Tom: Props do become true (and false) when the states of affairs they describe obtain or fail to obtain. Do you deny there is true ‘becoming’ in the actual world?

Post Edited (Alan Rhoda) : 3/3/2008 4:54:53 PM (GMT-6)

Post Edited (Alan Rhoda) : 3/3/2008 6:08:42 PM (GMT-6)

Tom: Future-tense propositions are either true or false at all times. That is, they are bivalent. Props do become true (and false) when the states of affairs they describe obtain or fail to obtain.

Chaz: Thomas thank you for setting things straight!

Tom:  I’m at the point now where I’m in the conversation for the entertainment value! I should be over debating eschatology with Bruce and Dwayne, but this is more fun!

Let me posit a future-tense proposition I believe to be true based on present reality:

“Chaz will respond to this thread at least one more time!”

It has a truth value and its value is TRUE!

Dude, come on. Alan explained it and you’re still coming back as if nobody has said a thing.

Bivalence does not mean that all props have one and the same truth value (either true or false) FOR all time. It means that at any given time, all props will have a truth value (either true or false). That is, the same prop may be true at SOME times and false at OTHER times, but at any given time it will have one or either or those truth values; not becoming one or either, but determinately either true or false.

I can’t wait to see what your response will be! ;o)

Tom

I have been lurking on this thread and have read (some) of the Boyd, Rhoda, Belt (BRB) papers whose links were provided and was wondering if I could get a clarification on something.

BRB, in order to not compromise God’s divine omniscience, have turned the focus from whether God has divine omniscience to the content of  divine omniscience.  My guess is they are sensitive to people being alarmed at hearing that God cannot know the future and want to reassure them that God, indeed, has divine omniscience, it’s just that the content of that omniscience is different than traditionally thought. BRB then divide God’s omniscience of the future into two categories:  roughly what God knows will/will not happen and what God knows might/might not happen.

My take is that they view the total content of God’s omniscience as being:

1. God knows all that has happened and could have happened
2. God knows all that will/will not happen
3. God knows all that might/might not happen

Is this a fair assessment of your view? 

If we subtract the future events that God knows will happen and the future events that God knows will not happen, then we're left with the future events that God knows "might and might not" happen.

I'd like to look at the content of "might and might not".

Post Edited (Duigan MacBoyd) : 3/3/2008 9:46:32 PM (GMT-6)

Hi Duigan! Glad you jumped in. Happy to have you.

Duigan: I have been lurking on this thread and have read (some) of the Boyd, Rhoda, Belt (BRB) papers whose links were provided and was wondering if I could get a clarification on something.

Tom: Fire away! By the way, though, it’s RBB (Rhoda, Boyd, Belt). I guess there’s a protocol to that sort of stuff!

Duigan: BRB, in order to not compromise God’s divine omniscience, have turned the focus from whether God has divine omniscience to the content of divine omniscience.

Tom: I’m gonna be a bit anal, OK? Forgive me. But I’ll just jump in along with way with comments if that’s OK.

So to begin with, I wouldn’t say that we focus on the content of God’s knowledge “in order to not compromise omniscience.” In other words, it’s not a tactic, as it were. It’s just working through the definition of ‘all-knowing’.

Duigan: My guess is they are sensitive to people being alarmed at hearing that God cannot know the future and want to reassure them that God, indeed, has divine omniscience…

Tom: That was a bit of a concern I suppose.

Duigan: …it’s just that the content of that omniscience is different than traditionally thought. BRB then divide God’s omniscience of the future into two categories:  roughly what God knows will/will not happen and what God knows might/might not happen.

Tom: Two categories if will/will not are taken together to describe what is causally closed with regard to the future and might/might not taken together to describe what is causally open with regard to the future. But I sometimes prefer to think in terms of three categories: will (causally entailed), will not (causally precluded), and might /might not (causally open).

Duigan: My take is that they view the total content of God’s omniscience as being:

1. God knows all that has happened and could have happened
2. God knows all that will/will not happen
3. God knows all that might/might not happen 

Is this a fair assessment of your view? 

Tom: Yes (if you mean what we mean by those terms).

