Newcomb's Paradox provides an illuminating non-theological illustration of the problem of divine foreknowledge and human freedom. We are to imagine a being with great predictive powers and to suppose we are confronted with two boxes, B1 and B2. B1 contains $1,000; B2 contains either $1,000,000 or nothing. We may choose either B2 alone or B1 and B2 together. If the being predicts that you choose both boxes, he does not put anything in B2; if he predicts that you choose B2 only, he puts $1,000,000 in B2. What should you choose? A proper construction of the pay-off matrix for the decision vindicates the one-box choice. If this is correct, then those who claim that God's knowledge is counterfactually dependent on future contingents foreknown by Him are likewise vindicated.
Let's analyze this problem.
I. Initial Analysis
As an initial analysis, let's assume that (a) we want more money than less money, and (b) the predictive ability of the being is perfect, not just very great.
In that case, the solution is obvious, pick B2. Result %100 chance of receiving $1M.
II. Return to the Presented Question
When we take away (b), such that the predictive power is great, but not perfect, we are faced with options that are somewhat more complicated. We'd like to increase our amount from $1M to $1.001M, but we don't want to receive only $0.001M or, even worse, nill.
There are four possible scenarios:
1. You pick both, and the being predicts that correctly.
2. You pick both, but the being predicts you pick only B2.
3. You pick B2, and the being correctly predicts that.
4. You pick B2, and the being predicts that you pick both.
If each were to occur, the results (payout) would be as follows.
1. $0.001M
2. $1.001M
3. $1.000M
4. Nada
Looking only at your payouts, there is not a monotonic preference between picking B2 or both. In other words, there is no one choice that is always better than the other.
A. Strategies that do not involve assessing the being's predictive ability
i. Maxi-Min
There are a couple game theory strategies that you could employ at this stage. If you were aiming to minimize your worst outcome, you would pick both. This is called the "maxi-min" strategy. Employing that strategy, you are guaranteed at least $0.001M, and you could get lucky and strike it rich. A person whom we would consider very risk averse would choose both to avoid getting nothing.
ii. Maxi-Max
Likewise, a very risk loving person would (using a different game theory strategy) choose both, becuase doing so provides the possibility of the maximum payout. This is called the "maxi-max" strategy. Employing this strategy, there is some chance (however remote) that you will obtain the big prize of $1.001M. Such a person would be willing to take the risk that he could get the low payoff in the hope of obtaining the big prize.
Notice that neither of these strategies requires any knowledge about how good the being is at predicting, as long as the being does not have perfect predictive ability.
B. Strategies that requiring assessing the predictor
i. Expected Value
The most analytical strategy for making a selection is based on assessing the ability of the predictor. This is the expected value strategy.
In the expected value strategy, we multiply the payout for each outcome of each of the scenarios by the chance of the scenario occurring. Thus, we would have the following, in which P is the probability that the predictor predicts correctly, expressed as a decimal.
1. $0.001M x P
2. $1.001M x (1-P)
3. $1.000M x P
4. Nada
Item number 4 remains zero, because zero times anything is zero.
Notice that there are two pairs A (1,2) and B (3,4). The expected value strategy cannot pick just one of the items, it must pick one of the pairs. The value of each pair is the sum of the outcomes within the pair. The expected values of the pairs is:
A. ($0.001M x P) + ($1.001M x (1-P))
B. $1.000M x P
B is equal to 3, because adding zero adds nothing.
Let's examine a few sample values for P.
If P = 0, A = $1.001M and B = Nada.
Such a scenario is the scenario where the predictor always picks wrong.
In contrast, if P = 1, A = $0.001M and B = 1.000
Such a scenario is the scenario where the predictor always picks correctly.
In the first scenario, the Expected Value strategy would be to pick A, and in the second scenario, the Expected Value strategy would be to pick B. As you might expect, as P increases from zero chance to a 100% chance, A loses favor to B.
The precise point at which the Expected Value stategy says both A and B are equally good, is:
($0.001M x P) + ($1.001M x (1-P)) = $1.000M x P
which simplifies to
$1.001M = $2M x P
or P = 0.5005
When P = 0.5005, A = $0.5005M and B= $0.5005M
When P is less then 0.5005, A is going to be higher than B, and when P is greater than 0.5005, B is going to be higher than A.
Thus, if we believe that the being's predictive power is greater than 0.5005, and we use the expected value strategy, we will pick B, and if we believe that the being's predictive power is less than 0.5005, we will pick A.
If we had no information about the predictive being's guessing abilities, we might default to the view that the predictive being guessed correctly 50% of the time. If we had that view, and we employed the expected value strategy, we would pick A.
But the problem stipulates that predictive being does not just have average guessing ability, but that the predictive being has great predictive ability. Accordingly, we would be inclined to pick B using the expected value strategy, as long as we believed that 0.5005 is not >> 0.5.
