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JET
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| Posted 5/29/2003 4:51 AM (GMT -6) |   | From an article by Alfred J. Freddoso:
quote:
Take an arbitrary proposition describing what we would ordinarily consider to be a free action performed at a given moment, e.g., Katie's washing her car at some determinate moment T. Then we can formulate the deterministic argument as follows:
(P1) The proposition that Katie will wash her car at T is true now, long before T. (assumption)
(P2) So the proposition that it was the case that Katie will wash her car at T will be necessary per accidens at every future moment, including every moment that precedes or is identical with T. (from (P1)and (C))
(P3) But the proposition that it was the case that Katie will wash her car at T entails the proposition that if T is present, then Katie is washing her car. (assumption)
(P4) Therefore, no one (including Katie) will have the power at or before T to bring it about that it is or will be false that if T is present, then Katie is washing her car. That is, no one will have the power at or before T to bring it about that it is or will be true that Katie is not washing her car when T is present. (from (P2), (P3), and (B))
* * *
There are only three philosophically interesting lines of response to this rather compelling argument. "Aristotelian" responses all deny assumption (P1), claiming either (a) that where p is a future contingent proposition, both p and its negation are neither true nor false, or (b) that where p is a contingent proposition, it is false both that p will be true and that the negation of p will be true. The first claim is commonly attributed to Aristotle, while [Arthur] Prior is responsible for the second claim.
http://www.nd.edu/~afreddos/papers/anld.htm
From another article:
quote:
Prior's first paper on the logic of tenses, ‘Three-Valued Logic and Future Contingents’, appeared in the Philosophical Quarterly for 1953. In 1949 he had learned from Geach's review of Julius Weinberg's Nicolaus of Autricourt: A Study in 14th Century Thought that for the scholastics an expression like ‘Socrates is sitting down’ is complete, in the sense of being assertable as it is, and is true at certain times, false at others. Prior had been brought up on the view -- prevalent even today -- that such an expression is incomplete until a time-reference is supplied, and hence that one cannot speak of the truth-value of the expression as altering with the passage of time. This was a crucial discovery for Prior: the idea that propositions which are subject to tense-inflections are liable to be true at one time and false at another was to become central to his philosophy. In a summary of his mature views on temporal realism composed nearly two decades later he wrote:
Certainly there are unchanging truths, but there are changing truths also, and it is a pity if logic ignores these, and leaves it ... to comparatively informal ‘dialecticians’ to study the more ‘dynamic’ aspects of reality. (Prior 1996a: 46.)
http://plato.stanford.edu/entries/prior/
Sounds very similar to Doc’s take on the Principle of Bivalence.
Anybody familiar with this guy?
Earl
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Tom
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| Posted 5/29/2003 7:49 AM (GMT -6) | | Freddoso (on Prior’s denial of P1): …(b) that where p is a contingent proposition, it is false both that p will be true and that the negation of p will be true.
Tom: I don’t know Prior, but if he means by “contingent proposition” a might-counterfactual, like “x might do y,” then he’s right (and this would entail an open future wouldn’t it?). If p is “x might do y” then it is both false that “x will do y” and that “x will not do y.” But I’m not sure this is what he means by “it is false both that p will be true and that the negation of p will be true,” that is, I don’t know exactly how he’s using “will.” If p is a contingent proposition, and it’s a true proposition, then it IS true. What does Prior mean by saying “it won’t be true”?
Freddoso is a Molinist isn’t he?
Tom 
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JET
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| Posted 5/29/2003 9:07 AM (GMT -6) | | Freddoso (on Prior’s denial of P1): . . .(b) that where p is a contingent proposition, it is false both that p will be true and that the negation of p will be true.
I'm assuming these are Freddoso's words to describe Prior's response. Freddoso is talking specifically about "future contingent propositions". I'm assuming (from the above quote) he means a proposition "describing what we would ordinarily consider to be a free action"; i.e., the truth of the proposition is "contingent" on a future free choice. I will try to find more on Prior's thought when I can. If my assumption is correct, though, this would be an example of a "might counterfactual", right? If so, then isn't Prior saying the same thing that you, Doc and Alan have been saying (i.e., that p is false, in contrast to the true "Aristotelian" position that p is neither true or false)?
TGB: If p is a contingent proposition, and it’s a true proposition, then it IS true. What does Prior mean by saying “it won’t be true”?
JET: He's saying if p is a future contingent proposition, then it cannot be a true statement until the contingency is satisfied which makes it true.
p - Kathy will wash her car.
If whether or not p is true is "contingent" on a future free choice, then it is false that "Kathy will wash her car". It is also false that "Kathy will not wash her car" (the negation of p). Thus, "it is false both that p will be true and that the negation of p will be true."
TGB: Freddoso is a Molinist isn’t he?
