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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 6/19/2004 11:24 PM (GMT -6) |   | quote:
JET: "States-of-affairs" may or may not correspond with reality, though, right? "Earl smoking a cohiba" is a state of affairs, even though the proposition "Earl is smoking a cohiba" is False, right?
Tom: Right.
quote:
TGB: Now, the state-of-affairs ‘a cow jumping over the moon’ is a proposed state-of-affairs. But since it’s physically impossible (as Alan pointed out) it’s not an actual state-of-affairs. So it’s not a slice of reality. It’s a state-of-affairs in that it proposes to be a state-of-reality, it presents itself for our consideration, it runs for membership, but it doesn’t qualify.
JET: Why not just say "a cow jumping over the moon" is a state of affairs, while the proposition "a cow is jumping over the moon" is False?
Right, that’s what a meant. It is a state-of-affairs. But since it’s a physically impossible state-of-affairs it’s not a “slice or reality.” It can’t be an actual state-of-affairs. Sorry I was unclear.
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JET: I’m not sure I understand your objection to saying “Ontological Values”. The ontological status or quality of any future state-of-affairs is one of three possibilities: Z, Z~, or Q. My dictionary defines “value” as “the quality or number represented by a figure or symbol”. I want to say that Necessarily, Necessarily Not, and Contingently are the ontological qualities represented by the symbols Z, Z~ and Q, respectively (hence, “Ontological Values”).
Tom: “States” would work well for this then. But since “values” attach to something other than themselves that determine what they are…
JET: I don't understand what you mean by this. "Ontological Values" attach to something other than themselves (states of affairs). What do you mean by ". . . that determine what they are"?
Values are attributes of things other than themselves. A truth value is an attribute of propositions, right? So “values” point to something as an attribute of that something. But states-of-affairs aren’t values of something else. They are the ground floor. The state-of-affairs “Tom’s understanding Alan” doesn’t point to anything else as an attribute of that something. It IS the something which can be truthfully or falsely described by a proposition.
Now, the state-of-affairs “Tom’s understanding Alan” can be expressed in one of several propositions:
Past: Tom did understand Alan
Past: Tom did not understand Alan
Present: Tom does understand Alan
Present: Tom does not understand Alan
Future: Tom will understand Alan
Future: Tom will not understand Alan
Future: Tom might and might not understand Alan
It’s my understanding that Z and Q only prefix future tense truth claims. To say Zp for “It’s determinately the case that Tom understood Alan” where I in fact did understand Alan is a waste of a Z and a misapplication of indeterminacy logic (in my view). We came up with the modal operators Z and Q to express indeterminacy logic, or the logic of contingency. But I always thought this was historical contingency, thus, the logic of the future, and not logical contingency per say. Q for me only means ‘historically contingent’, whereas for Alan it seems (also?) to mean ‘logically contingent’. So if I wanna say “Tom might and might not understand Alan tomorrow” I posit Qp: The state-of-affairs “Tom’s understanding Alan tomorrow” is historically contingent. For me, every future-tense proposition is by definition a Zp, Z~p, or Qp: thus, for every future-tense p, either Zp, Z~p, or Qp. Whereas I hear Alan saying: for every future-tense p, either p, Zp, Z~p, or Qp. It seems to me he posits future-tense propositions making truth claims which are neither Z, Z~, nor Q. For example, he posits the proposition “There is a sea battle tomorrow,” admits that this is a meaningful proposition, admits it makes a truth claim (as all propositions by definition do), but denies that it is either Z, Z~, or Q.
quote:
TGB: Now, since states-of-affairs can be such that they determine future states-of-affairs (Z or Z~) or determine a range of future states-of-affairs (Q), we can speak of the “status” of ontological states-of-affairs, and that’s what Z and Q do. Z and Q tell us what the “status” of a particular state-of-affairs is, that is, whether the actual state-of-affairs at the time the proposition is made (viz., the truth conditions of the proposition) is such that the state-of-affairs about which the proposition makes some truth claim follows determinately or indeterminately from the state-of-affairs that constitute the proposition’s truth conditions. (JET’s emphasis)
JET: Or doesn’t follow at all (ie, Z~), right?
Right, but this is just to say that “~the state-of-affairs” follows determinately. We’ve been saying Z, Z~, and Q, but in actuality there are only two operators, Z and Q. The “~” in Z~p belongs to the state-of-affairs ~p, and the operator Z. Reality is bivalent. It’s determinacy vs indeterminacy, thought what follows determinately may be p or ~p. So we get three states-of-affairs, Zp, Z~p, or Qp, but only two operators, Z and Q.
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JET: Do we agree that “states of affairs” can include things that are actual and things that are not actual, as Alan says?
Yeah.
quote:
Tom: . . . so long as by “contingency” you mean historical contingency and not logical contingency. A state-of-affairs can be historically determined (i.e., it can be already actual or determined to be actual) but logically contingent (i.e., the state-of-affairs is not what it is necessarily like the state-of-affairs ‘God’s existing’ is what it is necessarily).
JET: I’m not sure I totally understand, but I think I have been talking about historical contingency.
The difference is huge and really affects how one uses and expresses indeterminacy logic. Mathematical truths are ‘logically necessary.’ 2+2=4 is a ‘necessary truth’. God’s existence is a ‘necessary truth’ (so we argue). Things couldn’t be otherwise and to suggest so would be to suggest a logical impossibility. So, x is logically contingent if ~x does not constitute a logical impossibility. My existence for example is logically contingent. My not having existence would not constitute an incoherence or a logical impossibility. Historical contingency on the other hand is different. Events of the past are by definition no longer historically contingent because they cannot now be other than they are. Z and Z~ events in the future are also NOT historically continent because by definition they cannot be other than they “will” or “will not” be. The only historically contingent events are Qp events, states-of-affairs which either might become actual or might not become actual. So to say a proposition is logically contingent doesn’t say anything to me about whether it’s a Z, Z~, or Q event.
I reserve Q to mean “It is historically contingent that…” while Alan (I think) understands Q to mean BOTH “It is historically contingent that…” and “It is logically contingent that…” and that’s got me confused too.
Tom | | Back to Top | | |
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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 6/19/2004 11:27 PM (GMT -6) | | My goodness Tom we posted almost simultaneously: is this Jungian synchronicity?
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Tom
Registered Member
Date Joined Jul 2001
Total Posts : 10353
| Posted 6/19/2004 11:42 PM (GMT -6) | | Albert: Regarding the "three valued future" of Z, ~Z and Q:
Tom: Yeah, it just sounds weird to say “three-valued” in this instance if we’re assuming bivalence.
Albert: But the point is, if you want to use the term "ontological values", there are still only two ontological values: existence or non-existence. There are no others. Ontology is bivalued just like truth; in fact the reason truth is bivalued is because ontology is bivalued.
Tom: Sounds right on to me.
Albert: Now as for the future, statements about the future are three-valued because their truth value is logically dependent on the present, not on the future.
Tom: Precisely!
Albert: They are not, strictly speaking, ontological statements, but logical inferences from ontological statements [my bold]. The wonderful irony of the position we are advocating is that future-tensed statements derive their truth value from the present, not the future.
Tom: That is, by definition, what ‘Presentism’ is. But I prefer the bold part to read: but logical inferences from ontological 'states' (those states being the present state of reality at the time the inference in made). But we're reading off the same page. It's OK.
Albert: Now for any X there are three types of logical entailment from the present: X being logically entailed by the present, not-X being logically entailed by the present, and neither X nor not-X being logically entailed by the present (and both being logically consistent with the present). For this reason, future-tensed statements appear to have three values (Z, ~Z and Q).