C. Second Guess Strategies
In addition to the strategies that evaluate risk or payoff alone, and the strategy of using expected value, there is an additional level of strategy that is intuitively attractive. This intuitively attractive strategy is to try to predict the prediction of the predictor.
In other words, we ask the question, what would the predictor expect me to pick? If we predict that the predictor will predict our selection of B (i.e. that we pick B2), then we will actually pick A (i..e. both boxes) because then we will have $1.001M instead of $1.000M. If we predict that the predictor will predict our selection of A (i.e. that we will pick both boxes), then we will pick A again because that way we will have $0.001M instead of nada.
If we employ this second guess strategy, we will always pick A, because (regardless of what we think that the predictor will predict) the result is that A will be better.
III. Comparison of the strategies
There is really no one strategy that is better than the other strategies. One might argue that the Expected Value strategy is the best strategy, but such a strategy assumes that one is willing to accept the risk of a zero payout, and willing to lose the thrill of the maximum payoff. Likewise, such a strategy assumes that one cannot second guess the predictor and try to choose based on predicting the predictor. The strategy also assumes that the predictor has a predictive ability that exceeds (or at least equals) 0.5005.
IV. Comparison to W. L. Craig's claims
Recall that W.L. Craig had claimed:
A proper construction of the pay-off matrix for the decision vindicates the one-box choice. If this is correct, then those who claim that God's knowledge is counterfactually dependent on future contingents foreknown by Him are likewise vindicated.
As has been shown above, a pay-off matrix "vindicates" the one-box choice if and only if the other available game strategies are ignored, and the predictive ability of the being is assumed to be greater than a certain threshold. Such a qualified vindication cannot be said to vinidicate those who say that "God's knowledge is counterfactually dependent on future contingents foreknown by Him."
Additionally, there is no apparent link between this game and the point to be proved. But let us briefly review and critique W. L. Craig's own analysis detailed analysis of the problem.
V. A Common-Sense Strategy
The common sense strategy is simply to deny that what one does now will have any effect on what is in the second box. That is to say, either the predictive being placed the money in the box already or he did not. If he did, picking both boxes won't hurt, and if he did not, picking only the second box is foolish, because it automatically discards the $0.001M in the first box, leaving you with nada.
VI. A critique of W. L. Craig's analysis (Link to his analysis, here.)
In W. L. Craig's article, he favors the expected value strategy, while noticing various objections, including the common sense objection noted above.
W. L. Craig's main point appears to be that God already knows what you are going to pick, i.e. P = 1. As we have shown above, if P = 1, we should choose B2, in order to maximize our wealth.
The problem is that such a state of perfect predictability requires, as a mechanism, backwards causation. In other words, the only reason to favor the one-box strategy over the common-sense strategy, is if one believes that one's choice will actually affect the contents of the box. But the contents of the box have already been determined. Accordingly, one's choice must have a causal effect in the past, in order for one's choice to matter in whether the box is empty or full.
WLC attempts to interact with this rebuttal in a manner that reminds me greatly of Godismyjudge's comments in previous posts. Here goes:
This analysis, however, seems to rest upon a misunderstanding in which the causal relation between an event or thing and its effect is conflated with the semantic relation between a true proposition and its corresponding state of affairs. For if at tn I choose B2 alone, then the proposition "W chooses B2 alone" is true at tn because of the semantic relation which obtains between a true proposition and the corresponding state of affairs which makes it true; by the same token " W will choose B2 alone" is true prior to tn. "W chose B2 alone" is true subsequent to tn, and " W chooses B2 alone at tn" is omnitemporally true. The relation obtaining between a true proposition and its corresponding state of affairs is semantic, not causal. Now God, knowing all true propositions, therefore knows the true future contingent proposition concerning my choice of the boxes. Again no causal relation obtains here. Hence, the charge of backward causation seems entirely misconceived: we have simply the semantic relation between true propositions and their corresponding states of affairs and the divine property of knowing all true propositions.
I respond:
Here WLC makes much the same error that we have seen previously in Godismyjudge's posts. There is confusion between the proposition and the event. This confusion is somewhat subtle. Let's see if we can make it evident in a line-by-line analysis.
WLC writes: "This analysis, however, seems to rest upon a misunderstanding in which the causal relation between an event or thing and its effect is conflated with the semantic relation between a true proposition and its corresponding state of affairs. "
I respond: This is WLC's thesis, that cause-and-effect relationship has been confused for "the semantic relation between a true proposition and its corresponding state of affairs." Before we rush to judgment regading this thesis, let's see what WLC tenders as support.
WLC writes: "For if at tn I choose B2 alone, then the proposition "W chooses B2 alone" is true at tn because of the semantic relation which obtains between a true proposition and the corresponding state of affairs which makes it true; by the same token " W will choose B2 alone" is true prior to tn."