Duigan: If we subtract the future events that God knows will happen and the future events that God knows will not happen, then we're left with the future events that God knows "might and might not" happen. I'd like to look at the content of "might and might not".

Tom: Lead the way.

Duigan: Now intuitively, "might and might not" does not seem to consist of knowledge or information. If I ask someone, "What is 666 raised to the power 2" and they answer "It might and might not be 42." I would think that they don't really know…

Tom: Several things, if I may:

Might and might not may be conjointly true ONLY as a future-tense propositions positing the indeterminacy of some future state of affairs. Present actualities (like “666 raised to the power of 2” [is that a cryptic reference to Alan and I (2 persons) being evil (666)?] are just that—actualities. So there’s nothing contingent or indeterminate about the outcome is of “666 raised to power of 2.” Thus, to say that it’s outcome “might and might not be 42” can only be an expression of grave ignorance.

But as for the semantic field that covers the range of meanings/uses for might and might not (included our intuitions) these aren’t limited to the example you share. Yes, “might” can and does express merely a state of mind, say doubt, regarding some truth. But it doesn’t always do so. If I say “Chaz will come to the part tonight” (claiming that it’s a done deal), and someone wanted to contradict me, all they need claim is, “No, he might not come” and everybody knows these are contradictory claims. But if “might” and “might not” only posit logical possibility, there’s no contradiction generated by claim that “Chaz might not come tonight,” for it’s being logically possible that he might not come is perfectly compatible with its being absolutely determined that he will come.

So sometimes MIGHT carries only epistemic force (that is, it’s an expression of doubt) and sometimes it carries causal force (as a claim about the objective world).

Same thing for ‘will’. The example Alan used the paper, I think, was a mother’s telling her child not to go outside in the cold without a jacket “or you will catch cold.” Is the mother employing ‘will’ with causal force? Does she mean, “Your catching a cold is causally entailed in your going outside without a jacket”? No. She’s only speaking approximately. It’s probable that you’ll get a cold. Be careful.

So the semantic fields for will/will not, might and might not are diverse in common parlance. But for logic, and especially for constructing a doctrine of omniscience, the knowledge of all truths, knowledge which is co-extensive, co-terminous with reality, we need to narrow the semantic field and focus on truths that capture reality as it is, not loser sort of usages that don’t even intend to aim at strict correspondence to reality.

Duigan: If I toss a fair coin and ask them, "heads or tails" and they answer, "It might and might not be tails." how could they be wrong?

Tom: In the case, since it regards a future contingent, and since the truth is that it might be tails and might not be tails, they’re not wrong. But note, they’re not predicting what it shall be. They’re just stating the truth that the outcome in this case is not entailed in the conditions of the toss, and it would be false to claim that it is so entailed (will, will not).

Duigan: If I toss a fair die and they say, "It might and might not be five." how could they miss?

Tom: There’s nothing to “miss” or “hit” Duigan. They’re not aiming at any particular number. To say truthfully that 5 is one of several numbers that might or might not turn up on the dice is not to predict which number will be. If it comes up five, they didn’t correctly PREDICT 5. Positing future contingents isn’t prediction at all.

Duigan: Let’s say Joe is going into the Sherwin-Williams store to buy paint and the store has 330 colors.   I say, “I have omniscience, I know what color paint Joe will buy.  It might and might not be color number 1, it might and might not be color number 2…. It might and might not be color number i, it might and might not be color number i+1….. it might and might not be color number 330.” This doesn't appear to be knowlege of Joe's future choice, rather simple inventory.

Tom: If Joe’s choice is libertarian and you're omniscient, then it's not the case, as you say, that you “know what color Joe will buy.”

Duigan: Information theory sheds further light on this via it's definition of information as "uncertainty and the resolution of uncertainty", John Pierce, An Introduction to Information Theory.  "Information is always a measure of the decrease of uncertainty at a receiver (or molecular machine)."