Tom: For any FUTURE-TENSE X, right. So long as Qx is admitted alongside Zx and Z~x on equal footing in our logic, expressing what is NOW the case. Indeterminacy is as real as determinacy, however real determinacy is.
Albert: But this is because they are not ontological or existential statements (which only have two values, X exists and X does not exist), but logical inferences from existential statements.
Tom: You said above “They [Zp, Z~p, and Qp] are...logical inferences from ontological statements.”
How about they’re being logical inferences about the future based on the present state of reality?
Albert: Just as things either exist or do not exist, so states of affairs either are the case or are not the case. So "states of affairs", like ontology and truth, are bivalued also.
Tom: That is what I understand ‘Presentism’ to be. But all this talk of bi-this and bi-that does not limit the number of true and false future-tense statements to two (either “will” or “will not”), for there are three (Z, Z~, and Q). So it can also BE THE CASE THAT, or be an actual state of affairs now, that a particular state of affairs might and might not be the case in the future (as I know you agree).
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JET
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Date Joined Jun 2002
Total Posts : 397
| Posted 6/20/2004 2:24 AM (GMT -6) | | | | |
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 6/20/2004 7:46 PM (GMT -6) | | Hey Tom, Earl, Albert, et al. Hope you guys have been having a good weekend.
I haven't had a chance yet to catch up with the discussion on this thread, so I'm not responding to anyone's post in particular. However, I've been mulling over the disagreement that Tom and I have been having about propositions, state-of-affairs, contingency, etc. and ... are you sitting down, Tom? ... I'm prepared to make a major concession to you.
You and Earl have finally convinced me that the "p" is Qp can't be properly construed as a proposition.
Contingency and necessity are fundamentally properties of states-of-affairs and not propositions. Accordingly, we should reflect it as such in our logic. In this vein, here's what I propose:
First, we can't use a lower-case 'p', for it is the nearly universal convention in logic to use lower-case letters p, q, r, ... as variables that take propositions as values. So if we say Qp, Zp, and Z~p, we will be misunderstood. It is, however, not inconsistent with common practice to use capital letters for states-of-affairs, so if S is a state-of-affairs, then we could say Q(S), Z(S), and Z(~S).
A couple notes: (1) We might want to discuss whether the "~" should go inside the parentheses or outside. I put it because it falls within the scope of the operator, and because it is part of the state-of-affairs that is asserted to be necessary. Thus, Z(~S) means "S's not obtaining is necessary". Z applies to the state-of-affairs S's not obtaining. (2) In terms of the symbolism, there is a fourth possibility, Q(~S). But this is equivalent to Q(S), so we really only have three possibilities.
Now, if we want to express the proposition "S will obtain at time t" then, since we've already used S in the proposition, we need to define another state-of-affairs, T, which is S's obtaining at time t. Thus,
"S will obtain at time t" = Z(T) = "S's obtaining at time t is necessary"
"S will not obtain at time t" = Z(~T) = "S's not obtaining at time t is necessary"
"S might and might not obtain at time t" = Q(T) = "S's obtaining at time t is contingent"
As is clear, Z(T), Z(~T), and Q(T) are propositions, not states-of-affairs.
What about things like Q[Q(T)], Q[Z(T)], etc. Can we iterate operators? Yes we can, but not like that. The operators take states-of-affairs as arguments, not propositions, so if we want to express second-order contingencies and necessities we need to recast first-order contingencies as states-of-affairs. Thus, Q[Q(T)] is nonsense, but we can meaningfully say Q[Q(T)'s being true], since "Q(T)'s being true" is a state-of-affairs. Since operators Q and Z can be applied to any state-of-affairs, we can in principle iterate operators endlessly, as long as the arguments are states-of-affairs.
One more complication. As I pointed out in a previous post, contingency and necessity are dyadic relations between states-of-affairs. So, whether S is contingent or not depends on which state-of-affairs we take as our reference frame. When future-tense statements are in view, the natural reference frame is the state of the world at the present moment. But, in general, a reference frame could be provided by ANY state-of-affairs. Notationally, if we let R stand for the state-of-affairs that establishes the reference frame in which S is said to be either necessary or contingent, then we can express this by subscripting our operators as follows:
QR(S)
ZR(S) and
ZR(~S)
Since the present truth of future-tense statements is always judged relative to the reference frame of the present, we don't have to spell that out by adding a subscript every time. The reference frame is understood. In general, though, every application of operators Q and Z presupposes some reference frame or other, which in some circumstances may need to be made explicit.
The advantage of this generalized way of developing indeterminacy logic is that it doesn't just apply to future-tense truth claims. Rather, it can be used to assess the logic of contingency and necessity within ANY frame of reference: past, present, possible futures, any hypothetical situation we might dream up. Indeterminacy logic, therefore, has more potential applications than to future contingents.
For example, the very same arguments that Tom and Earl have used to argue that Q and Z apply to states-of-affairs and not propositions can be used to argue that modal logic makes a fundamental mistake by applying necessity and possibility to propositions when they should be applied to states-of-affairs. By putting states-of-affairs in their proper place, our indeterminacy logic has the potential to lead to a complete reformation of modal logic along the same lines. In fact, indeterminacy logic in the generalized form I have outlined above, just is modal logic done right, or so it seems to me. The philosophical ramifications of this are, quite frankly, enormous.
Thanks for pressing me on the proposition / states-of-affairs issue, Tom. As they say, iron sharpens iron.
God bless,
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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 6/21/2004 1:02 AM (GMT -6) | | Alan: ... are you sitting down, Tom? ... I'm prepared to make a major concession to you.
Tom: I’m sitting, but breathing heavily.
Alan: You and Earl have finally convinced me that the "p" in Qp can't be properly construed as a proposition.
Tom: Yaaay!
Alan: Contingency and necessity are fundamentally properties of states-of-affairs and not propositions.
Tom: And the sort of “contingency” we’re speaking of then is “historical” and not “logical,” right?
Alan: First, we can't use a lower-case 'p', for it is the nearly universal convention in logic to use lower-case letters p, q, r, ... as variables that take propositions as values. So if we say Qp, Zp, and Z~p, we will be misunderstood. It is, however, not inconsistent with common practice to use capital letters for states-of-affairs, so if S is a state-of-affairs, then we could say Q(S), Z(S), and Z(~S).
Tom: If we have to do that, OK. But isn’t there a difference between small case p, q, r, and s (letters from the latter half of the alphabet) and a, b, c, c (from the front end of the alphabet)? Something’s telling me these are used differently. Could we use the latter set of small case letters if it worked? Still, if S is commonly known as a state of affairs, then that’s what we want.
Alan: A couple notes: (1) We might want to discuss whether the "~" should go inside the parentheses or outside. I put it because it falls within the scope of the operator, and because it is part of the state-of-affairs that is asserted to be necessary. Thus, Z(~S) means "S's not obtaining is necessary". Z applies to the state-of-affairs S's not obtaining.
Tom: I’d say Z(~S) as well, but I’d say perhaps more precisely that this means: “Not-S’s obtaining is determinately the case.” No biggie.
Alan: (2) In terms of the symbolism, there is a fourth possibility, Q(~S). But this is equivalent to Q(S), so we really only have three possibilities.
