Dr Greg Bahnsen - Philosophy of Christianity: God and Time: Indexical Reference Part 2 (Part 14)

I got to thinking about our discussion of indexical reference. And I'm afraid that the way we were approaching the subject, although those of you who have done the reading may very well have been keeping up with it, was not the most perspicuous, which is to say not the clearest way to approach it. And so I devised another attack on the subject. And it won't conflict with what I told you before, but if you want to disregard what we've said thus far, it will not hurt you either. I'm going to try to start again and make it a little bit simpler for you. I think perhaps in part of my explanation I was assuming too much. But before I do that all over again, at the very end of the hour, Dr. Kikasola asked a question which you may recall. I said something to the effect, I know there's a compression in this. And it dawned on me finally when I, you know, got my thoughts together on the flight home, just exactly what the problem was. We were talking about the transitive doctrine of knowledge, that if S knows that P knows that P, that necessarily S knows that P, okay? So that if Kikasola knows that Bronson knows that 2 plus 3 is 5, then necessarily Kickasola knows that 2 plus 3 is 5. But now Dr. Kicasola suggested if S knows that P knows the answer, then it would appear that S knows the answer. And probably I misled you because when I wrote on the board, my guess is I did not repeat this, that. And that's what I figured out on the way home, I said, there's something wrong with that illustration for very good reasons. In epistemology, the verb knows, and if you will, the pseudo verb knows that are different verbs, okay? Knows is open ended in a way that knows that is not knows, that must always be followed by a proposition, whereas knows can be followed by objects which are not propositions. And so when Dr. Kikasola said s knows that P knows the answer, you notice that the word that is missing. And here you have an object that is not a proposition, okay? And that is a compression for a proposition that the Math answer is 5 or something like that, okay? So if you were following that at the very end of the hour, and if you weren't, I'd understand why. But if you were, that is the difficulty, okay, let's try to come to grips with this indexical reference difficulty and the omniscience of God again, especially since you're going to do a little bit of writing on that for me, I think isn't that one of your questions? No, no. So I can keep it in my mind. Where are you going to? Wait, that is one of your questions on the exam, isn't it? Oh, oh, I thought it was burning within me. No, it wasn't. Okay. Now, the question that you have rather than the one I gave you, I've been thinking about where we've been going in the class, and I think it'll help me sometimes to know where we're going to end up.

It's in the syllabus.

Well, maybe. Maybe that's all I need to know. But in the discussion each day, somehow, if I know where I'm headed and can somehow maybe see more just in a sentence or two, is that possible? Oh, sure, no problem at all. The first week of class, of course, we are doing orientation to the whole subject matter. Now, what I am attempting to do as we go through each one of the topics is to. Is to resolve the difficulty that is being raised in the reading in a presuppositional fashion. Okay? So that's the broadest way I can answer your question. Now, in particular, when we're talking about the existence of God, the goal was to see the internal philosophical problems of the traditional formulation and then to find a reformulation that would suit the thrust of each of the arguments and be true to Scripture. Okay. When we talked about language about God, we were trying to show. We were trying to, in a straightforward apologetical way, defend the meaningfulness of religious claims even though we treat them as unfalsifiable, as well as the meaningfulness of making attributions to God using human language. Okay. By means of analogy. Okay. Now, as we're talking about the attributes of God, we're trying to defend the traditional Christian dogmas about the character of God against certain philosophical paradoxes or counter instances that have been raised against the truth of such claims as God is omnipotent or God is omniscient. Now, with respect to God is omnipotent, if God is omnipotent, then that would suggest that he can do things which he cannot do. For instance, to make a stone so heavy that he can't lift it. And so how do we deal with that difficulty? And I suggest that at the end of our discussion, remember that little pastoral P.S. at the end, that if you've never worried about this before and you're wondering why people are getting so upset about this paradox, it's because you recognize probably as a biblical and evangelical Christian, that explicating the doctrine of omnipotence is not a matter of exploration. How the phrase God can do anything is true. It's a matter of explaining how the phrase God can do anything matches the biblical evidence. That is, it's simply a question of explaining what we mean by the almightiness of God. And so here's how we get around these paradoxes. Now we're into something else. That brings us to last hour's class, which is going to be this hour's class as well. The objection is that if, if God knows everything, then he cannot know what time it is. That would seem to be a significant paradox to resolve that if God knows everything, that he can't know what time it is. That is, the omniscience of God cannot be squared with the immutability of God, because if God is unchanging, he cannot know now that it is whatever 130. And he cannot know five minutes from now that it's 1:35, because that would indicate a change in God. Okay, so now what do you want to give up? We'll put it that way. Would you rather have an omniscient God who is mutable, or would you rather have an immutable God who is not omniscient? Okay, now that philosophical challenge is very seriously taken, you know, in Kretzmann's article, I mean, he's dead serious. This, this is not just playing games. It says the traditional Christian coalition of attributes in God is incoherent. You can't have both at the same time. And so unless you're willing to choose one or the other, then we've got to spend some time finding a way to say that it is not incoherent to hold that God is both omniscient and immutable. And that's what the goal of this hour is going to be. And if we have time, I'm going to start talking about predestination or foreknowledge, as well as human freedom, which probably doesn't need as much of an introduction to you, because that's a hotly disputed issue in evangelical theology and has been for years. So we're going to try to take a philosophical approach to it and see if we can do anything. You can take an exegetical approach to that question, too. But in this class, we're taking philosophical issues and trying to relate them to our Christian theology. And so we'll try to resolve that philosophically. And I might say just in advance that I think there's good reason to do that, for my own conviction is that most people who attempt to resolve the problem exegetically have to have some philosophical conception of what problem it is that they're resolving exegetically. And that philosophical preconception is going to affect their exegesis, and for my own money, usually infectious, their exegesis. Okay, but let's go back to omniscience and immutability. Is that getting at the sort of thing you wanted by way of introduction? Didn't have to be that lengthy. All I was thinking of mostly was a brief outline of today, what we were going to deal with. Sure. Okay. Well, if that does it, then we'll get on to it.