Tom: You’ll have to talk to Alan about this. My guess is that in the case of finite knowers such as ourselves, we never REALLY close the gap between knowledge and reality. Propositional knowledge may be fine so far as their language is able to capture and express the realities they describe, but such knowledge in, arguably, not the most perfect sort of knowledge imaginable. Some question whether God’s knowledge is propositional at all. Propositions are linguistic entities. Does God speak a particular language? There may be good reasons to suppose God’s knowledge is a pre-linguistic, non-discursive, direct experiential apprehension of reality. I’m open. Certainly God can abstract out from his direct apprehension of reality to propositions IF he wishes to (in order to communicate to us, for example). But that God essentially conducts his knowing and apprehending of the universe in propositional terms? I doubt it.

I think what we want to include in our description of an ‘omniscienct’ knower are at least the following:

God’s knowledge is:

a)      Exhaustive (in scope; God cannot fail to apprehend reality fully)

b)      Infallible (in operation; God cannot fail to apprehend reality accurately)

c)       Unmediated (in access/apprehension; God cannot depend for his knowledge of reality upon mediaries)

Duigan:  A simple example is a fair coin toss.  The probability of the coin landing heads in 1/2, the probability of it landing tails is 1/2. Using Shannon's formula for information entropy (for this trivial example) yields one bit of information gained once the coin is tossed.  One possibility is ruled out and uncertainty is resolved. But notice, before the coin toss, "might and might not be heads" yields no information, no knowlege because possibilities are not ruled out and information/knowlege is not actualized.

Tom: Again, Alan can elaborate if he wants to. It may be that understanding God’s omniscience in terms of his apprehension of all reality is the better way to go. Propositional knowledge/information is necessarily one step removed from reality itself. I’m open. But I’d object to the idea that once the coin is tossed, one possibility is ruled out and uncertainty resolved. That the probability of heads/tails is 50/50 is something that holds even after the toss is made. The probabilities are objective features of the world—they’re ontologically based.

I’d disagree that knowing that the probabilities of heads/tails is 50/50 doesn’t qualify as knowledge. On the contrary, you just said it: We know that the probabilities of heads turning up on a fair toss of a coin is .50. This qualifies as a proposition in my view. And as far as we understand the world, it’s true. Its’ TRUE that the probabilities are .50. One only needs to disqualify this as ‘knowledge’ IF one supposes there really is some fact of the matter out there, over and against this probability, about WHICH outcome (heads or tails) actually occurs. But that is the point of contention. We’re arguing that indeterminists OUGHT to deny that there is some fact of the matter, some truth, positing the outcome of such events before they occur. Over what slice of reality would this supposed truth supervene prior to the reality of the event’s occurance?

Duigan: Another simple example is a fair die toss, six possibilities each having 1/6 of a chance.  Using the formula for information entropy yields 2.58 bits of information per throw.  Before the die toss, "might and might not...." yields no information because uncertainty has not been reduced.

Tom: But there’s no ‘uncertainty’ regarding the possibilities is there? No. And there’s no uncertainty regarding the probabilities either. Right? That much counts as knowledge. It’s not ‘nothing’ to know this. Now, if this doesn’t tell us which of the possible outcomes of the toss will eventuate, that doesn’t count against knowing all there is to know IF the indeterminacy is an objective feature of the world. I think you’re still thinking that there’s some truth, some fact of the matter out there, that contains or posits the result, the outcome, of the toss. You think that because one of the possible outcomes does actually turn up after the toss is made that certainty about this bit of information has to be antecedently available and knowable. But that’s the point at issue, Duigan. Take indeterminism seriously. That is, grant it ontological status as an objective feature of the world. Then grant that truth supervenes on that world. The conclusion is that it’s the TRUTH about indeterminism about which we must not be uncertain.

So yes, we are ‘uncertain’ about which of the possible outcomes of the toss will turn up. But this uncertainty is not a failure of knowledge. It’s the certain anticipation of the openness of becoming.

Duigan: It appears to me that "God knows all possibilities" has the information content of 0.  It's simple inventory.

Tom: Inventories are void of information? Inventories serve no purpose? Inventories are ‘nothing’? On the contrary, knowing what possible and probable outcomes one faces is extremely useful information.

What's not useful information is eternal knowledge of eternally true propositions positing all the future event of the world. How would you propose God makes providential use of such knowledge?