Tom: Right. Q(S) = Q(~S)
Alan: What about things like Q[Q(T)], Q[Z(T)], etc. Can we iterate operators? Yes we can, but not like that. The operators take states-of-affairs as arguments, not propositions, so if we want to express second-order contingencies and necessities we need to recast first-order contingencies as states-of-affairs. Thus, Q[Q(T)] is nonsense, but we can meaningfully say Q[Q(T)'s being true], since "Q(T)'s being true" is a state-of-affairs. Since operators Q and Z can be applied to any state-of-affairs, we can in principle iterate operators endlessly, as long as the arguments are states-of-affairs.
Tom: I’ll get this eventually! 
quote:
Alan: One more complication. As I pointed out in a previous post, contingency and necessity are dyadic relations between states-of-affairs. So, whether S is contingent or not depends on which state-of-affairs we take as our reference frame. When future-tense statements are in view, the natural reference frame is the state of the world at the present moment. But, in general, a reference frame could be provided by ANY state-of-affairs. Notationally, if we let R stand for the state-of-affairs that establishes the reference frame in which S is said to be either necessary or contingent, then we can express this by subscripting our operators as follows:
QR(S)
ZR(S) and
ZR(~S)
Since the present truth of future-tense statements is always judged relative to the reference frame of the present, we don't have to spell that out by adding a subscript every time. The reference frame is understood.
Right. But event if the reference frame was some OTHER time, the proposition claiming THIS would still be true or false based on the present moment. Yes? No?
I’m still wondering whether Q for you means “It is logically contingent that…” or “It is historically contingent that….” If the latter, then QZ(S) = “It’s being determinately the case that S will obtain is logically contingent.” In that case Q(S) means “S is a logically contingent state of affairs.” But that’s not saying much. It doesn’t even tell us whether S is a “will”, “will not” or “might and might not.”
Alan: The advantage of this generalized way of developing indeterminacy logic is that it doesn't just apply to future-tense truth claims.
Tom: Then you must be taking Q to mean It is logically contingent that….” I’m not sure how that works.
quote:
Alan: Rather, it can be used to assess the logic of contingency and necessity within ANY frame of reference: past, present, possible futures, any hypothetical situation we might dream up. Indeterminacy logic, therefore, has more potential applications than to future contingents.
For example, the very same arguments that Tom and Earl have used to argue that Q and Z apply to states-of-affairs and not propositions can be used to argue that modal logic makes a fundamental mistake by applying necessity and possibility to propositions when they should be applied to states-of-affairs. By putting states-of-affairs in their proper place, our indeterminacy logic has the potential to lead to a complete reformation of modal logic along the same lines. In fact, indeterminacy logic in the generalized form I have outlined above, just is modal logic done right, or so it seems to me. The philosophical ramifications of this are, quite frankly, enormous.
I like breaking furniture. So count me in!
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Tom
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| Posted 6/21/2004 3:07 AM (GMT -6) | | Hey Alan-
Let’s say it’s now indeterminately the case that S obtain, thus Q(S), but that S’s obtaining might and might not become determinately the case. In this case, we have a new state-of-affairs S1, or S’s obtaining becoming a settled matter. How would you express S1? I’d say QZ(S), or Q(Z), not sure which, to mean “S’s obtaining is now indeterminate, but it might and might not become a determinate matter.” The point is, S and S1 are two different states-of-affairs. S1 is that event after the time the proposition is made but prior to S at which time S’s obtaining might and might not cease being Q(S) and become Z(S).
Thus, one could postulate that though S is now indeterminate, or Q(S), there is an event S1 (prior to S) at which time S’s obtaining will either continue to be Q or become Z: QZ(S). This proposition would rule out S’s becoming Z~ at the time of S1, but not rule out S’s continuing to be Q. But we could postulate another proposition claiming that though S is now indeterminate, there is an event S2 (prior to S) at which time S’s obtaining will either continue to be Q or become Z~: thus, QZ(~S). It would also seem to me that QZ(S) and QZ(~S) are contrary propositions.
Eventually we’ll have to hammer out a way to notate these propositions. But I don’t think we have to do so now for the paper do we? I wouldn’t add more than I’ve said already to announce that we intend (and invite others to intend) to work out the implications of this.
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Humphrey Bogart
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Date Joined Jun 2003
Total Posts : 205
| Posted 6/21/2004 4:19 AM (GMT -6) | | Excellent discussion Tom and Alan!
Can I add my two cents worth?
"Necessity" and "contingency" do indeed relate to states of affairs and not propositions, BUT
The concepts "analytic" and "synthetic" apply to propositions, not states of affairs AND
It might be argued that all analytic propositions describe necessary states of affairs and all synthetic propositions describe contingent states of affairs. I'm not necessarily claiming that they do, in fact I'm not convinced that is so, but I'm just putting it out there as a possibility. If it is true that there is a 1:1 correspondence between analytic propositions and necessary states of affairs on the one hand, and synthetic propositions and contingent states of affairs on the other, then surely there is a such a 1:1 correspondence between the representation (propositions) and the reality (states of affairs) that the distinction is relatively unimportant?
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 6/21/2004 1:06 PM (GMT -6) | | Hi Tom,
Tom: And the sort of “contingency” we’re speaking of then is “historical” and not “logical,” right?
Alan: Hmmm. I'm not quite sure I understand the distinction. You probably explained this in an earlier post that I haven't read yet. I'll have to go back and check. My preliminary answer, I think, is that I'm talking about both. Contingency is a relation between states-of-affairs. Which kind of contingency we have--logical or historical (=causal?)--depends on the states-of-of-affairs in question. Are the states-of-affairs in question logical states of propositions or relations among propositions (e.g., "2+2=4"'s being true, or "All men are mortal and Socrates is a man"'s entailing "Socrates is mortal")? If so, then I suppose that we are in the sphere of logical contingency and necessity. Are the states-of-affairs in question concrete states of the world or relations among states of the world (e.g., the cat's being on the mat)? If so, then I suppose we are in the sphere of historical or causal contingency and necessity.
Tom: Isn’t there a difference between small case p, q, r, and s (letters from the latter half of the alphabet) and a, b, c, d (from the front end of the alphabet)? Something’s telling me these are used differently. Could we use the latter set of small case letters if it worked? Still, if S is commonly known as a state of affairs, then that’s what we want.
Alan: You're right that different letters are used differently. Letters p,q,r, ... are used for propositional variables. They take propositions as values. Letters x,y,z,w are (I'm not sure of the technical term) individual variables. They take individual "things" as variables. For example, (x)(Px --> Qx), means "for all x, if x has property P, then x has property Q"). Letters a,b,c, ... represent specific values that individual variables can take. For example, a="Tom", b="Dick", c="Harry". Thus, I could say (x)(Px --> Qx), Pa, therefore, Qa. The applies the general principle (x)(Px --> Qx) to a particular case. I don't know of any set of lower-case letters that is customarily used for states-of-affairs.
quote:
Alan: Contingency and necessity are dyadic relations between states-of-affairs. So, whether S is contingent or not depends on which state-of-affairs we take as our reference frame. When future-tense statements are in view, the natural reference frame is the state of the world at the present moment. But, in general, a reference frame could be provided by ANY state-of-affairs. Notationally, if we let R stand for the state-of-affairs that establishes the reference frame in which S is said to be either necessary or contingent, then we can express this by subscripting our operators.
Tom: But even if the reference frame was some OTHER time, the proposition claiming THIS would still be true or false based on the present moment. Yes? No?
Alan: Whether it is NOW true is based on the present moment, but if we wanted to ask what WAS true at some point in the past, then we would have to use a reference frame in the past. Of course, we can only assessing matters in the present, so it would be true NOW that something WAS true (or false) then.