JET: Yep. He's definitely not endorsing Prior's resonse to the determinist argument. I think he is or was a contemporary of Plantinga's (another Molinist, right?) at Notre Dame.
Anyway, I've got this hunch (from what little I've read) that Prior has laid some groundwork for Boyd's position vis-a-vis Craig, for example. Apparently Prior was known for his work in "tensed logic" and so I'm also wondering how his "three-valued logic" would resond to Craig's tensed logic (recall the Refuting Molinism thread).
Later,
Earl
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GregBoyd
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| Posted 5/29/2003 9:16 AM (GMT -6) | | Thanks for the tip JETS. I now recall reading something from Prior when doing my dissertation (Trinity and Process) and agreeing with him that language is incurably "tensed", for reality is irreducibly "tensed." But I have totally forgotten about him. Most definitely, he needs a re-looking at!
Greg
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JET
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| Posted 5/29/2003 5:33 PM (GMT -6) | | Here’s another article which gives Arthur Prior credit for the variation on the Aristotelian response to Fatalism which seeks to preserve the law of bivalence:
http://plato.stanford.edu/entries/fatalism/#1.2
quote:
It is worth noticing some other solutions which are closely related to the Aristotelian solution, but avoid some of the problems.
1.2 Related solutions
1. (Prior 1967). One could agree with Aristotle that "there will be a sea-battle tomorrow" is not true, even if it turns out that there is a sea battle; but instead of saying that it is neither true nor false, one could say that it is false. What is more, one could say that the negation, "there will not be a sea-battle tomorrow" is true. Then we could retain the law of bivalence, and the equivalence between "p" and "p is true". Effectively we would be treating "p" as equivalent to "it is necessary that p". And we would, no doubt, distinguish between "there will not be a sea-battle tomorrow", where this is the negation of "there will be a sea-battle tomorrow" and "there will be no sea-battle tomorrow" which, like "there will be a sea-battle tomorrow", is false. One might even say that "there will not be a sea-battle tomorrow" is ambiguous; it could be equivalent to "it is not necessary that there will be sea-battle tomorrow" or it could be equivalent to "it is necessary that there will be no sea-battle tomorrow". Certainly it is in favour of this view that one would retain the law of bivalence and also the truth-functionality of "or" and "and". But there would be a heavy price to pay. Now we should have to say what the person said about Red Rum was false.
The author (Hugh Rice, Oxford) reveals his bias when he says this is a “heavy price to pay”. Earlier in the article, Rice says:
quote:
But there is another objection to the Aristotelian solution which makes it harder to accept - the way we treat bare predictions. If someone had said in 1972, "Red Rum will win the Grand National next year", surely, we would think, he was right. Not right in 1973, but right in 1972. That is to say, surely what he said was true, when he said it; not just later. Of course, we would not have known in 1972 that what he said was true; nor, presumably did he. Nor, of course would we have supposed that there was anything inevitable about the victory; these things, we naturally suppose, are a matter of chance. But, of course, this objection to the Aristotelian solution is also an objection to the argument for fatalism which was based on the assumption of bivalence. We are, effectively, rejecting the idea that if what someone says at a time is true at that time, then the state of the world at the time must determine that it is true. What we seem to be quite prepared to accept instead is the idea that for what is said to be true at a time it is sufficient if the state of the world will sometime be such as to determine that it is true.
It may be true that people are generally “quite prepared to accept” this. In fact, it is awkward in ordinary parlance to say, for example, that in 1990 the proposition “George W. Bush will become president” was false. However, as we have seen, this is technically correct (per Boyd, Prior).
Question: Why is it that the author says “there will not be a sea-battle tomorrow” is true, while “there will be no sea-battle tomorrow” is false?
Perhaps the author is equating:
- “There will not be a sea-battle tomorrow”
with:
- “It is not the case that there will be a sea-battle tomorrow” (=true)
which is different from saying:
- “There will be no sea-battle tomorrow” (=false)
all of which is just another way of saying that if it is true that:
- “There might be a sea-battle tomorrow”,
then it is false that:
- “There will be a sea-battle tomorrow”
and it is likewise false that:
- “There will be no sea-battle tomorrow”
In any event, it is interesting that this author (along with Freddoso) both credit Prior with this line of response.
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Tom
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| Posted 5/30/2003 12:30 AM (GMT -6) | | JET: I'm assuming (from the above quote) he means a proposition "describing what we would ordinarily consider to be a free action"; i.e., the truth of the proposition is "contingent" on a future free choice. I will try to find more on Prior's thought when I can. If my assumption is correct, though, this would be an example of a "might counterfactual", right?