We're at the end of unit four, in other words, on God's attributes, and we're dealing with an objection to omniscience.

Okay, here we have the claim that no person can know a statement. That contains an indexical reference by another person. Now, as I understand it, that summarizes very well the thrust of Kretzmann's argument that no person can know a statement that contains an indexical reference by another person. Of course, you have to know in an indexical references, and I trust we don't have to go over that, Graham. That should have been fairly clear. A statement containing words like I. Now, that here, anything that indexes the person, place, thing, time that you're dealing with would be an indexical reference. The claim is that no person can know a statement containing an indexical reference by another person. So that if I say it is now 1/3 30, that is my indexical reference statement, and nobody else can know that statement. No other person can know that statement as I've made it with that indexical reference. Now, if that's true, then a person's indexical statements cannot be known by another. Okay, I'm restating what's up here in the board so you don't get confused. A person's indexical statements. I'm using that as short for a statement containing an indexical reference. Okay, A statement containing an indexical reference. I will call from time to time simply an indexical statement. No person can know another person's indexical statements. Now, if no person can know another person's indexical statements, then let's say this person here is God. That means God cannot know any other person's indexical statements. That is to say, he can't know my indexical statements. And so if I have an indexical statement that's true, then I know something that God doesn't know. That in the simplest outline is the Argument of Kretzmann. I'm going to give it to you in detail in just a minute, but do you understand, basically, we're going to be running now with the wall. Which direction? If I can show you that no person can know an indexical statement by another person, then I showed you that God can't know everything I know because he can't know my indexical statements, my true ones. So far, so good. You may be waiting for some flesh to be put on those bones, but, I mean, you understand what the structure of the argument is now. Okay, let's see if we can find a way of putting the argument. Okay, S knows. It is now T1 and not T2. Okay, that is going to be one statement. A second one will be s knows quote, it is now T2 and not T1. Okay. Now, these statements within quotations, I'm putting them in quotations so you can keep track of just exactly what we're dealing with. These statements in quotations are not identical, obviously. It is now T1 and not T2. It is now T2 and not T1 cannot in any sense be considered the same statement. Now, can both of these be known? Now, I'm not talking about can both of all of these things, but simply the part in quotations. Can these two quoted propositions both be known at T1? Kretzmann says these cannot, cannot both be known at T1. They cannot both be known at T1. Does that have any prime offensive plausibility to you, that these cannot both be known at T1? Well, sure. It doesn't seem likely that I could know it is now 1 o' clock and not 1:30, and also know that it is now 1:30 and not 1 o'. Clock. Can't know both of those at the same time. I mean, it's so. It's seems on the surface of things. Go ahead. Yeah, that's on the surface only. Oh, yeah. We're going to argue against him in just a minute. But is that what you were going to get to. Because if you are, I'd like you to hold it just so I can kind of get the whole thing out. Well, I don't know about this conception of time. You've read Penny's article, I trust, on Answering Aquinas Approach to Foreknowledge and Human Freedom and all that. Okay. As long as you know some of the problems there. We'll come back to it in a little while. Okay. If these cannot both be known at T1, or so it seems, then Kretzmann's conclusion is going to be that a person can know both of these things, that S can know both of these things only by changing. Okay, If S cannot know both at T1, then he's got to know one at T1 and two at T2. That is, he must know proposition one at T1, proposition two at T2. I'm going to repeat, if he cannot know both of them at the same time, namely the former time T1, then he can only know both of these by first knowing one and then the other, and that means there's a change. And. And if there's any change going on, then he's not immutable. Okay, Now I'm going to argue that this is in fact wrong. We're going to take this step by step and piece by piece. So it seems you cannot know both of these@t1. But there's some difficulty in all of this. And what Castaneda is pointing out in his article is that this one now is the speaker's indexical. And as the speaker is indexical, it can only be truly used at T1 and at T2 when we're dealing with proposition one and proposition two respectively. That is the speaker. I'm the speaker. Now let's pretend when I say S knows that it is now T1 and not T2, that can only be true at T1. I can only say kick a soul and notice it's 130 that it is now 130. When it is 130, it's only at T1 that I can say truly as a speaker that somebody else knows that it is now such and such. What is the importance of pointing out that this is the speaker's indexical? Because the use of the word now is qualified by the speaker, that is, it's attached to the speaker's use. However, the person who is being spoken about may refer to the same object of knowledge non indexing. That is, I use the word now to say Kikasola knows it is now 130. However, it's very possible that Kickasola could refer to the same object of knowledge without using the word now. He could just say it is 130. I know it is 130. Okay? The person spoken about may refer to the same object non indexically. Okay? Consequently, Krutzman has not shown about these two statements that they imply that S himself refers to T2 indexically. And so if the two known propositions can contain no indexicals, if it's possible to put the propositions that are known to non indexically, then it's at least possible that they can both be known at T1. We're not arguing that they are known non indexically or that they are referred to. The argument is that it's at least possible to refer to these objects of knowledge, these two quoted propositions, without the use of the word now, that the knowing subject may refer to the object of his knowledge without the use of the word now. And if that's possible, then it's also possible that he knows both of these objects of knowledge at T1. It cannot be true from the standpoint of me as a speaker that S knows it is now T1 and not T2 and S knows it is now T2 and not T1 at T1. From the standpoint of the speaker, I cannot say these things and have them both be true. But the person who knows may very well know at T1 both the objects of knowledge. Now again, before you get worried about, well, I can't figure out how he could know at 1:30 that it's 2 o'. Clock. Don't worry about that. Right now the question is whether logically and semantically we have to use the word now. And what is the effect of saying we don't have to use the word now if we're the person knowing? Well, the effect is that it's at least conceivable that the person can know both at the same time, and we won't get into the logistics of how it might happen, but it's just logically possible. And now the analogy Castaneda uses is, Okay, S knows. I don't want to. The one about the poundage. S knows that so and so weighs so many pounds. Right.