I respond: Let's leave aside the portion after the semi-colon for now. Looking at the first part of WLC's assertion, you will notice the following terminology, "... if ... then ... true ... because ... which makes it true." This is the language of causation, with the effect being the truth of the proposition. If the word "broken" were used instead of "true," no one would have the least doubt that the omitted portion of the quotation explained how the object came to be broken.
Calling this relationship between the cause of the proposition being true, and the truth effect of the cause a "semantic" relationship, appears intentionally obfuscatory. The term "semantic" usually conveys the sense of "relating to meaning," and derives from the Greek word semantikos, which indicates signification. Yet, WLC's explanation is one of cause and effect, not signification or meaning.
In other words, the correspondence to reality is the reason that a statement about reality is either true or false. That relationship is a causal relationship. If reality is as the statement says, then the statement has a "true" truth value. If reality is contrary to the statement, then the statement has a "false" truth value. In other words, the state of reality is the cause of the truth/falsehood value of propositions that describe reality.
WLC appears to attempt to bolster his view by the following example pair: ""W chose B2 alone" is true subsequent to tn, and " W chooses B2 alone at tn" is omnitemporally true. "
I respond: This difference between the two statements is something semantic, it has to do with the relation between the action verb and time. The first statement employs the past tense, and thus is making a claim regarding the past. The second statement employs language that simply states an event at a particular point in time (without a relative reference) and thus states a general, or gnomic, truth. As such, it avoids the semantic problem of the first statement.
Nevertheless, the same causal relationship exists between the second statement and the event. The second, gnomic, statement is true or false as result of its correspondence or lack thereof to reality. The fact that there are semantic differences between different descriptions of an event does not mean that the proposition's truth is causally independent of the event. Such a conclusion cannot possible follow from the demonstration provided.
WLC then simply asserts: "The relation obtaining between a true proposition and its corresponding state of affairs is semantic, not causal."
I respond: But we have shown that the truth value is causal, and even WLC's own explanation testifies to the causal relationship.
WLC continues: "Now God, knowing all true propositions, therefore knows the true future contingent proposition concerning my choice of the boxes."
I respond: Since WLC acknowledges that God knows all true propositions, it would appear that WLC is acknowledging that God not only knows them, but knows their truth or falsehood value. If so, then there is no way to exclude from God's knowledge the gnomic absolute proposition concerning the act of choosing the boxes. For if God knows the proposition, and if God knows that the proposition is true, then God knows the reality of the act/event, because God surely recognizes that the only proposition to be true is for it to have a positive correspondence to reality. If not, (i.e. if God does not know which propositions are true, and which are not true), then knowing the "the true future contingent proposition concerning my choice of the boxes," cannot help Him.
Either way, WLC's argument again collapses. As shown above, God knows the absolute gnomic truth of the proposition "A picks B2 at tn," regardless of whether God additionally knows the reason why the event occurs (either "contingently" or "determinately").
WLC again simply states: "Again no causal relation obtains here."
I respond: And of course, WLC's saying three times does not make it so. We have shown above, that there is a cause and effect relationship between the proposition's truth and reality. That's enough to show backward causation IF God has advance knowledge of the truth of the proposition.
WLC then concludes: "Hence, the charge of backward causation seems entirely misconceived: we have simply the semantic relation between true propositions and their corresponding states of affairs and the divine property of knowing all true propositions."
I respond: I have shown above why this conclusion is incorrect. There is more than just a semantic relationship between gnomic propositions and events - if the gnomic proposition corresponds to reality, then (and as a result of that correspondence) it is true. That is a causal relationship, and even WLC's own explanation (as demonstrated above) shows that it is a causal relationship.
Since WLC acknowledges that backward causation is a problem for his view of what he calls God's "foreknowledge," we are in a position to refuse to accept WLC's view of God's omniscience.
WLC has the opportunity to make one more attempt to address the shortcomings of his argument. WLC provides the following discussion and objection.
Choosing B2 alone is the right strategy, but one must live with the "uncomfortable knowledge" that at the time of choosing B2 alone God's belief is "unalterably tucked away in the past" and there is really $1,001,000 in the boxes. After choosing B2 alone one must be prepared to say, "If I had chosen both boxes, I would not have gotten the $1,001,000. " But an opponent might retort, "Of course you would have, since it was there! Therefore, you must not have been free to choose both."
Interestingly, WLC never finds time to the opponent's retort described above.
VII. A Reformed alternative
The Reformed alternative is to deny that God acts based on what he foresees us doing. The Reformed alternative indicates that God has, out of his infinite wisdom, foreordained all that will occur, and that includes both His and our actions. God is immutable and impassive. Acordingly, nothing that a creature does can cause God to do anything.