Tom: I don’t think so, but I don’t know what Prior might say. As I understand it, the principal of bivalence tells us that all propositions possess a truth-value NOW; they’re either true or false now. So the truth-value of a might-counterfactual, say “x might do y in situation z,” is not contingent. It is now either true or false that x might do y. What’s contingent is x’s doing y in z, not the truth that x might do y in z.
quote:
TGB: If p is a contingent proposition, and it’s a true proposition, then it IS true. What does Prior mean by saying “it won’t be true”?
JET: He's saying if p is a future contingent proposition, then it cannot be a true statement until the contingency is satisfied which makes it true: p - Kathy will wash her car.
Oh, OK, I see now. He’s talking about propositions describing what “will” or “will not” take place. These are not “might-counterfactuals.” They’re not counterfactuals at all.
Now, I’d disagree (and I think Doc would too), with Prior here when he says that “Kathy will wash her car” is neither true nor false and that it becomes true when Kathy washes her car. First, this denies that the principal of bivalence is universally true. Secondly, when Kathy actually washes her car, the proposition “Kathy will wash her car” doesn’t become true. It becomes false. After Kathy washes her car the event is past, but the proposition describes a future event. How can a future tense proposition (“x will do y in z”) describe a past tense event (“x did y in z”). Once Kathy washes her car, the proposition “Kathy will wash her car” no longer corresponds to reality, since it must refer to an event that has not yet occurred.
JET: If whether or not p is true is "contingent" on a future free choice, then it is false that "Kathy will wash her car".
Tom: I’m confused. Isn’t p = “Kathy will wash her car”? OK, so your saying, “If whether or not “Kathy will wash her car” is true is contingent on a future free choice, then it is false that “Kathy will wash her car.” So you’re saying that NOW “Kathy will wash her car” is false if we’re to maintain that she’s free in washing her car. Then what need is there to say “Kathy will wash her car” becomes true when Kathy washes her car. On the contrary, if Kathy is free to wash or not wash her car, and if she ends up washing her car, then the proposition “Kathy will wash her car” is NEVER true, not before and not after she washes.
Sounds like Prior agrees that future free choices cannot be known. On this we agree. But he also thinks that propositions describing future free choices ‘become’ true when those choices are made. He seems to think that “Kathy will wash her car” must be true at some time if Kathy washes her car.
JET: Question: Why is it that the author says “there will not be a sea-battle tomorrow” is true, while “there will be no sea-battle tomorrow” is false?
Tom: I think you mean to say “there will be a sea battle tomorrow” is false. Take the “no” out of that second proposition.
The author says this because he has totally ignored a set of propositions describing the future: might-counterfactuals.
1. He wants to hold on to bivalence, and…
2. He wants to affirm that “There will be a sea-battle tomorrow” is false, but…
3. He won’t admit “might” propositions into the equation at all. He just works with “will” and “will not” propositions. Bummer. You can’t solve the problem if you don’t admit all the evidence. This is his problem. If bivalence is true, and if “There will be a sea battle tomorrow” is false, then “There will not be a sea battle tomorrow” has to be true (per bivalence) according to Prior.
But if you admit might-counterfactuals, then you can affirm that “There will be a sea battle tomorrow” and “There will not be a sea battle tomorrow” are BOTH false, because what is true is “There might be a sea battle tomorrow.” Bivalence is maintained and we can speak logically about contingent future events.
Hugh Rice’s comment is the same. You can see bivalence tripping him up like a ball and chain, and all because he completely overlooks a set of propositions (might-counterfactuals). Admit might-counterfactuals and you can celebrate bivalence AND believe in a partly open future.
Tom
Edited by - TGB on 05/30/2003 05:31:10 AM
Edited by - TGB on 05/30/2003 05:32:26 AM | | Back to Top | | |
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JET
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| Posted 5/30/2003 3:34 AM (GMT -6) | | quote:
JET: I'm assuming (from the above quote) he means a proposition "describing what we would ordinarily consider to be a free action"; i.e., the truth of the proposition is "contingent" on a future free choice. I will try to find more on Prior's thought when I can. If my assumption is correct, though, this would be an example of a "might counterfactual", right?
Tom: I don’t think so, but I don’t know what Prior might say. As I understand it, the principal of bivalence tells us that all propositions possess a truth-value NOW; they’re either true or false now. So the truth-value of a might-counterfactual, say “x might do y in situation z,” is not contingent. It is now either true or false that x might do y. What’s contingent is x’s doing y in z, not the truth that x might do y in z.
Prior is credited with "inventing" tense logic which I understand to be (or at least include) the idea (contrary to the prevalent view) "that propositions which are subject to tense-inflections are liable to be true at one time and false at another." (Freddoso, above)
Forget about the word "contingent". The interesting thing is that Prior is credited with the idea that "x will do y in situation is z" can be false NOW, even if it turns out that x does y.
Prior was also said to adopt the idea that time "branches into the future" like a tree. http://plato.stanford.edu/entries/prior/ Sounds kinda OV, eh?