While you're looking for that, may I have a clarification?

Sure.

Clarification.

Did you say that we use we.

Can use now nondexically or that we omit the word?

We omit it. We omit it.

You're not implying that we could somehow use now nondex. That would be equivocation.

Oh, sure it be.

Would.

Now is an indexical reference word if anything is. And consequently, whenever it's used, it's used indexically. What Castaneda is saying is that the person who knows these things doesn't have to use the word now. He doesn't have to make indexical reference to the object of his knowledge, but we would. Okay. His example is Privatus believes that I weigh 150 pounds. Page 379 toward the bottom. Privatus believes that I weigh 150 pounds. Now, in saying this, I do not imply that Privatus has made an indexical reference to me. That's obvious, isn't it? Okay, I speak of the knowledge that Privatus has, and I say of him that he knows that I, the word I is an indexical referent, that I weigh 150 pounds. I have to speak of the object of privilege, Privatus knowledge by using an indexical reference. Does he have to use an indexical reference to speak of the object of his knowledge? No. Privatus simply says Kikasola weighs 150 pounds or Bonson weighs 150 pounds. If I speak of the knowledge that Privatus has of my weight, I use an indexical reference indicate me. But he speaks of what he knows without an indexical reference. And so there's a significant difference between the speaker's perspective in using s knows whatever and the person himself who knows it. I have to refer to what he knows in terms of indexical referencing, But S wouldn't have to refer to what he knows in terms of indexical referencing. Okay? And so the upshot of it all is that it is not true that S could not both that S could not know both these propositions at the same time. He might very well know both at the same time. The indexical reference is not a problem here. Now, Castaneda says what we have to do is try to reconstruct the argument that Kretzmann has formulated that gets around this indexical reference slippage. Okay? From the speaker's perspective, you have to use the indexical reference, but from the knower's perspective, you do not. And consequently there's. There's no problem. And so what we're going to do is reformulate the argument of Kretzma and strengthen it by using quasi indicators. Now, okay, we're going to change indexer reference to quasi indexical reference, or what is called a quasi indicator. And he defines a quasi indicator for you on page 380, about three quarters of the way down the page, in case you've forgotten. Okay? So let's make an attempt to formulate the argument using a quasi indicator. And this is what at T1, S knows it is then T1 and not T2. At T2, S knows that it is then T2 and not T1. Okay? Now, what we have changed, as you can tell, is now has been replaced with then with all appropriate syntactical shuffling taken factored in here at T1, S knows it is then T1, not T2. At T2 S knows that it is then T2, not T1. Now this word then being used does not express indexical reference by the speaker. That is not an indexical reference, but rather attributes an indexical reference to the speaker. Okay, it's very important that you catch that this does not express an indexical reference. The word now expresses indexical referencing, doesn't it? I mean, it's picking out something. But the word then used here attributes to the speaker himself an indexical reference. Or if it's true that at T1s knows that it is, then T1, then he would express his knowledge as it is now T1. So this is attributing to the speaker the use of an indexical reference. And so as. Let me correct that sentence just so you know, get this left. It attributes to the knower the use of an indexical reference. It's it attributes to the knower use of an indexical reference. And with respect to the speaker, now the speaker is the one who states all of this. Okay, again, I'm the speaker here. S is somebody else, usually Kickasola, for our class purposes. Okay, if I'm saying that at T1, Kikasola knows, it is then T1 that I am attributing to kick the soul of the use of an indexical reference. But I'm not expressing an indexical reference myself. The speaker is not expressing one. The speaker is attributing to the knower an indexical reference. If that's too fast, we can go over it again. It's not complicated. There's nothing here that you won't be able to follow. It's just that because the sentences are long, you may get lost. Okay, speaker, that's the person saying everything that you find up here on the board. The knower is the one referred to S or Kickasola. For the sake of clarifying this at T1, okay, now I'm the speaker and what I speak is the following statement. At T1 Kikasola knows it is then T1. I do not express any indexical reference in that statement. The word then is not an indexical reference. It's a quasi indicator. However, it does attribute to Kickasola the use of an indexical reference. Because if he's going to express what I have expressed, he'll say it is. Now, T1 is the word then used in this place as a time reference or as a logical kind of thing. As a time reference. As a time reference. Right. You're going to get lost if you the word, then like the word game and any number of other words in English language has many functions. And we're now talking about the temporal and dexican and dexicoling function of it. Yeah. What is it then? The speaker knows. Speaker knows that it is now T1 in comparison to what the knower knows. What does the speaker know? What does the speaker know in relationship to what the knower knows? Is it the same knowledge? We have the same object of knowledge. It's the way it's being expressed. I have to express the objects