Tom:Let’s say it’s now indeterminately the case that S obtain, thus Q(S), but that S’s obtaining might and might not become determinately the case. In this case, we have a new state-of-affairs S1, or S’s obtaining becoming a settled matter. How would you express S1? I’d say QZ(S), or Q(Z), not sure which, to mean “S’s obtaining is now indeterminate, but it might and might not become a determinate matter.” The point is, S and S1 are two different states-of-affairs. S1 is that event after the time the proposition is made but prior to S at which time S’s obtaining might and might not cease being Q(S) and become Z(S).
Alan: I would represent this with different subscripts. Let's say that R0 is the reference frame of the present and that R1 is a possible later reference frame with respect to which S would be determined. In that case each of these propositions is true:
QR0(S)
QR0(R1)
ZR1(S)
We can combine the last two to get: QR0[ZR1(S)].
Hope that's clear.
Alan
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Alan Rhoda
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Date Joined May 2002
Total Posts : 680
| Posted 6/21/2004 2:06 PM (GMT -6) | | quote:
Albert: "Necessity" and "contingency" do indeed relate to states of affairs and not propositions, BUT the concepts "analytic" and "synthetic" apply to propositions, not states of affairs AND it might be argued that all analytic propositions describe necessary states of affairs and all synthetic propositions describe contingent states of affairs. ... If it is true that there is a 1:1 correspondence between analytic propositions and necessary states of affairs on the one hand, and synthetic propositions and contingent states of affairs on the other, then surely there is a such a 1:1 correspondence between the representation (propositions) and the reality (states of affairs) that the distinction is relatively unimportant?
Hi Albert. You raise a good point here. It may be that all state-of-affairs-talk is translatable into proposition-talk and vice-versa, but it's far from obvious to me that there is a one-to-one correspondence here. Take, for example, the state-of-affairs C = "the cat's being on the mat". We can posit C by means of several different propositions: "The cat is on the mat", "The cat was on the mat", "The cat will be on the mat", "The cat was on the mat in the summertime", "The cat was on the mat sleeping", etc. There seems to be an infinite number of propositions that could be used to posit C. Similarly, the proposition "The cat is on the mat" posits several different states-of-affairs: the cat's existing, the mat's existing, the cat's and the mat's existing concurrently, the cat's being situated above the mat, the cat's not being somewhere else, etc.
The difficulty with establishing a 1-1 correspondence between states-of-affairs and propositions, it seems to me, it that we have no precise way to enumerate either. As illustrated by the example above, one state-of-affairs can contain many other states-of-affairs (e.g., "the cat's being on the mat" contains both "the mat's existing" and "the cat's existing"). And one proposition can contain many other propositions (e.g., "the cat is on the mat" contains by implication both "there is a mat" and "there is a cat"). Maybe there are such things as atomic states-of-affairs and atomic propositions (a la the early Wittgenstein), but I doubt it. If there were, then we could presumably establish a 1-1 correspondence between them. The only other way of getting a 1-1 correspondence, it seems to me, is to deal with maximal states-of-affairs (possible worlds) and maximal propositions (roughly, a conjunctive series of propositions fully describing every possible existent, e.g., "S is P,Q,R,... AND T is ~P,Q,R, ... AND ...). But since we could never make either completely explicit, how could we ever SHOW that they stand in a one-to-one relation?
That said, there does seem to be a parallel between necessity and analyticity and between contingency and syntheticity, however. Both sets of distinctions seem to me to presuppose a reference frame. Necessity and contingency are defined relative to some presupposed background state-of-affairs. Analyticity and Syntheticity are defined relative to a set of background assumptions that are taken as axiomatic. For example, "the sum of the interior angles of a triangle is 180 degrees" is analytic in Euclidean geometry, but not in Riemannian geometry.
I'll have to think about it some more.
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Tom
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| Posted 6/21/2004 7:47 PM (GMT -6) | | quote:
Tom: And the sort of "contingency" we're speaking of then is "historical" and not "logical," right?
Alan: Hmmm. I'm not quite sure I understand the distinction. You probably explained this in an earlier post that I haven't read yet. I'll have to go back and check. My preliminary answer, I think, is that I'm talking about both.
"JFK was assassinated in 1963" is logically contingent but historically necessary. That's the difference. A logically necessary state-of-affairs is a state-of-affairs that can't possibly be other than it is (like mathematically truths). Necessary truths describe necessary states-of-affairs. So, does Q posit logical contingency or historical contingency? Obviously if a state-of-affairs is historically contingent (it might and might not obtain) then it's also logically contingent. But if a state-of-affairs is logically contingent, it doesn't follow that it's historically contingent (like JFK's being assassinated in 1963). So I think Q should mean "historically contingent" (which covers both) and not merely "logically contingent" (which may or may not include a state-of-affairs being historically contingent).
quote:
Alan: Which kind of contingency we have--logical or historical (=causal?)--depends on the states-of-of-affairs in question. Are the states-of-affairs in question logical states of propositions or relations among propositions (e.g., "2+2=4"'s being true, or "All men are mortal and Socrates is a man"'s entailing "Socrates is mortal")? If so, then I suppose that we are in the sphere of logical contingency and necessity. Are the states-of-affairs in question concrete states of the world or relations among states of the world (e.g., the cat's being on the mat)? If so, then I suppose we are in the sphere of historical or causal contingency and necessity.
Let's stick to CLAIMING historical contingency and then logical contingency follows by implication. We're arguing the former, not the latter.
quote:
Tom: But even if the reference frame was some OTHER time, the proposition claiming THIS would still be true or false based on the present moment. Yes? No?
Alan: Whether it is NOW true is based on the present moment, but if we wanted to ask what WAS true at some point in the past, then we would have to use a reference frame in the past. Of course, we can only assessing matters in the present, so it would be true NOW that something WAS true (or false) then.
This is a legitimate use of indeterminacy logic, yes. Gotcha. And it's a good place to posit the theorem that if Q(S) now then Q(S) at all times prior to the present but not necessarily Q(S) at all times after the present moment leading up to S, for it might become the case that Z(S). But if Z(S) now, then not necessarily Z(S) at all times prior to now (for it might have been the case that Q(S) became Z(S), but necessarily the case that Z(S) at all times after the present leading up to S's obtaining.
quote:
Tom:Let's say it's now indeterminately the case that S obtain, thus Q(S), but that S's obtaining might and might not become determinately the case. In this case, we have a new state-of-affairs S1, or S's obtaining becoming a settled matter. How would you express S1? I'd say QZ(S), or Q(Z), not sure which, to mean "S's obtaining is now indeterminate, but it might and might not become a determinate matter." The point is, S and S1 are two different states-of-affairs. S1 is that event after the time the proposition is made but prior to S at which time S's obtaining might and might not cease being Q(S) and become Z(S).
Alan: I would represent this with different subscripts. Let's say that R0 is the reference frame of the present and that R1 is a possible later reference frame with respect to which S would be determined. In that case each of these propositions is true:
QR0(S)
QR0(R1)
ZR1(S)
Two problems: One, if R1 is only a possible latter reference frame, then Zr1(S) can't be true. R1 may render S's obtaining determinate and it may not render S's obtaining determinate. It might and might not become true that Zr1(S). Two, there's a state-of-affairs that is ignored. R1 is not just a reference frame. There's an event there which may and may not impact S. But it is not the event S. It is its own state-of-affairs (prior to S). So why shouldn't we recognize it as such, that is, as an "S", thus, S1? In the future we may want to talk about how different future events impact one another in this way. Are we only going to mention the final state-of-affairs in the string with an "S"? Let's give each independent event its own place on the playing field.