Thus, the Reformed critic can look at the problem two ways:
1) as absurd, because God knows the future as a logical result of knowing His eternal decree, not as a result of prediction,
2) as absurd, because whatever God decided to put in the box is already in the box, and will not come out, or
3) with slight modification, as a confusing revelation: i.e. God has revealed the consequence of picking one or two boxes. If two boxes are picked, the person will receive $0.001M and if one box is picked, the person will receive $1.000M; but how that would be implemented is simply a mystery, because it would appear that the only way that prophecy could be true with respect to the one-box-choice is if there is already the cash in the box, and likewise that for the two-box-choice if there is already no cash in the box. The solution being that God is behind both the cash placement and your choice. If God has ordained that you will choose both, he has already prepared no cash in box 2, and likewise if God has ordained that you will chose box 2, he has placed in that box. This solves the problem, solves the paradox, and leaves the reader wondering why WLC holds to an autonomous view of man in the first place.
VIII. Conclusion
WLC leaves a couple of gems in his own conclusion, and it is worth touching on them here.
WLC states:
A proper understanding of the counterfactual conditionals involved enables us to see that the pastness of God's knowledge serves neither to make God's beliefs counterfactually closed nor to rob us of genuine freedom. It is evident that our decisions determine God's past beliefs about those decisions and do so without invoking an objectionable backward causation.
Neither of these propositions have been established in WLC's article, nor can they be. Furthermore, the straw man is the "counterfactual conditionals" in contrast to the gnomic absolutes. God both knows the truth of hypothetical scenarios, but also the reality of the future. Finally, the second sentence is shocking in obvious self-contradictory nature. "... determine ... past ... without invoking an objectionable backward causation." The only possible hope for WLC to extricate himself from the self-contradiction would appear to be to rely on the "an objectionable" to qualify (rather than describe) the kind of backward causation that the present determination of a past event implies.
And of course, that's the penultimate problem with WLC's position: it is internally inconsistent and self-contradictory. The ultimate problem is that it is unscriptural. That it is internally inconsistent and self-contradictory is an outworking of its failure to begin from the presuppositions contained in the Word of God.
In short, in this critique of WLC, we see the practical impact that a flawed epistemology has.
-Turretinfan
Dear Turretinfan,
ReplyDeleteI wanted to respond to your post regarding Craig’s analysis of Newcom’s paradox. Rather than going line by line, I will pick out what I think is the key point: causal vs. semantic (or definitional) relationships.
You said:
“WLC writes: "This analysis, however, seems to rest upon a misunderstanding in which the causal relation between an event or thing and its effect is conflated with the semantic relation between a true proposition and its corresponding state of affairs. "
I respond: This is WLC's thesis, that cause-and-effect relationship has been confused for "the semantic relation between a true proposition and its corresponding state of affairs." Before we rush to judgment regading this thesis, let's see what WLC tenders as support.
WLC writes: "For if at tn I choose B2 alone, then the proposition "W chooses B2 alone" is true at tn because of the semantic relation which obtains between a true proposition and the corresponding state of affairs which makes it true; by the same token " W will choose B2 alone" is true prior to tn."
I respond: Let's leave aside the portion after the semi-colon for now. Looking at the first part of WLC's assertion, you will notice the following terminology, "... if ... then ... true ... because ... which makes it true." This is the language of causation, with the effect being the truth of the proposition. If the word "broken" were used instead of "true," no one would have the least doubt that the omitted portion of the quotation explained how the object came to be broken.
Calling this relationship between the cause of the proposition being true, and the truth effect of the cause a "semantic" relationship, appears intentionally obfuscatory. The term "semantic" usually conveys the sense of "relating to meaning," and derives from the Greek word semantikos, which indicates signification. Yet, WLC's explanation is one of cause and effect, not signification or meaning.
In other words, the correspondence to reality is the reason that a statement about reality is either true or false. That relationship is a causal relationship. If reality is as the statement says, then the statement has a "true" truth value. If reality is contrary to the statement, then the statement has a "false" truth value. In other words, the state of reality is the cause of the truth/falsehood value of propositions that describe reality.
WLC appears to attempt to bolster his view by the following example pair: ""W chose B2 alone" is true subsequent to tn, and " W chooses B2 alone at tn" is omnitemporally true. "
I respond: This difference between the two statements is something semantic, it has to do with the relation between the action verb and time. The first statement employs the past tense, and thus is making a claim regarding the past. The second statement employs language that simply states an event at a particular point in time (without a relative reference) and thus states a general, or gnomic, truth. As such, it avoids the semantic problem of the first statement.
Nevertheless, the same causal relationship exists between the second statement and the event. The second, gnomic, statement is true or false as result of its correspondence or lack thereof to reality. The fact that there are semantic differences between different descriptions of an event does not mean that the proposition's truth is causally independent of the event. Such a conclusion cannot possible follow from the demonstration provided.”
Your thesis seems to be that reality has a causal relationship with the truth value of a proposition. I will unfairly boil your argument into two parts:
First, WLC implicitly admits this thesis by using causal language such as “if, then” or “because” to describe the relationship between reality and the true of propositions.