While Prior is credited with this variation on the "Aristotelian" response (i.e., retaining both indeterminancy and bivalence), it seems like maybe Prior also saw another option in the idea of "three-valued logic". In addition to "true" and "false", there is another value called "indeterminate". It seems Prior recognized that our language of logic must reflect that reality includes "might" and "might not".
TGB: Now, I’d disagree (and I think Doc would too), with Prior here when he says that “Kathy will wash her car” is neither true nor false and that it becomes true when Kathy washes her car.
First, this denies that the principal of bivalence is universally true.
JET: I don't think your're disagreeing with Prior, just my impricise language. You are describing what Freddoso attributes to Aristotle. In contrast with this, Freddoso is saying that Prior would say it is NOW false that "Kathy will wash her car" even though at some time in the future it may turn out to be true that Kathy washes her car. This is the same thing you are saying, right?
TGB: Secondly, when Kathy actually washes her car, the proposition “Kathy will wash her car” doesn’t become true. It becomes false. After Kathy washes her car the event is past, but the proposition describes a future event. How can a future tense proposition (“x will do y in z”) describe a past tense event (“x did y in z”). Once Kathy washes her car, the proposition “Kathy will wash her car” no longer corresponds to reality, since it must refer to an event that has not yet occurred.
JET: Got it. Again, I think your responding to my imprecision.
quote:
JET: Question: Why is it that the author says “there will not be a sea-battle tomorrow” is true, while “there will be no sea-battle tomorrow” is false?
Tom: I think you mean to say “there will be a sea battle tomorrow” is false. Take the “no” out of that second proposition.
JET: Here's the quote from Hugh Rice:
What is more, one could say that the negation, "there will not be a sea-battle tomorrow" is true. Then we could retain the law of bivalence, . . . And we would, no doubt, distinguish between "there will not be a sea-battle tomorrow", where this is the negation of "there will be a sea-battle tomorrow" and "there will be no sea-battle tomorrow" which, like "there will be a sea-battle tomorrow", is false.
TGB: The author says this because he has totally ignored a set of propositions describing the future: might-counterfactuals.
1. He wants to hold on to bivalence, and…
2. He wants to affirm that “There will be a sea-battle tomorrow” is false, but…
JET: I don't think Hugh Rice wants to affirm this. He is describing a response to fatalism that he attributes to Prior.
TGB: 3. He won’t admit “might” propositions into the equation at all. He just works with “will” and “will not” propositions. Bummer. You can’t solve the problem if you don’t admit all the evidence. This is his problem. If bivalence is true, and if “There will be a sea battle tomorrow” is false, then “There will not be a sea battle tomorrow” has to be true (per bivalence) according to Prior.
JET: I think Rice has tipped his hand. He thinks retaining Prior's approach has a "heavy price to pay" because he can't understand how it could be false in 1972 that "Red Rum will win the Grand National next year". If he can't see this, then I'm wondering if he really understands where Prior is coming from.
Thanks for the feedback.
Earl
Edited by - JET on 05/30/2003 08:38:03 AM
Edited by - JET on 05/30/2003 08:46:37 AM | | Back to Top | | |
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JET
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| Posted 5/30/2003 4:34 AM (GMT -6) | | TGB: But he [Prior] also thinks that propositions describing future free choices ‘become’ true when those choices are made. He seems to think that “Kathy will wash her car” must be true at some time if Kathy washes her car.
JET: Take a look at http://plato.stanford.edu/entries/prior/
I don't think Prior would say "Kathy will wash her car" can be true at one time and false at another. (This is Freddeso's example.) However, Prior would say "Socrates is sitting down" can be true at one time and false at another (contra, Craig).
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JET
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| Posted 5/31/2003 2:04 AM (GMT -6) | | More on Prior, from an interview with his wife Mary:
In his early writings, before tense logic, Arthur Prior several times dealt with the Christian – and in particular Calvinist – idea of predestination. In a similar vein, the difficult question of God's foreknowledge versus human freedom was discussed by him – the latter question in fact also in his late writings. Can you tell us about the development of his views on these issues and how they influenced his thought? A related and lasting preoccupation within Arthur's work was the problem of free will. What were his views on this matter?
Yes, it is true that Arthur was preoccupied by the problem of free will. At first he saw it in a semi-theological context. I have never felt quite sure how seriously Arthur really took the Calvinism which intellectually attracted him. It was rigorous and logical, unlike the Methodism of his childhood. But it's God lacked humanity. I think sometimes he entertained Calvinism in its various forms rather than quite believing it. He was very aware of the dilemmas it posed. Perhaps his failure to resolve them was a reason why despite so much preparation the book on Scottish Theology never came to anything. In his later work I think he was prepared to go where logic led him, but the idea of the future as open to choice, where the past and present were not, may also have had deeper emotional attractions. But here I speculate.
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