Q(S at t2) at t0 [or you can place the "at t0" immediately after Q. I don't know. I mean to say that it is now true at t0 that S might and might not obtain at t2.]
Q(S1 at t1) at t0 [It is now true at t0 that S1 might and might not obtain at t1]
If S1 then Z(S at t2) [If S1 (at t1 of course), then determinately S at t2.
Now, since all propositions are true or false NOW (that is, presentism), we can remove the reference to time and still have it work:
P1: Q(S)
P2: Q(S1)
P3: S1 --> (S)
C: Therefore, Q(Z)
It's that simple. This is true without mentioning anything about frames of reference.
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Tom
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| Posted 6/22/2004 1:26 AM (GMT -6) | | Alan-
Wouldn’t these “frames of reference” you’re talking about be PART OF a state-of-affairs? States-of-affairs can have any number of temporal and other defining characteristics:
“a sea battle tomorrow at noon off the coast of Athens”
“Kasparof losing to the world’s worst player next Monday while Lee referees”
These are complete enough to prefix Z or Q to them and end up with a truth claim.
Sure, one can posit what otherwise appear to be identical states-of-affairs:
“the sum of the interior angles of a triangle’s equaling 180 degrees”
Assuming Euclidean geometry this is an actual state-of-affairs and propositions claiming so would be true. But if, as you suggested, we drop Euclid's parallel line postulate and open up the field of possibilities to curved geometries in which the sum of the interior angle's of a triangle may or may not equal 180 degrees, depending on the curvature of space, then the state-of-affairs in question would not necessarily obtain and propositions claiming it did would be false.
It looks to me like you want to posit states-of-affairs extracted from any frame of reference whatsoever and THEN posit the frames of reference with separate variables. But why do that? Why not require states-of-affairs to carry their own luggage? Then if somebody asks, “Do the interior angles of a triangle equaling 180 degrees?” we’d have to say, “Well, that depends on whether you’re talking Euclidean or curved geometries.” It’s like the claim that x > 2. Is x > 2 a state-of-affairs? I’m thinking not. But saying x > 2 is like saying “the sum of the interior angles of a triangle’s equaling 180 degrees.” Where S is itself not specified as reflecting Euclidean or curved geometry, claiming Z(S) is like claiming x > 2. No truth claim is actually being made. But we want Z(S) to make a propositional truth claim. So why not just say that states-of-affairs carry their frames of reference with them? So when you posit any S, you posit the what, when, where, etc., of that state-of-affairs but still without making any truth claim about the determinacy vs indeterminacy of S’s obtaining:
S: “the sum of the interior angles of a triangle’s equaling 180 degrees in Euclidean geometry”
S1: “the sum of the interior angles of a triangle’s equaling 180 degrees in curved geometries”
So it only appears that we have two identical states of affairs until the full context (apart from any truth claims about it) is made explicit, after which time then we really have two different states-of-affairs (as with the triangles above). So isn’t it really the case that if we are to make a truth claim about a state-of-affairs, the state-of-affairs must be complete, i.e., it must include enough information to make prefacing it with Z or Q a true or false proposition. You want to posit “in Euclidean geometry” and “in curved geometries” as separate variables, so that Se is the former and Sc is the latter. I guess that works, but it only confirms my point, namely, that until all the frames of reference are included, one can’t make a true or false truth claim about a state-of-affairs.
Not sure if any of this makes any sense. All gut and no logic, right?
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Alan Rhoda
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| Posted 6/22/2004 2:54 PM (GMT -6) | | Tom: "JFK was assassinated in 1963" is logically contingent but historically necessary. ... A logically necessary state-of-affairs is a state-of-affairs that can't possibly be other than it is (like mathematically truths). Necessary truths describe necessary states-of-affairs. So, does Q posit logical contingency or historical contingency? Obviously if a state-of-affairs is historically contingent (it might and might not obtain) then it's also logically contingent. But if a state-of-affairs is logically contingent, it doesn't follow that it's historically contingent (like JFK's being assassinated in 1963). So I think Q should mean "historically contingent" (which covers both) and not merely "logically contingent" (which may or may not include a state-of-affairs being historically contingent).
Alan: Restricting Q to historically contingent narrows the applicability of indeterminacy logic to only matters that are BOTH historically AND logically contingent, and excludes matters that are not historically contingent. I don't think this is the way to go. In my view we should strive for as much generality as possible, which means taking "Q" to refer to contingency simpliciter, not any specific subcategory of contingency. That's the only way to preserve the applicability of indeterminacy logic to hypothetical situations, which is essential for extending it to cover counterfactuals.
Tom: Let's stick to CLAIMING historical contingency and then logical contingency follows by implication. We're arguing the former, not the latter.
Alan: I think we need to be able to accommodate contingencies that aren't historical. Historical contingency is enough if we are only interested in assessing the truth values of simple future-tense claims, but our logic will be seriously incomplete if it cannot help us in assessing the truth values of hypothetical or counterfactual claims (Like, "If Peter were placed in circumstances C, he would deny Christ").
quote:
Alan: Let's say that r0 is the reference frame of the present and that R1 is a possible later reference frame with respect to which S would be determined. In that case each of these propositions is true:
Qr0(S)
Qr0(r1)
Zr1(S)
Tom: Two problems: One, if R1 is only a possible latter reference frame, then Zr1(S) can't be true. R1 may render S's obtaining determinate and it may not render S's obtaining determinate. It might and might not become true that Zr1(S).
Alan: Au contraire, mon frere. The meaning of Zr1(S) is "On the assumption that r1 is actual, S is necessary". It doesn't matter that r1 is only a possible reference frame because for the purpose of evaluating Zr1(S) it is assumed to be actual.
Tom: Two, there's a state-of-affairs that is ignored. R1 is not just a reference frame. There's an event there which may and may not impact S. But it is not the event S. It is its own state-of-affairs (prior to S). So why shouldn't we recognize it as such, that is, as an "S", thus, S1?
Alan: I haven't forgotten any state-of-affairs, for that is all included in R1. In other words, R1 is a state-of-affairs that in this case INCLUDES the event S1, as well as other relevant facts like the laws of physics, other initial conditions obtaining concurrent with S1, and so forth.
Tom: Wouldn’t these “frames of reference” you’re talking about be PART OF a state-of-affairs? States-of-affairs can have any number of temporal and other defining characteristics.
Alan: What I am calling reference frames aren't just part of a state-of-affairs, they are states-of-affairs in their own right. You are correct, of course, that states-of-affairs can have any number of "parts", from very simple states-of-affairs like a cat's being on a mat, to full-blown possible worlds.
Tom: It looks to me like you want to posit states-of-affairs extracted from any frame of reference whatsoever and THEN posit the frames of reference with separate variables. But why do that? Why not require states-of-affairs to carry their own luggage? Then if somebody asks, “Do the interior angles of a triangle equaling 180 degrees?” we’d have to say, “Well, that depends on whether you’re talking Euclidean or curved geometries.” It’s like the claim that x > 2. Is x > 2 a state-of-affairs? I’m thinking not. But saying x > 2 is like saying “the sum of the interior angles of a triangle’s equaling 180 degrees.” Where S is itself not specified as reflecting Euclidean or curved geometry, claiming Z(S) is like claiming x > 2.