of Kickasola's knowledge in terms of the quasi indicator, then Kickasola would necessarily express his knowledge in terms of the indexical reference. Now, are you saying that is known as the same? Yeah, the object is the same. What is how that object is expressed is different. See, that's why. That's why this reformulation of the argument is supposed to be getting at what Kretzwan should have been saying all along. He's still trying to formulate that argument that these two can't be known at the same time. Okay, it's just that we have to get it right by using the word now in his argument. Pretzmann gave us a way out of the problem because it's a feature of indexical reference that the speaker may use it even though the knower doesn't. We're reviewing what we've gone over, so nobody get lost. Okay, we've already said that when the word now is used, it may be true that the speaker has to use the word now, but the knower in mind here wouldn't have to. Okay, let's see if we can go on with this and make the argument float this time. We're speaking for Kretzmann now. We're still trying to reconstruct his argument. Okay, now the important thing is that the word then may be used repeatedly at any time by anybody to make the same statement. The word then as any quasi indicator. The word then can be used repeatedly at any time by anybody to make the same statement. By way of contrast, the word now doesn't have that feature. Only the speaker could use the word now. If he uses the word now and the knower use the word now, they're making different statements, but the word then doesn't have that feature. It can be used repeatedly to make the same statement. Okay, that shows why we don't have the same out as we did a minute ago or a few minutes ago. We can't escape the difficulty by saying, well, there's a difference between speaker and knower's perspective in the use of the word now. But there is no difference between the speaker and the knower's perspective using the word then. So it turns out that both of these. Statements here are the objects of knowledge here. That it is then T1, that is then T2, that both cannot be known at T1. Okay, using the same device here, both cannot be known at T1. Now, if both cannot be known at T1, then if God knows both, he only knows them at different times. He knows one at T1, namely this one. At T1, he knows that it is then T1, and at T2, he knows that it is then t2. But since they both cannot be known at T1, God could only know both of them by changing. There must be a difference in God at T1 and God at T2 so far. Are you hanging in there? Let me simplify the whole thing now. I'm going to step back and I'm going to recapitulate. Kretzmann says it is now T1, and another statement, it is now T2. Cannot both be known at T1. Seems reasonable. However, it turns out there's some slippage in his argument because the word now expresses the reference of the speaker and not the person who knows these propositions. That being true, it's at least conceivable that the knower knows both of those propositions without the use of the word now. Okay? And so if he can know both of these at T1, there's not necessarily a change in the knower in the fact that he knows them both. So now we've reformulated it. Now we're using the quad quasi indicator, then, and we're saying at T1, God knows it is then T1, and at T2, God knows that it is then T2. Those can't both be true at T1, God can't know it is then T1, and it is then T2 at T1. That's the same problem on the surface as we were having previously, but we've changed the vocabulary to make it a little bit tougher to get around the problem. And now how does Castaneda get around the problem? This is where he introduces his principle P. Okay, principle P. And you say, where does principle P come from? Well, it comes from long years of experience in modal logic and epistemology and just knowing that this is the. The right thing to introduce at this moment. He does not tell you where it comes from. He says it seems trivial. It seems Irrelevant. But notice what happens when we start using this trivial and irrelevant principle on the problem that's before us. Okay, let's talk about that principle for just a minute. The principle is that transitive principle of knowledge that we have looked at already, that if S knows that Y knows. Well, let me see. If S knows. Let me change this. That R knows that P, then it is the case that S knows that P. Okay, let me give you the same illustration we had earlier. If Kickasola knows that Bonson knows that 2 plus 3 is 5, then Kikasola knows that 2 plus 3 is 5. If he knows that I know that such and such, and that is to imply. It isn't to capture everything that we're saying, but it does imply that he knows that such and such also. Now, that is a rather indisputable principle here. You may be a little misled by the fact that Castornita says, well, now look, there is kind of exception to the rule. And he gives an example that doesn't fit this. And what he does after that is he goes on to show that what we're talking about here has nothing to do with the exceptional case. So having said that it has nothing to do with the exceptional case, then we're just going to accept his principle and go on. In looking at that again, I got to thinking. Somebody who is not trying to be as thorough as Castaneda will try to find more significance in that little paragraph than he was given. All he was saying is we usually accept that, okay, there's an exception. However, the exception is irrelevant to what we're talking about. It's not that sort of thing that constitutes an exception. That's not found in this illustration. So now back to the principle. S knows that R knows that P means that S knows that P. So let us assume there's something that needs