Duigan: So my question is, how can "might and might not" be regarded as the actualization of knowlege/information when there is no reduction of uncertainty before the event happens?

Tom: It’s knowledge because that’s the reality, the fact of the matter, which we call ‘indeterminism’ (as an objective feature of the world). It has ontological status, not MERELY epistemic status. And there is no reality, and so no fact of the matter, about which of the possible outcomes shall in fact actualize. To not know the latter is no more a failure of knowledge than is not knowing that Hobbits are real creatures.

Blessings,

Tom

Post Edited (HumanHypostasis) : 3/4/2008 4:40:18 AM (GMT-6)

Tom: Posit away. Anyone can posit propositions. Only God will immediately know their truth value. We can posit, but we won’t necessarily know if they’re true or false. God does. Take the proposition: <An American solider named John, from Missouri, age 23, might and might not die tomorrow in Iraq>. There, I just posited a M/MN prop. Do you or I really know if it’s true? No, we don’t. I don’t know that we even COULD know this. There might not BE any soldiers in Iraq from Missouri today named John age 23, in which case <It is not the case that an American solider named John, from Missouri, might and might not die tomorrow in Iraq>. It would then be true that…

Duigan: And the immedidate truth value would be "might and might not"?

Tom: “Might and might not” can’t be a truth value at all. Bivalence provides two truth values: ‘true’ and ‘false’. Those are our truth values. “Might and might not,” like “will” and “will not,” is a future-tense operator and so part of the proposition it helps form.

I left “It would then be true that” hanging there. Sorry. Was gonna write more.

So I’ll finish. On our (Peircean) bivalent semantic: If <An American solider named John, from Missouri, age 23, MIGHT AND MIGHT NOT die tomorrow in Iraq> is FALSE, then one of two propositions is true: Either <An American soldier named John from Missouri, age 23, WILL die tomorrow in Iraq> or <An American soldier named John from Missouri, age 23, WILL NOT die tomorrow in Iraq>.

Duigan: I could add "There might and might not be an American soldier named John, from Missouri, age 23" to "and he might and might not die tomorrow in Iraq". Hedging my bets.

Tom: OK, you’ve offered me a compound sentence (note the “and”). Notice now (this is important). Look at your first clause:

<There might and might not be an American solider named John, from Missouri, age 23 [in Iraq]…>. What’s this describing? The present or the future? It’s describing the present. And in this case, Duigan, we’re not talking about future contingents at all. Because the present is ‘actual’ and determinate, it is now either the case that there is an American soldier named John (etc.) serving in Iraq or not. Nothing difficult about this. God knows if there is such a solider serving presently in Iraq, right?

Your second clause then makes a claim about the future. And we’ve already talked about this. It the first clause is false (if there’s no such solider in Iraq) then obviously the second if false (and WILL NOT expresses the true prop).

But if by your first M/MN you mean to express some doubt about what the case is regarding such a soldier, that is, you don’t know whether there’s such a solider in Iraq or not so you hedge your bets and just say, “Hey, it might be that there’s such a solider in Iraq and it might not be the case that there’s such a soldier in Iraq.” That amounts to admission of ignorance. You don’t’ know what the present state of reality is. But God does.

Duigan: Sorry, didn't mean to wind you up. Some scientists have tried to quantify information content and when applied to "might and might not", that construct appears to come up empty.

Tom: Thanks Duigan. Not wound up, just a bit surprised sometimes. Never mind me!

Tom

Duigan: Let's say that someone asks, does God know the outcomes of all future coin tosses? The answer is, yes, because God knows that coins have two sides. Is that correct?

Tom: No, not in my view. God doesn’t now know the outcomes of all future coin tosses.

Just to be clear…by “outcomes” you mean the event of the coin’s landing either heads or tails, right? That’s how I’m taking you. To say God knows the actual ‘outcomes’ of all future coin tosses is to say God knows which tosses will land heads and which will land tails. And this, in our view, is false. God doesn’t now know these outcomes.

Duigan: In knowing that coins have two sides, God knows that in all future coin tosses, one side might and might not land up and the other side might not and might land up.