Alan: I follow your argument. Certainly one could go that route, but it complicates matters to a point where application of the logic becomes impractical. The reason is that it would require us to spell out explicitly EVERY possible fact upon which a state-of-affairs might "depend". For example, on your suggestion I could not just posit the state-of-affairs "Felix the cat's being on a red mat". Why not? Because if someone asks, "Is Felix the cat on a red mat?" we'd have to say, "Well, that depends on whether Felix exists or not, on whether Felix is a cat, on whether the particular mat in question exist, on whether spatial relationships are possible between cats and mats, on whether Felix is above the mat, etc." Frankly, I don't want to have to spell out all the implications of my states-of-affairs before I can make meaningful truth claims about them.
More fundamentally, however, the very notion of contingency requires a distinction between a state-of-affairs and a set of conditions (a reference frame) on which that state-of-affairs may be said to depend or be contingent upon. Your suggestion involves packing all possible contingencies into the states-of-affairs that we discuss, but then the distinction between state-of-affairs and reference frame collapses and with it any meaningful sense in which that state-of-affairs may be contingent. For example, in a geometry that does not take the parallel line postulate for granted, "the sum of the interior angles of a triangle being 180 degrees" is contingent--it's true for some triangles, but not for others, depending on the curvature of geometrical space in the vicinity of a given triangle. But if we expand the state-of-affairs to settle this contingency (viz., "Euclidian geometry being true and the sum of the interior angles of a triangle being 180 degrees" then it is necessary that the some of the interior angles of triangle be 180 degrees. By packing more into our state-of-affairs we no longer have a contingency. If we made it a policy, as you suggest, to always pack enough into our states-of-affairs to settle any dependencies, then we would lose contingency altogether. To keep contingency we need reference frames, i.e., states-of-affairs in relation to which other states-of-affairs are both possible but not necessary.
God bless,
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Tom
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| Posted 6/22/2004 6:52 PM (GMT -6) | | Alan: Restricting Q to historically contingent narrows the applicability of indeterminacy logic to only matters that are BOTH historically AND logically contingent, and excludes matters that are not historically contingent. I don't think this is the way to go. In my view we should strive for as much generality as possible, which means taking "Q" to refer to contingency simpliciter, not any specific subcategory of contingency.
Tom: This is a huge difference then. First, I’d say there is no contingency simpliciter. There is either the merely logically contingent or the historically contingency (which is by definition also logically contingent, for whatever is historically contingent cannot be logically necessary, but what is logically contingent may be either historically necessary or historically contingent). So you can say you're arguing for "contingency" simpliciter but you mean either 'mere logical contingency' or 'historical contingency'. There IS a difference between these, so why should we not have a logic that makes that difference explicit?
Second, what we argue depends upon making the distinction explicit. If Q(S) can mean “S is a logically contingent state-of-affairs,” then Q(S) says nothing at all about whether S will, will not, or might and might not obtain. Logical contingency can't tell you what the truth of the matter is. Personally, I have absolutely no interest in developing a system for pointing out which states-of-affairs are merely logically contingent and which are not. All states-of-affairs besides mathematical truths and God’s own existence are logically contingent. There. That’s done. How much of a system do you need for that? But historical contingency? Now that does need someone to blow its trumpet and that’s what I thought we were doing.
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Tom
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| Posted 6/23/2004 8:13 PM (GMT -6) | | Hey Alan-
If Q(S) can mean merely “S is a logically contingent state-of-affairs” then does Z(S) mean “S is a logically necessary state-of-affairs”?
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GregBoyd
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| Posted 6/24/2004 8:38 PM (GMT -6) | | Haven't followed the discussion, to be honest. My apologies, but I've been crazy busy yada yada. But from a cursory reading of the last several posts, I gotta say I'm weighing in with TGB on this one Alan. I've always assumed our interest in developing the hexagon (and beyond) was restricted to historical contingencies -- viz. future indeterminacies. Z = historically settled. Q = historically open. Can't say I fully understand your concern to keep things "broader" to cover logical contingencies and necessities. Is there a problem in delineating these two categories that we are solving? I'm not aware of it.
You raised a concern about covering "counterfactuals." As I see it, counterfactuals that are now historically impossible fall into the Z category. e.g. it is determinate the case that Greg will not break 2:30 in the marathon in 2004. (It may have once been possible I'd break 2:30 in 2004, but it SURE as heck ain't possible NOW -- now that I've made the choices I've made). Counterfactuals that are yet historically possible fall into the Q category, but in this case we shouldn't call them counterFACTUALS, or better COUNTERfactuals... for what is factual is that they are POSSIBLE and may yet become actual facturals (gotta love it). It may be that some counterfactuals were once possible (e.g. once Qp) but are no longer (my above illustration). (Indeed, all but ONE line of counterfactuals were either a) never historically possible or b) were historically possible but now unactualized and hence not possible.
In short, my question to Alan is, what is the problem you are seeking to fix by expanding our Q and Z category to cover logic as well as historical possibilities? It strikes me, as it does Tom, that this muckies up the water considerably. (e.g. most future Zp's are still LOGICALLY contingent... e.g. I will wake up male tomorrow).
Hoping I can now enter into this conversation more fully,
Blessings
Greg
"The responsibility is with the chooser -- God is blameless." Plato, Republic, 10. | | Back to Top | | |
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JET
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| Posted 10/14/2004 1:26 PM (GMT -6) | | http://www.religion-online.org/showarticle.asp?title=2771
Hey Tom, have you seen this article? The author defends Hartshorne’s view of omniscience, foreknowledge and indeterminancy logic against Craig. I thought the author’s description of Hartshorne’s views was tracking with your indeterminacy logic (i.e., Hartshorne came to reject the Aristotelian solution), but then he says Harshorne denied bivalence. I can’t figure out why, since he agrees with “Z or ~Z or Q”. I don’t have time to re-read this now, but I thought I’d share it in case you’re interested. | | Back to Top | | |
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Tom
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| Posted 10/14/2004 1:53 PM (GMT -6) | | Thanks JET! I'll read that right away.
Oh how I remember this whole thread. What a roller coaster ride!
Where do we stand after those last few posts plus Greg's?
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Tom
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| Posted 10/14/2004 2:01 PM (GMT -6) | | Just skimmed it. Excellent. I'm not sure why the author thinks Hartshorne has to deny bivalence. He doesn't quote Hartshorne saying as much. But we're arguing the same thing and insisting on bivalence. Hartshorne is sooo right about "will" and "will not" being contraries and NOT contradictories as Craig incorrectly objected. Too bad for Craig. He's on the ropes on this one.
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Tom
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| Posted 10/14/2004 2:07 PM (GMT -6) | | The other kink in this that our article fixes is dispelling the notion that if an omniscient God knows some true "might and might not" propositions then God DOES NOT have 'absolute foreknowledge'. Only if one assumes that foreknowledge is only foreknowledge if what is foreknown is determined to come to pass is this the case. But that's the whole point. Knowledge of what "might and might not" occur counts as foreknowledge. So we should not suggest God does not posses foreknowledge, even 'absolute' foreknowledge (unless absolute means "immutable," but since when does absolute mean that?).
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Tom
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| Posted 10/14/2004 4:36 PM (GMT -6) | | Don Viney’s paper is interesting. It’s great to see someone bringing this up for discussion (I mean his paper—but this thread too!). I have not read Hartshorne (CH) and won’t pretend I know his work. I know he’s a process theologian (which means he’s an open theist as well). Other than that I’m going only on what Viney says about him. There are a couple of good points this paper makes about CH that tempt me to get a couple of his books. But, eh, I’ve spent too much already this Summer on books.