to stay up on the board. Anybody know? No. Absence data now says we can formulate a new pair of propositions. He wants to say at T1. Now he's going to have both of these propositions at t1.s knows first of all that it is then t1. And he knows. Secondly, okay, S knows this and he knows this. S knows that it is, then T1 and S knows that somebody. That somebody would know. At T2 that it is, then T2, and I mean, there's hardly any objection to that suggestion that God knows. Let's say it's 2 o', clock, at 2 o', clock, God knows that it is, then 2 o' clock and at 2 o' clock. God knows that somebody would know at 2:30 that it is then 2:30. Now there's no difficulty in that and there's certainly doesn't seem to be any reason to object that at 2:00 clock God knows that somebody at 2:30 will know that it's 2:30. Let's now use our principle P, the unobjectionable principle that seemed trivial and irrelevant a minute ago. Let's now bring it to bear on this. What can we imply from the second thing that S knows or that God knows? Well, God knows that somebody would know if he that it is then T2, then by transition God knows that it is T2 that it is then T2. Okay, following that, there we have the S knows, okay, that R knows that R this somebody is R. S knows that R knows. The grammar has changed. Just so you can follow that's a tense verb. And so in logic you have to do this. There's nothing improper in changing knows to would know. Okay, S knows that r knows at t2 then it is then t2. We can then say that s knows that at t2 it is then t2. Okay, so this number two here implies that. S knows at T2 that it is then T2. Does anybody have any trouble seeing how we got from number two here by means of principal P to this implication? I'm not suggesting you should. It's not really difficult. But if I lost you somewhere, I want to go over it again because we're not going to get to the end of this if we lose each other. Go ahead. Should that be at T1 that is. That's the genius of it. Exactly. Exactly. Right. At T1s knows two things and it turns out that the second thing he knows implies still at T1 that at T2 it is then T2. That apparently trivial principle of the transition of knowledge from S knowing that somebody knows something to the fact that he knows it indicates that at one and the same time God can know both the principles propositions. It is then T1 and it is then T2. At T1 it is then T1. At T2 it is then T2 and he can know those at T1. Alright, if God knows both of those things at T1, then there is no change in God when we get to T2 because he already knew at T1 that at T2 it would then be T2. I would never come into class and say that to you as an opening remark, but now that we've gone through all this, it's just Perfectly logical, isn't it? Well, maybe not perfectly, but it's beginning to come up, I guess. Do you understand it? Okay. What Castaneda has done is he's pulled the rug completely out from under Kreutzmann. By distinguishing an indexical reference and a quasi indicator with respect to indexical reference, he shows that the speaker's perspective and the knower's perspective may be different. Privatus knows that I weigh 150 pounds. He has to say that. The speaker has to say, I. Privatus knows that I weigh 150 pounds. But the word I doesn't appear in privatus remark. He doesn't say I know I weigh 150 pounds. That'd be false. What he says is I know you weigh 150 pounds. Consequently, the difference between the speaker and the knower gives us a way out of the first formulation of the problem. Then, with respect to quasi indicators, we reformulate the problem and then introduce this principle. P and lo and behold, we can at t1 say that God knows both of the statements again. Now, if God knows both at the same time and at the former time, then when the latter time rolls around, God's knowledge hasn't changed because he already knew that at T2 it was then going to be T2. Okay, I don't want you to lose. I don't want to lose you in what I'm doing. I'm going to now summarize this whole debate, okay, Very simply, you see, in a drop this very quick way of putting the whole thing. We began by claiming this is the claim of the critic. No person can know a statement that contains an indexical reference by another person. Which is to say a person's indexical statements cannot be known by another person. Why does he bother to say that? If a person's indexical statements can't be known by any other person, they can't by be known by the other person, God. And if God can't know my indexical statements, he can't know everything, so he can't be omniscient. The answer to that, the answer to that general claim. I'm summarizing all the internal work we've been doing now, the overall way we've been answering that is to say, well, as a matter of fact, we can formulate another person's indexical statements qua indexical. That is, we can capture the indexical reference of another person intact. We can keep the indexical quality of the other person's statement. We can formulate that person's statement and capture the indexical quality of it. How? By using quasi indicators. Changing now to. Then reformulating the sentence a little bit, and you get the same effect. And how do we do that? By using indexical. I'm sorry. By using quasi indicators and the principle P, which is the transitive principle of knowledge. Okay, one more time over this. The critic says a person's indexical statements cannot be known by another person. So? So God can't know everything. Namely he can't know my indexical statements. That it is now 2 o'. Clock. We answer that by saying, as a matter of fact, we can capture the indexical reference of another person's statement intact. And we can do it by using quasi indicators and the transitive principle of knowledge.