Second, the correspondence of truth to reality is evidence that reality causes the truth value of propositions.
The answer to the first argument is that it is common to speak of logical and definition relationships using expressions such as “if, then” and “because”. However, Craig clarifies that he does not see this relationship as causal.
The answer to the second argument is threefold.
First, a simple denial that correspondence is evidence of causation and request for elaboration.
Second, by pointing out that the sense you are using for cause is abnormal.
Here’s dictionary.com’ definition of cause:
1. a person or thing that acts, happens, or exists in such a way that some specific thing happens as a result; the producer of an effect: You have been the cause of much anxiety. What was the cause of the accident?
Causes relate to action. Truth is not action. Events are caused, truth is not caused. Truth isn’t an action as such cannot participate in a causal relationship.
Third, by point out the omni-temporality of truth.
Craig states: W chooses B2 alone at tn" is omnitemporally true
TF responds: Nevertheless, the same causal relationship exists between the second statement and the event. The second, gnomic, statement is true or false as result of its correspondence or lack thereof to reality.
Your response seems to rely on backward causation.
Causation works temporally foreword (i.e. causes temporally precede effects). But as Craig points out truth or falsehood of certain statements are true or false at all points in time. This means that before an event happens, statements about the event are true or false.
At T=n-1 Craig’s statement (W chooses B2 alone at tn) is either true or false, but the reality of W choosing B2 has not yet exited. Now if reality causes the truth of the statement it must do so temporally backwards. But causation works temporally backwards. Therefore the relationship is non-causal.
You might deny the statement, before the event, is either true or false. Alternatively, you could seek a different basis of truth for the statement, such as God’s plan at the time the statement is made. But either of these would undercut your thesis that events have a causal relationship with truth.
God be with you,
Dan
Dear Dan,
ReplyDeleteThanks for your comments.
You wrote:
"Your thesis seems to be that reality has a causal relationship with the truth value of a proposition. I will unfairly boil your argument into two parts:"
I respond:
You seem to have identified my claim correctly, but misunderstood it, as we will see below. I'm not too worried about the boil-down.
You wrote (summarizing me):
"First, WLC implicitly admits this thesis by using causal language such as “if, then” or “because” to describe the relationship between reality and the true of propositions."
You later responded:
"The answer to the first argument is that it is common to speak of logical and definition relationships using expressions such as “if, then” and “because”. However, Craig clarifies that he does not see this relationship as causal."
I rebut:
WLC does assert that he does not see the relationship as causal, but the very terminology he uses suggests that it is a causal relationship. WLC does not demonstrate that it is not a causal relationship. Furthermore, as will be shown shortly (if God wills)in my review of his book, WLC goes beyond the language of syllogism when he describes the relationship.
Furthermore, "logical" is not mutually exclusive of "causal."
The second point of your summary of me was:
"Second, the correspondence of truth to reality is evidence that reality causes the truth value of propositions."
You later responded:
"The answer to the second argument is threefold."
I rebut:
Here's where you seem to have misunderstood my argument. Your summary is not a correct summary of my position. I don't claim that "reality causes the truth value of propositions." Instead, I claim that correspondence to reality causes the truth value of the propositions. In other words, the reason that "Today the sun is shining brightly" is true (if it is true) is because it corresponds to reality.
Nevertheless, let's examine your three-fold response.
You first argue:
"First, a simple denial that correspondence is evidence of causation and request for elaboration."
I respond:
This point seems to be moot, based on your apparent misunderstanding of the argument presented.
You next argued:
"Second, by pointing out that the sense you are using for cause is abnormal.
Here’s dictionary.com’ definition of cause:
1. a person or thing that acts, happens, or exists in such a way that some specific thing happens as a result; the producer of an effect: You have been the cause of much anxiety. What was the cause of the accident?
Causes relate to action. Truth is not action. Events are caused, truth is not caused. Truth isn’t an action as such cannot participate in a causal relationship."
I respond:
With all respect due Dictionary.com, it is hardly the best place to go for authoritative definitions on the English lanugage. Furthermore, it may be abnormal to speak about the causes of the truth value of propositions, but the word "cause" is being used in its conventional sense, as being the reason for the effect (here, "truth value" is the effect).
Nevertheless, perhaps part of this objection is moot in view of the misunderstanding noted above.
You finally argued:
"Third, by point out the omni-temporality of truth.
Craig states: W chooses B2 alone at tn" is omnitemporally true
TF responds: Nevertheless, the same causal relationship exists between the second statement and the event. The second, gnomic, statement is true or false as result of its correspondence or lack thereof to reality.
Your response seems to rely on backward causation.
Causation works temporally foreword (i.e. causes temporally precede effects). But as Craig points out truth or falsehood of certain statements are true or false at all points in time. This means that before an event happens, statements about the event are true or false.
