the English conjunction ‘if”; that there are other uses of the conjunction doesn’t seem to matter.
Richard Brown 