What did you call that principle of knowledge just now?

Transitive principle of knowledge.

You don't mean that in the grammatical sense. Transitive in the grammatical sense?

Well, it functions transitively as in, no, I hit the ball.

Transitive.

I hit the ball. It's transitive in the sense that the object of R's knowledge is also known by S. If S knows that R has that object of knowledge, it's transitive in just this simple sense. If S knows that R knows that P, then we by transition S knows that P. The object is the same.

Of each transitive verb. In this case, knows X, knows X.

Okay, now that's the toughest part of the article. What Castanedis pointed out is that there is no change in God's knowledge because at T1 God knows that it is then T1, and He also knows that at T2 it is then T2. So God knows without changing all, somebody would know at 2:30 that it's 230. Now, you may challenge that I could really know that. I mean, the world may come to an end before 2:30. Okay, but assuming that it's true that I could know that somebody at 2:30 would know that it's then 2:30, then we could say the same thing for me too. That's right. We have an assurance of God's knowing that somebody would know the time of day at that time of day in a way that we don't have ours. But to the degree that we can have that assurance, we can say it of ourselves too. But you see, if it's an easy feat for you and I to know that at T2 is then T2, then it's no difficulty for God. And if he's omniscient, then he knows what time of day it is. You see, the Strength of this polemic is just, you know, that is almost a proverbial expression. You know, somebody who knows anything knows the time of day. If God doesn't know the time of day, can he be said to know everything? And Kretzwein was showing God can't know the time of day. If you say he's unchanging and if he can't know the time of day, he can't be omniscient. But Kasumnieris pointed out that as complicated as it is with these indexical references and quasi indicators, you can get around that. Objection. And as you're pointing out, we can get around it for us too. And I think that matches, if you will, the emotional thrust of the critical God can't even know the time of day. On your theology, we'll say, wait a minute, given the problem you're raising, anybody can know the time of day before it's that time of day. Just look what we did here. So, I mean, what we're saying is, I mean, this kind of absurdity you're bringing up, I can point out, is as easily matched as the statement of the problem. Therefore, knowing the time of day does not imply a change of knowledge. That's right.

Okay.