At T=n-1 Craig’s statement (W chooses B2 alone at tn) is either true or false, but the reality of W choosing B2 has not yet exited. Now if reality causes the truth of the statement it must do so temporally backwards. But causation works temporally backwards. Therefore the relationship is non-causal.
You might deny the statement, before the event, is either true or false. Alternatively, you could seek a different basis of truth for the statement, such as God’s plan at the time the statement is made. But either of these would undercut your thesis that events have a causal relationship with truth."
I rebut:
Your final comment is precisely correct: I reject backward causation, and explain the causal relation with respect to the divine plan. What you seem to have overlooked is that a causal relation can exist between two effects (one, the truth value of the proposition, and two, the reality of history).
Probably it is the oversight that led you to misinterpret my argument as you did above. (I should point out that WLC similarly overlooks this solution to the dilemma.) In view of the clarification, however, the rebuttal of WLC's claims remains firm.
Nevertheless, I think you will find many similar issues raised in my response to WLC's book, which D.V. should be posted within the next few weeks.
-Turretinfan
Dear Turretin,
ReplyDeleteThee: I don't claim that "reality causes the truth value of propositions." Instead, I claim that correspondence to reality causes the truth value of the propositions. In other words, the reason that "Today the sun is shining brightly" is true (if it is true) is because it corresponds to reality.
Interesting. In that case I would argue that there is no difference between what you are calling a cause and what you are calling an effect.
The cause: “a proposition’s correspondence to reality” is the same thing as the effect: a proposition is true. They are not temporally sequential. As if at one moment a statement corresponds to reality, but the proposition is not true, the next moment it is true. Nor are they separate things, but definitionally the same.
Hence the relationship is definitional and not causal.
Restating my first argument, I request evidence in support of your claim that the relationship between the correspondence of reality to a proposition and the truth value of that proposition is causal.
I don’t think my second argument needs restatement.
Me: Causes relate to action. Truth is not action. Events are caused, truth is not caused. Truth isn’t an action as such cannot participate in a causal relationship.
Thee: Furthermore, it may be abnormal to speak about the causes of the truth value of propositions, but the word "cause" is being used in its conventional sense, as being the reason for the effect (here, "truth value" is the effect).
“True value” is not “normally” spoken of as an effect. Normally, effects are physical or spiritual actions. So to call the relationship causal is to use a special sense for the word cause.
My third argument should be modified such that your view leads to the conclusion that no true statements can be made about the future, because the statement cannot correspond to reality.
Even if a statement corresponds to God’s plan for what He wills to happen, that statement is not now true in the sense you are taking about truth. A sense, which seems critical to your critique of WLC, albeit perhaps not critical to your counter claim.
God be with you,
Dan
Dear Dan,
ReplyDeleteYou fail to respond to the fact that "logical" is not mutually exclusive of "causal." That failure is critical.
As to the three-part argument regarding the second point of the summary you provided:
Sure, the relationship between "truth" and "correspondence to reality" is definitional (although WLC cannot possibly accept such a definition of truth, so you - as his advocate - cannot really make that your argument), but to correspond is a verb, and consquently provides a mechanism for asserting causation.
So, in other words, establishing a definitional relationship (what you have attempted to do) does not negate a causal relationship.
You requested evidence of the causal link. That's simple. Consider a fallible proposition, such as, "Moscow, Russia contains Europe's biggest hotel." What makes this true is whether it corresponds to reality or not: namely, whether or not there is a bigger hotel in Europe. The cause of the proposition being true, consequently, can be seen to be connected with reality. I'm surprised that such a fact would not be blindingly obvious.
You fail to address the fact that: "Furthermore, it may be abnormal to speak about the causes of the truth value of propositions, but the word "cause" is being used in its conventional sense, as being the reason for the effect (here, "truth value" is the effect)."
You commented: "“True value” is not “normally” spoken of as an effect. Normally, effects are physical or spiritual actions. So to call the relationship causal is to use a special sense for the word cause."
I rebut: The first sentence is trivial. "Truth Value" is simply not often spoken of at all. The second sentence is not true. Effects do not have to be actions, and can be simply states of being. For example, guilty is an effect of the cause of sin, and red-faced is the effect of being caught in the act. Since the third sentence is alleged to follow from the second, and the second is clearly false, the conclusion should be rejected.
Your third argument, as modified, is more interesting, but still incorrect.
You wrote: "My third argument should be modified such that your view leads to the conclusion that no true statements can be made about the future, because the statement cannot correspond to reality.
Even if a statement corresponds to God’s plan for what He wills to happen, that statement is not now true in the sense you are taking about truth. A sense, which seems critical to your critique of WLC, albeit perhaps not critical to your counter claim."