I’d like to post a few paragraphs of what Viney says and then discuss it if anyone else wants to. The bold P for ‘paragraph’ is mine as are the numbers. They’re not from Viney’s article. I just wanna post a few paragraphs and have a way to refer to them later.
Begin Viney--
P1: He [CH] characterizes divine foreknowledge as God’s view of all events that, from our standpoint, are future (ER 284). It is noteworthy that, as Hartshorne explains it, the concept of foreknowledge does not specify whether the knowledge of future events is temporally prior to those events. The Boethian God who surveys all of time in a single eternal vision has foreknowledge in Hartshorne’s sense even though it is incorrect to say that such a God knows future events in advance (CP 116). Equally, a God whose existence is temporal and who is prescient of all future events has foreknowledge in Hartshorne’s sense. The idea that future events are known -- not the knowing of them as future -- is the essential meaning that Hartshorne assigns to the concept of divine foreknowledge.
P2: A characteristic feature of Hartshorne’s central argument is that it concerns God’s knowledge of events and not God’s knowledge of truths about events. At one point, Hartshorne alludes to the distinction, made famous by Bertrand Russell, between knowledge of things and knowledge of truths. Knowledge of things sometimes involves an immediate awareness of an object that Russell calls knowledge by acquaintance. Knowledge of truths does not require a direct awareness but applies solely to beliefs, convictions, or judgments about what is the case (PP Chapter V). According to Hartshorne, God’s knowledge is best conceived as a knowledge by acquaintance (ER 547). This is not to say that God cannot have knowledge of truths. However, Hartshorne argues that if God’s knowledge is to be conceived as the highest form of knowledge, it must be conceived as a knowledge by acquaintance. Hartshorne follows Whitehead in viewing divine knowledge as a form of participation in the feelings of the creatures. Without participation, Hartshorne says, omniscience "would be only an abstract and inadequate knowledge of the creatures" (CSPM 263; cf. HPPT).
P3: If the law of excluded middle is to be retained for propositions concerning future contingents, then how is the indeterminacy of the future to be expressed in language? Hartshorne finds the clue to solving this problem in the unfolding causal history of the universe that makes certain events inevitable and others merely probable. Rather than speaking of indeterminate truth values, however, Hartshorne speaks of indefiniteness as a predicate: “We need no third truth value, but we do need a third type of predicate for future moments of process besides ‘definitely P’ and ‘definitely not P’, namely ‘indefinite with respect to P’.” To conceive of indefiniteness as a predicate for future moments of process allows one to put statements about the future into three categories, corresponding to the formally exhaustive triad of all/none/some. Either (a) all causal possibilities include P (definitely P), (b) no causal possibilities include P (definitely not P), or (c) P is included in some but not all causal possibilities (indefinite with respect to P). As Hartshorne notes, this view does not require the sacrifice of the law of excluded middle. "The truth of one of the three (a, b, or c) is the falsity of the other two" (CSPM 135).
P4: Craig claims that Hartshorne’s view of future tensed propositions sacrifices what he calls the traditional law of excluded middle. According to this law, for any statement and its contradictory, one must be true and the other false. According to Craig, "Hartshorne’s position with regard to future contingent statements is that any such statement and its contradictory are both false" (PS 16:198; PT 96). As evidence for his interpretation, Craig notes that, for Hartshorne, statements of the forms ‘x will occur’ and ‘x will not occur’ are both false where x is a future contingent. Craig does not mention Hartshorne’s repeated insistence that, technically, such statements are contraries, not contradictories (JP 61:476; MIGB 74:49; CSPM 16).
P5: Although Hartshorne’s view does not violate the traditional law of excluded middle, his view requires that the principle of bivalence be rejected. According to this principle, the probability of something’s being P is 0 if and only if the probability of its being P is not 1 (FP 5:188). For Hartshorne, propositions concerning an indeterminate future have a probability greater than 0 and less than I. On the other hand, for classical theists, like Craig, the probability calculus must be a concession to human ignorance of what the future will hold. For classical theists, there could be no probabilities between 0 and 1, from the divine standpoint, except insofar as God understands that, from a creaturely standpoint, the future is uncertain. According to this view, whatever is uncertain for the creatures is certain for God. If God’s standpoint represents the final truth of things, and if classical theism is true, then the principle of bivalence is true. Hartshorne denies the classical theistic view of divine knowledge, and with it, the principle of bivalence.
P6: If there is a brief answer to why one should adopt Hartshorne’s view of future tensed propositions it is that it does not commit one to the principle of bivalence. Richard Purtill notes that, if the principle of bivalence is true, then "probability theory simply collapses into standard propositional logic" (FP 5:188). This consequence seems too high a price to pay to preserve certain intuitions about the omnitemporality of truth.
End Viney--
Well, I just wanted to get these ideas posted. We can come back to them and refer to them as P1, P2, etc. If it’s just me that talks, then…well, I’ll obsess alone. Won’t be the first nor the last time. Thanks again JET for posting it!
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Tom
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| Posted 10/14/2004 6:40 PM (GMT -6) | | Here we go—
Re: P1. My first thought was, “What a strange way to define ‘foreknowledge’.” If as CH says, the ‘concept’ of foreknowledge doesn’t specify that the knowing is done prior to the events, then what sort of ‘concept of FOREknowledge’ is it? For just this reason those who take Boethius’ timeless view prefer not to call God’s knowledge ‘fore-’ anything. It’s just ‘knowledge’. I don’t want to discuss the pro’s and con’s of timeless knowledge here. We’ve done that elsewhere. Of all the options we have for understanding God’s knowledge of the world, this is the weakest of all in my view. Providentially useless knowledge.
Maybe somebody who knows CH can explain why as a process theologican he should make this particular point regarding God’s foreknowledge, viz., that it amounts to nothing more than “the idea that future [to us] events are known.”
Re: P2. The distinction between knowledge of things and knowledge of truths is OK. But why argue, as CH does, that ‘knowledge by acquaintance’ is a “higher form of knowledge”? This colors everything else for CH. It explains why he has such difficulty coming to terms with God’s propositional knowledge. Why not argue God possesses both forms of knowledge when appropriate?
Re: P3. Yes! So much good stuff here. It’s amazing to stumbled into something relatively on your own and then read it later! Cool.
CH is right. The law of the excluded middle is maintained. Open theists don’t have to sacrifice it. It holds. CH’s is so right on in arguing that ‘indeterminacy’ is NOT a truth value but a predicate! Oh my how I’ve shouted THAT on this thread. And there are our three operators! CH’s “definitely P,” “definitely not P,” and “indefinite with respect to P.” Oh my oh my. Somebody beat us to it Alan! There’s our Z, Z~, and Q. Good as money in the bank. But we can argue it better than Hartshorne and leave Craig lickin his wounds, baby.
Two quick quotes: First: “To conceive of indefiniteness as a predicate for future moments of process allows one to put statements about the future into three categories, corresponding to the formally exhaustive triad of all/none/some.” We talked about this too, how all/none/some parallels definitely/definitely not/indefinitely. I like this. But Prior played it down. Didn’t think there was much to this.
Second: “Either (a) all causal possibilities include P (definitely P), (b) no causal possibilities include P (definitely not P), or (c) P is included in some but not all causal possibilities (indefinite with respect to P). As Hartshorne notes, this view does not require the sacrifice of the law of excluded middle. ‘The truth of one of the three (a, b, or c) is the falsity of the other two’ (CSPM 135).” Alan, I’m freaking out here. This is too good to be true. We argued this precisely. Z, Z~, and Q are mutually exclusive and jointly exhaustive. One has to be true. Whichever is true, the other two are false.