It probably does for us. I know right now that it's 2:10 or 2:11 and in four minutes I'll know that it's 2:15. And so there'll be a change of my knowledge in that sense. But it's also true that at 2:15, Lord willing, we're still here, somebody will know it, that it's then 2:15. And so I know at 2:11 that at 2:15 somebody will know that at 2:15 it will then be 2:15. It all becomes very elementary, my dear Watson. You see, after you get these, you ring in these quasi indicators Kretzmann has just been dissolved. I mean, there's just no problem left, it seems. It always says that we know how to tell time, so does God. There's no problem in what you're saying. But that you said all that we're saying is this. And I'm not sure that captures the whole thing. That may be a little too quick, at least on your exam. Go through a little bit of this for me, okay? Yeah. Is there any reason that T2 could not be a time prior to T1 instead of in the future? Yeah, because you don't have the same difficulty in knowing past events. It's God knowing the future when the future is going to indicate a change of time. Now, I Don't want to preclude the possibility you could reformulate the problem that God couldn't have known, you know, in 1812 that it was 1820 in the same way that he knows in 1980 that it's 1980. But that really would be a changing of the whole logical mechanism and the thrust of the argument. In 1980. I know that in 1812 it was 1812, and I also know in 1980 that it's 1980. You see, that doesn't seem to imply, even on the surface of it, any change. Whereas the surface impression of future knowledge of time is that there's going to have to be some change. See, the past is set and it's gone, if you will. In fact, I need to speak naively for a minute. We don't seem to have any problem. But the future, you know, there's going to be some changes. Now can't change the past, but you can change the future. I don't know why it is the argument. I mean, I can't plummet to the psychological depth of why the argument has the force it does here, but it doesn't with respect to the past. So I'm going to resist. It seems to be more of an emotional type thing because the fact that there was no change between 1812 and 1980, in my knowledge. In my knowledge of. Yeah, in knowledge of. Does not imply that there could not have been a change. Yeah, I suppose somebody could say that God has changed because in 1812 he knew that it was then 1812, 1980, he knows that it's 1980. And in that sense you'd only be putting the same problem. How can I put it? We are expressing future tenses. And what you're doing is you're expressing a future tense in terms of a past reference. In 1812, did God know that it would then be 1980? I think you're really reintroducing the same problem now running around the barn the other way. In other words, you're not really using past because you're speaking from the standpoint of the past about the future. God's knowledge has changed from 1812 to 1980 as to, you know, what the year is or what the time, time of day is, or what have you. My last comment is not necessarily trivializing whole argument. Rather, it seems, because I've had a question about this whole thing, seeing where it's been going. Does he talk about propositional knowledge? Yes. Which is different from experiential knowledge? Well, that is a popular dogma that I don't subscribe to. But I know what you're talking about. Yeah. I can know that it will be 2:30 when it becomes 230. That's the proposition. But that's the same of experiencing the change that is time. Even if I held to the distinction that you're drawing, I don't believe that the distinction is meaningful here. Okay. I don't think that it's the experience of 230 over against the knowledge that it is 230. I don't think that has any relevance to this. Because if God experiences one thing at one time and experiences another thing another time, or if God knows one proposition at one time and another proposition at the other time, you still have a mutable God. Or so it seems. Right? Okay, same problem.

Just occurs to me now what you mean by transitive principle. Again, like you say, it's not the grammatical sense, but transitive principle and sense of transition principle in the sense of rewrite, the rewrite principle, the transition principle. I can say the top line, therefore, in transition. Therefore in rewriting, I can say the second line.

Well, it's not so much rewriting as this implies. This, this does not capture. I can make that transition, you can make that transition.

Therefore, it's a transitive principle.

But what we're talking about is knowing that somebody knows leads to the transition, that you know the same thing the person knows.

So it is a transition principle, transitive in the sense of a transition.

I was just trying to summarize it to some convenient way for the sake of putting it in your notes. Yeah, I have trouble with that statement. For instance, Kim knows that Einstein knew the theory of relativity. No, no, no, no, no. You're introducing the same thing that Dr. Picasola did. Kim knows that Einstein knows the theory of relativity. No, it has to be a knows that knows that such and such and such and such that relativity is true or relativity exists. Okay, well, then s knows that relativity exists too. But I. I don't know that principle. You know that it's true.

Say it with the bat and it makes sense to you. Say the whole thing.