I respond:
Your argument seems to assume that the future is not part of reality. Let me ask, for the sake of clarification, whether you consider the past to be part of reality, and whether a statement now can correspond to the reality of the past.
The fact that the statement corresponds to God's plan for the future is sufficient to make correspond to reality. If you disagree, please explain.
-Turretinfan
Dan:
ReplyDeleteCan you answer the question, "What makes a proposition true or false?"
I submit that if you cannot, you have subscribed to a philosophy that is unable to account for truth.
-Turretinfan
Dear Turretin,
ReplyDeleteTF: You fail to respond to the fact that "logical" is not mutually exclusive of "causal." That failure is critical.
I don’t see how this point is critical. Even if it’s true (and I doubt that it is), that doesn’t show that the connection is causal in this specific case.
TF: Sure, the relationship between "truth" and "correspondence to reality" is definitional (although WLC cannot possibly accept such a definition of truth, so you - as his advocate - cannot really make that your argument), but to correspond is a verb, and consquently provides a mechanism for asserting causation.
Correspond being a verb is not evidence that the relationship between “a proposition’s correspondence to reality” and “that propositions truth value” is causal. Verbs are not always causal. “Is” or “means” would be examples to show that verbs are not always conveying causation.
TF: You requested evidence of the causal link. That's simple. Consider a fallible proposition, such as, "Moscow, Russia contains Europe's biggest hotel." What makes this true is whether it corresponds to reality or not: namely, whether or not there is a bigger hotel in Europe. The cause of the proposition being true, consequently, can be seen to be connected with reality.
This is sufficient evidence that there is a relationship, but not that the relationship is causal. I submit that if the proposition corresponds to reality, it is true. It does not become true.
Here’s my argument.
P1: A propositions correspondence with reality is definitionally related to its truth value.
P2: But definitional relationships cannot be temporally successive.
C1:There is not, and cannot be, a temporal sequence to correspondence and truth value.
P3: But causation requires temporal succession.
C2: Hence the relationship cannot be causal.
TF: You fail to address the fact that: "Furthermore, it may be abnormal to speak about the causes of the truth value of propositions, but the word "cause" is being used in its conventional sense, as being the reason for the effect (here, "truth value" is the effect)."
I did address this point by denying truth value is normally spoken of as an effect, a point which you seem to grant.
TF: Effects do not have to be actions, and can be simply states of being. For example, guilty is an effect of the cause of sin, and red-faced is the effect of being caught in the act.
Becoming guilty is the effect of sin. The change is the effect. Before he was not guilty, now he’s guilty. The transition from not guilty to guilty is an action.
TF: Your argument seems to assume that the future is not part of reality. Let me ask, for the sake of clarification, whether you consider the past to be part of reality, and whether a statement now can correspond to the reality of the past.
The past was and the future will be reality.
TF: The fact that the statement corresponds to God's plan for the future is sufficient to make correspond to reality. If you disagree, please explain.
I agree. But the statement does not correspond with the future, but rather God’s plan. God’s plan is not the future, don’t you agree?
TF: What makes a proposition true or false?
As long as “makes” is not understood in a causative sense, correspondence to what reality is, was, will be, or would be.
If “makes” is understood in a causative sense, nothing.
BTW, I will be lurking in on your exegesis challenge and monergism debate. Nice blog you got going here…
God be with you,
Dan
Dear Dan,
ReplyDeleteThanks for your additional comments.
You disputed the criticality of the lack of mutual exclusisivity between logical and causal relationships, and doubted its truth. I'll provide a simple example to show its truth: a man named Stevenson is logically subsequent to the man named Steven. In other words, as a matter of logical priority, the man named Steven has a first priority, and the man named Stevenson has a lower, derivative priority. Furthermore, it can be (and for most Stevenson's it once was) that Stevenson has the derivative name as a reflection of paternity (which we will all agree is a causal relationship). Therefore, the fact that there is a logical relationship between Steven and Stevenson does not exclude a causal relationship between them, QED.
In this case the lack of mutual exclusivity is critical, because your (and WLC's) argument is irrelevant if there is no mutual exclusivity. Again, perhaps an example will assist. Suppose that I take the position that Stevenson is the descendent of an ancestor named Steven, and you respond that actually the name Stevenson is etymologically derived from the name Steven and the name son. Your comment would be correct, but you would not have rebutted the claim, because there is no mutual exclusivity between the names having an etymological relationship, and the people by those names having a paternal (causal) relationship.
You wrote: "Correspond being a verb is not evidence that the relationship between “a proposition’s correspondence to reality” and “that propositions truth value” is causal. Verbs are not always causal. “Is” or “means” would be examples to show that verbs are not always conveying causation."
I respond:
The fact that verbs do not always express causality only shows that identifying "correspond" as a verb does not prove causality - it does not negate the value of "correspond" being a verb as having evidentiary value. Furthermore, "correspond" does not carry the same sense as "is" and/or "means" and it is the meaning of the words that matters. Thus, appeals to those words cannot rescue the anti-causal position.