What I don’t get is why, in light of this second quote of his, CH (the author claims) denied bivalence. CH says just the opposite: “The truth of one of the three is the falsity of the other two.” Bivalence holds. Excluded Middle holds. And indeterminacy is a predicate and not a truth value.
Re: P4. This blew my mind. Because Craig’s objection to CH is so stinking off. Craig argues that “will” and “will not” are contradictories and that if bivalence holds, one has to be true and the other false. We’ve mentioned here so many times what CH points out: “will” and “will not” are ‘contraries’ and not ‘contradictories’ and may both be false (bivalence holding universally).
Re: P5. Now this I don’t get. Given what CH says in P3 (“The truth of one of the three is the falsity of the other two”) why deny bivalence? And if you deny it, what happens to the three mutually exclusive predicates CH mentioned? Here’s what Viney says:
quote:
According to [bivalence], the probability of something’s being P is 0 if and only if the probability of its being P is not 1 (FP 5:188). For Hartshorne, propositions concerning an indeterminate future have a probability greater than 0 and less than I.”
Bad boy. Bad, bad boy! We’ve talked about this. Bivalence is about truth values, of which there are only two (true and false). And truth values, remember, are attributes of what? Of propositions! Right. So you can only have TWO truth values (True and False). But determinacy and indeterminacy are NOT truth values, nor are they attributes of propositions. They are attributes of states of affairs. This is CH’s mistake. He believed in contingent, or indeterminate, events, but he knew that truly contingent events meant multiple probabilities greater than 0 and less than 1, since a probability of 0 meant “will not happen” and a probability of 1 meant “will happen.” But indeterminate events have probabilities in between 0 and 1. CH thought that believing in more than two probabilities (0, 1, and all that's between these two) meant believing in more than two truth values. He wasn’t about to give up believing in an open future (that is, in more than two probabilities), so he did the only thing he could do. He gave up believing in two truth values when it came to future contingencies. And lots of open theists have followed in his footsteps.
Too bad. The whole notion that we’ve got to abandon bivalence (a property of propositions) because we believe in contingent events having probabilities of occurring which are greater than 0 but less than 1 is based on a confusion of attributes of propositions and attributes of states of affairs. It’s that simple.
Then Craig chimes in:
quote:
On the other hand, for classical theists, like Craig, the probability calculus must be a concession to human ignorance of what the future will hold. For classical theists, there could be no probabilities between 0 and 1 from the divine standpoint...
Listen, Greg and Alan, we dumped the “Epistemology” and “Ontology” labels in our contrary triangles. That’s OK. But we were right when they were in the paper. And Craig’s objection is the proof. Craig makes the same mistake CH makes in confusing attributes of propositions (truth values) with attributes of states of affairs (determinately-p, determinately not-p, indeterminately-p). Craig simply assumes, like CH did, that the number of truth values must be the same as the number of predicates positing future events (“will” and “will not”). But this is just bogus assumption. There can be a hundred predicates positing states of affairs with only two truth values to do the job for them all. A hundred CONTRARY predicates, in which case one must be true (bivalence!) and all the rest false. Craig complicates this further by viewing “will” and “will not” as contradictory, which if bivalence holds must one be true and one be false. And Craig knows that spells the end of the open view. But if “will” and “will not” are contrary, bivalence is upheld even if they are both false. But bivalence must then demand that there be a ‘truth’ of the matter in question. And if “will” and “will not” are both false, Craig simply doesn’t know where to go to find the proposition that expresses the truth of the matter (as bivalence demands).
But we know what that third proposition is. And it’s been right there in logic since Aristotle...
"MIGHT and MIGHT NOT"
Alan, we gotta finish this paper dude!
Re: P6. I gotta repost it:
quote:
If there is a brief answer to why one should adopt Hartshorne’s view of future tensed propositions it is that it does not commit one to the principle of bivalence. Richard Purtill notes that, if the principle of bivalence is true, then "probability theory simply collapses into standard propositional logic" (FP 5:188). This consequence seems too high a price to pay to preserve certain intuitions about the omnitemporality of truth.
To Purtill I say this: If you stop assuming that probability ratios are only a measure of how ignorant we are and consider the possibility that they express what is ontologically the case, you’ll rejoice in bivalence AND probabilities. On the very last sentence of Viney’s I say: To hell with the omnitemporality of truth. Long live time and temporal truth.
Tom | | Back to Top | | |
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JET
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Date Joined Jun 2002
Total Posts : 397
| Posted 10/15/2004 2:13 AM (GMT -6) | | TGB: Bad boy. Bad, bad boy! We’ve talked about this. Bivalence is about truth values, of which there are only two (true and false). And truth values, remember, are attributes of what? Of propositions! Right. So you can only have TWO truth values (True and False). But determinacy and indeterminacy are NOT truth values, nor are they attributes of propositions. They are attributes of states of affairs. This is CH’s mistake.
* * *
The whole notion that we’ve got to abandon bivalence (a property of propositions) because we believe in contingent events having probabilities of occurring which are greater than 0 but less than 1 is based on a confusion of attributes of propositions and attributes of states of affairs.
* * *
Craig makes the same mistake CH makes in confusing attributes of propositions (truth values) with attributes of states of affairs (determinately-p, determinately not-p, indeterminately-p).
JET: Interesting. I asked Doc about the indeterminancy logic paper at the conference in Shipshewana. I opined that the mistake being made by those who affirm openness but deny bivalence is failing to properly distinguish between propositions and states of affairs (as you show in the foregoing quotes). However, Doc wasn’t having it. Either I wasn’t very clear or Doc disagrees that this distinction is critical to understanding bivalence and openness. Have you discussed this with Doc? | | Back to Top | | |
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JET
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Date Joined Jun 2002
Total Posts : 397
| Posted 10/15/2004 2:26 AM (GMT -6) | | | Also, as you already suggested, it may be that Viney is simply misinterpreting Hartshorne’s views. Viney claims that Hartshorne’s view “requires that the principle of bivalence be rejected”. However, Viney doesn’t actually attribute this claim to Hartshorne himself. This seems to be Viney’s conclusion about what Hartshorne’s view requires. However, he quotes Hartshorne as saying “we need no third truth value”. Doesn’t this mean Hartshorne affirms bivalence? | | Back to Top | | |
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Tom
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Date Joined Jul 2001
Total Posts : 10353
| Posted 10/15/2004 2:32 AM (GMT -6) | | quote:
JET: Also, as you already suggested, it may be that Viney is simply misinterpreting Hartshorne’s views. Viney claims that Hartshorne’s view “requires that the principle of bivalence be rejected”. However, Viney doesn’t actually attribute this claim to Hartshorne himself. This seems to be Viney’s conclusion about what Hartshorne’s view requires. However, he quotes Hartshorne as saying “we need no third truth value”. Doesn’t this mean Hartshorne affirms bivalence?
Exactly, JET. If Hartshorne says he doesn't need a third truth value then he's NOT denying bivalence.
Can't understand Doc's response to you. We've talked about the distinction between propositions and states of affairs before, and I think it's in our paper. Alan and I have kicked it around a bit more. But Doc was in on it as well. This whole thread is about that distinction. Maybe he was having a brain fart at the time! I don't know. 
Tom | | Back to Top | | |
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