If you know that Einstein knows that it's true, the theory of relativity, then you know that the theory of relativity is true. Okay, that doesn't mean you know the theory of relativity the way Einstein knows, just that you know that it's true. And it may very well be that you know that it's true because you know that Einstein knows that it's true. This may be that you accept his authority for it. So as long as you keep the knows that instead of just knows with an oblique reference or opaque reference, I'm going to get that right. Knows that instead of knows, then you won't run into the problem. Although I remind you, Castaneda does give a counter illustration. Okay. Where a quasi indicator or indexical reference is there. Mary knows that Joe knows that he is in the hospital. Does that imply that Mary knows that he is in the hospital? Where he is in the sense of he himself. Mary knows that Joe knows that he himself is in the hospital. Is it true that Mary knows that he himself is in the hospital? Doesn't even make sense. So obviously that's a counter illustration. But that doesn't infect what we're doing here because it doesn't affect what we're doing here either. Okay, I'm going to. That is the most difficult part of it. Let's do a little mopping up here. Kretzfont had also argued that there are certain propositions that only one person can know because they necessarily involve first person quasi indicators. The illustration is Jones knows that he himself is in the hospital. Okay. It appears that only Jones could know that he himself is in the hospital. I mean, other people can know that Jones is in the hospital, but only Jones can know the proposition that he himself is in the hospital. That's again, rather obvious. It's not all that great an insight, but it does seem to imply that God can't know something that Jones can know. Jones can know that he himself is in the hospital, but God can't know that he himself is in the hospital. God can only know that Jones is in the hospital. So there is. There is one proposition that can be known by Jones that cannot be known by God. Okay, you see, that can't be. I mean, there's something wrong here. As a pastor again, I can. I think I can hear that, you know, being cried out inside. Well, what you do is you use principle P. Again, Castaneda says, no problem, because by P, anybody who knows that Jones knows that he himself is in the hospital knows that he himself is in the hospital. Anybody. I'm going to call this S. Well, I'm not going to call him S, because I've used that something before. I'm going to call this simply A, I guess. Okay, Anybody who knows A knows the very same proposition as Jones knows because the principal P said that if S knows that R knows that P, then S knows that P. The same proposition is known. What's different? The way the proposition is expressed? God knows that Jones is in the hospital. Jones knows that he himself is in the hospital. But it turns out that those are the identical proposition. My guess is that you intuitively knew that anyway. You didn't even know why there was a problem here. So obviously they know the same thing. It's just they're expressing it differently. Well, that's what it comes to, except that it can be given philosophical plausibility by all that previous argumentation that went before. You remember that. Kretzmann concludes his article with just a couple of paragraphs. He says, I've already done my homework. I mean, I've done the proof I have to do. Let me just add one more thing. It turns out that God can't know what any person can know about himself. But of course God can know what that person knows. Just that the expression of God's knowledge or of our knowledge is not the same as the expression of that person's knowledge about himself. Okay, now we're getting to the point where we don't have to spend too much time on this because it doesn't seem there's any problem left at all. So if God is omniscient, Costa Nyeda concludes his article. I should tell you, by the way, this is a popular way of stating your conclusions. He says, first, this is page 383. He expresses his conclusion in a way that may throw you for a minute. He says, the existence of an omniscient being is impossible. Or an omniscient being does not know every proposition in oratio recta indexical propositions. He must know inoratio obliqua in the form of quasi indexical propositions. You say, well, wait a minute. An omniscient being does not know every proposition. He says, well, sure, he knows every proposition, but he doesn't know it in the same form as somebody else. And so the fact that God is omni. I'm going to give you now what this all comes down to. Okay? This is the bottom line. When we talk about God being omniscient, we don't imply that he must know indexical propositions. Let me see. I'm going to get this right. God knows everything implies that he knows indexical propositions in the form of quasi indicators. Okay? You say, it is now T1 he knows at T1 it is then T1. Okay? God knows the same thing you do. However, the expression of his knowledge is going to be different, but what he knows and what you know are identical.

Could we have a repeat of the indexical Quasi. Yes.

That God is omniscient does not challenge the fact that he must know indexical propositions in the form of quasi indicators. He must know indexical propositions in the form of quasi indicate or. Yeah, quasi indicators. Kind of a tough article, but I hope by now it's a little bit clearer. And I think that attack on the subject may have been a little bit easier to follow than the one we were using last Wednesday. Any last questions on this? Indexical references that are invalid. An invalid form that only caused by indicators of. The valid way to refer to what we're saying is that the omniscience of God requires that indexical statements be expressed with quasi indicators for Him. And again, that by the form of expression sounds like a limitation on God, but it's no more a limitation on God than it's a limitation on us. What that indicates is that God and someone else, God and one of his creatures are different persons and he can't speak from, if you will, inside the eyes of another creature. He expresses the knowledge. He knows what that other creature knows. But the expression of his knowledge is not with indexicals as the creature would use it. He knows them with quasi indicators. Yeah. What import does all of that have? For when Jesus said, you've done unto the least of these, my brethren, you have done also unto me, I don't see that it has anything to do with that. Well, there's a functional equivalent between the treatment given to Christ's people and Christ himself. But that has nothing to do with epistemological principles. Knowing is not something you do to somebody. It's true that if we insult a Christian, we insult the Christian's Lord. But what he says there is simply transition, you know, as to the. You know, the treatment given. And I don't think it applies to this. At least I can't see that it does.

Just a factual question. When we're doing graduate work and we're studying the indexical fallacy, let's say, what would that course be in? Would that be in a course of formal logic? What is the category we're talking about, the indexical fallacy that this may seem. We're talking about formal logic.

Well, it would be a. Most likely a course in epistemology and the philosophy of language. At least that's in my graduate work where we read cast and yada and.

Such things, philosophy of language. And when you took formal logic, you studied things like syllogism.

Yeah. Formal logic doesn't deal with the words then and now, because those are natural words. Formal logic deals with formalizations, PQ and all the rest.

Yeah, that's my question. So in terms of curriculum. I see. So this would be courses in language. Philosophical language.

Well, philosophy of language is a subdivision of epistemology. Yeah. Well, we've run out of time with only doing this one thing. But it was a difficult subject and if we're through it, I'll be happy, as I think you will be happy for that fact.

So we're doing unit Five next?

No, no. We still see there are two problems in the omniscience of God. We dealt with the easy one today. Didn't mean to discourage you. We dealt with one that's rather difficult. But the other one has been a problem for a number of years in the evangelical church. And that's a question of God's foreknowledge and human freedom. If God knows everything and he knows what I will do in five minutes, and if God knows that I will do it in five, five minutes, I don't seem to be free to do otherwise. Okay, when we come back on Wednesday, we'll try to resolve this Calvinist, Armenian controversy.