Tom: But this is not knowing the “outcome” of each toss, that is, for ever toss, knowing which will land heads and which will land tails. Knowing that each coin has two sides, God knows that every future coin toss M/MN land heads (or tails). WHICH side it lands on, that is, the event of its landing on one particular side, is not known. It’s not known because there is no reality for truth to supervene upon in grounding the truth for either WILL or WILL NOT. Thus any claim about a fair toss that it WILL or WILL NOT land heads or tails is false.

Duigan: Hence, regarding all future coin tosses, God preserves His "omniscience" due to His knowing the nature of coins. Unlike.........?

Tom: I hope you see this is not what we’re saying. (A) God doesn’t preserve his omniscience due to the nature of anything outside himself. (B) The truth regarding any future coin toss is grounded in the reality, the very ontology if you will, of coin tosses, which are indeterministic occurrences. Thus we feel the best way to express the truth that some future event is indeterminate or causally contingent is to simply SAY SO. And I know of no way in English to get that point across better than with “might and might not.”

Thanks,

Tom

Chaz: Well Tom you gave me the go-ahead... this has been nothing but entertainment to watch you twist your logic like a pretzel and I have held back with the LOL statements out of courtesy.

Tom: Bring it on baby! Let go the raging torrent!   

--------------------

Tom: So far so good. Future-tense propositions are either true or false at all times. That is, they are bivalent. Props do become true (and false) when the states of affairs they describe obtain or fail to obtain. Do you deny there is true ‘becoming’ in the actual world?

Chaz: If this doesn't violate the law of the excluded middle (further define it as bivalence also if you wish) I don't know what does.

Tom: Bivalence and EM are distinct claims or rules; not the same thing. I believe in both. I’m not sure you understand either.

But both Alan and I addressed your misunderstanding of <Future-tense propositions are either true or false at all times>. This has been dealt with and you must be choosing to ignore it. I did not mean that such propositions hold one and the same truth value at all times. That’s no denial of bivalence, and if one thinks it is, she doesn’t understand bivalence (whatever her credentials).

Gotta hit us with something harder! Come on. Bring out the heavy artillery!

Chaz: Essentially you are saying is that a future contingent is possibly true and possibly false but does not have a truth value today…

Tom: I’m going to charge you with a willful misdemeanor and have the administrator ticket you if you keep saying this! Come on. It’s not true. And I’m on record as having demonstrated so. You can’t produce a single proposition about which my view obliges me to deny that it has a truth value. All propositions about future contingents have one of two truth values, either true or false.

Let it go.

Chaz: …a more appropriate way of disambiguating your logic would be to say that future contingents are neither true nor false today.

Tom: Zzzzzzzzz.

--------------------------

Tom: Similarly, the prop “Tom is 48 years old” is true at some times and false at others. When I was 47 it was false. When I became 48 the prop became true. How long did the prop take to BECOME true? As long as it took me to BECOME 48; instantaneously I imagine. How long will it take the prop to become false? As long as it takes me to stop being 48 and become 49. That’s the point: TRUTH FOLLOWS REALITY.

Chaz: Here is an example of your combining multiple propositions into one; and then having to assign alternating truth values to this one “proposition” like a traffic cop LOL.

Tom: Ooo, Chaz. Ouch. That “LOL” there cut deep Bro. I'm drowining!    

Chaz: You state that necessary propositions and truth is eternal…

Tom: I’d never use “is” following a combination of nouns. I’d say “are.” And I don’t think I’d say “necessary propositions” either. I’d say “necessarily true” (or false) props, or I’d say “necessary truths.”

But yes, whatever is necessarily true is obviously eternally true.

Don’t tell me you doubt THIS!

Chaz: …because it has eternally exisited in the mind of God; but contingent truth is temporal and these true propositions and corresponding truth have not eternally existed in the mind of God - consistancy man.

Tom: I’m not sure I even follow you Chaz. A bit contorted, like one of my pretzels!

Necessary truths are necessarily (and so eternally) true. The ground of their truth value is the existence and nature of God.

Clear?

Tom