You also wrote: "This is sufficient evidence that there is a relationship, but not that the relationship is causal. I submit that if the proposition corresponds to reality, it is true. It does not become true."
In my example, the proposition can become true by Putin building a bigger hotel than the previously largest in Europe. In other words, if reality changes that change in reality causes a change in the "truth value" of the proposition. Surely you can see that.
You argue:
P1: A propositions correspondence with reality is definitionally related to its truth value.
P2: But definitional relationships cannot be temporally successive.
C1:There is not, and cannot be, a temporal sequence to correspondence and truth value.
P3: But causation requires temporal succession.
C2: Hence the relationship cannot be causal.
P3 is wrong. Causation can be (and frequently is) simultaneous. Consider the causal relationship between the force exerted by a keystone and the structual integrity of an arch. That example alone should serve to show that causation can be simultaneous.
Furthermore, P3 seems to have been invented out of thin air and specifically for the purpose of denying causal relationships in the noumenal realm. In other words, P3 is an example of special pleading.
I had written:
You fail to address the fact that: "Furthermore, it may be abnormal to speak about the causes of the truth value of propositions, but the word "cause" is being used in its conventional sense, as being the reason for the effect (here, "truth value" is the effect)."
You responded:
I did address this point by denying truth value is normally spoken of as an effect, a point which you seem to grant.
I answer:
That does not address the point above, because your original claim was that I was using "cause" in an abnormal way, not that I was applying "cause" to a rarely discussed topic. As I previously pointed out, the fact that this topic comes up rarely is a trivial objection that is not even worth mentioning: "Tom, the butcher's son," is also rarely discussed as being either a cause or an effect, but to posit that as an objection to his being treated as a cause or effect in a particular instance is precisely as absurd as your objection.
You wrote: Becoming guilty is the effect of sin. The change is the effect. Before he was not guilty, now he’s guilty. The transition from not guilty to guilty is an action.
I respond: Your position here is both internally inconsistent in a first respect, and wrong in a second respect.
It is internally inconsistent in that there is no temporal sequence between sinning and becoming guilty. There is a logical priority, between the two (and sinning has that logical priority), but there is no temporal sequence. Previously, however, in P3 you denied that causation could exist without temporal sequence between the cause and effect.
Second, you are wrong because the transition between binary states is not an action in the sense you had previously used that term, when denying that correspondence is an action. Nevertheless, as shown in the Moscovite Hotelling example, a change in reality can bring about a corresponding change in the truth value of a proposition.
Finally, of course, although we have considered an example where there is a transition between states, we could take an example where there is no transition between states: for example, God keeps us from falling. Here there is causality, but no action (no transition, change of states, or motion).
Thus, even if you define "action" such that it includes transitions between binary states, there are still examples of causality that do not include such transition.
I asked: Your argument seems to assume that the future is not part of reality. Let me ask, for the sake of clarification, whether you consider the past to be part of reality, and whether a statement now can correspond to the reality of the past.
You responded: The past was and the future will be reality.
I reply: Perhaps it is just me, but it seems like you did not really answer the questions asked. Let me try again:
- Do you consider the past to be part of reality?
- Can a statement now correspond to the reality of the past
I had written: The fact that the statement corresponds to God's plan for the future is sufficient to make correspond to reality. If you disagree, please explain.
You responded: I agree. But the statement does not correspond with the future, but rather God’s plan. God’s plan is not the future, don’t you agree?
I respond:
God's plan includes all of history - and part of history is the future. God's plan is not the occurance of the future event, which is probably what you meant to ask.
Aside: (There is any interesting dilemma posed by your faulty premise P3. If God has always known his plan, and if temporally sequence is required for causality, then God did not cause His own plan! Of course, the problem is that your P3 is wrong: God is the cause of His plan, although there was never a time when God did not have the plan that He has.)
If my agreement as set forth above is sufficient for your purpose, please explain why you asked.
I asked: "What makes a proposition true or false?"
You replied: "As long as “makes” is not understood in a causative sense, correspondence to what reality is, was, will be, or would be. If “makes” is understood in a causative sense, nothing."
I respond: A "not ... causative" sense of make, eh? I guess I should have closed that loophole in my question.
Allow me to restate:
What is the cause for a propisition being either true or false?
Is your answer "nothing" as it would seem to be above?
If so, then I would continue to hold that your philosophy does not account for the existence of true propositions.
-Turretinfan
Incidentally, Dan, feel free to jump into either challenge (the monergism one in a sidebar here, or the exegesis one in a parallel track backchannel).
ReplyDelete-Turretinfan
Dear Dan,
ReplyDeleteAs an additional note, I think you'll find it difficult consistently to defend the truth of "counterfactuals" using a "correspondence to reality" definition of truth.
-Turretinfan