Originally posted by LemonJelloYes, you're right, the universal quantifier should be an existential one. The Q-agent only needs one opportunity. So Q(x) is now:
□ªP(T) <-> P(T) & ¬◇(P(T) & ∃x ∃y ∀t [(t ≥ T) & S(x) & A(y) & B(x,y) & C(x,y,t) & □(D(x,y,t) -> ¬P(T))])
One preliminary point is that you are using universal quantification over times at T or later. Although the way Plantinga words (42) is somewhat ambiguous, I highly doubt that the universal quantification is what he intends. He ...[text shortened]... (3) to have the form of strict implication.
I may have to give this point more thought....
Q(x) = ∃y ∃t [R(x,y,t) & □(D(x,y,t) -c> ¬P(T))]
Where R stands for (non-counterfactual) requirements:
R(x,y,t) = (t ≥ T) & S(x) & A(y) & B(x,y) & C(x,y,t)
I hadn't really got the point that (3) contained a counterfactual conditional. So I've used -c> to indicate that. It's a really fuzzy point as he starts by asserting "it's not possible that" which means "in no possible world" and then has a counterfactual to a state of affairs which doesn't exist. So it must be counterfactual to all P-worlds, to use your language, in which case it's really not clear what the second necessity operator (3) is doing that isn't done by the first one in the necessarily not P(T) or not Q(x) rendering.
I think you are right about Plantinga's statement being some sort of accessibility criterion, he seems to intend the first necessity operator to only pick out P-worlds and the second to pick out non P-worlds. I think I need to read the page on counterfactual logic on plato.stanford.edu.
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Originally posted by LemonJelloI think I've got what he's saying, but I don't believe him.
□ªP(T) <-> P(T) & ¬◇(P(T) & ∃x ∃y ∀t [(t ≥ T) & S(x) & A(y) & B(x,y) & C(x,y,t) & □(D(x,y,t) -> ¬P(T))])
One preliminary point is that you are using universal quantification over times at T or later. Although the way Plantinga words (42) is somewhat ambiguous, I highly doubt that the universal quantification is what he intends. He ...[text shortened]... (3) to have the form of strict implication.
I may have to give this point more thought....
In some possible world w, we have:
D(x,y,t) > ¬P(T)
if x were to do y at time t then P(T) would not be true. D(x,y,t) is false in the actual world, that is the agent won't take the action (otherwise P(T) would not be true). Then in the nearest possible world where D(x,y,t) is true we have ¬P(T). So the necessity operator quantifies over worlds where D(x, y, t) is true. If we call the set of such worlds D then:
□(D(x,y,t) > ¬P(T)) = ∀w ((w∈D) & ¬P(w,T))
where I've added an extra argument to P(T), P(w,T) is the proposition in possible world w. Applying this to his ants example:
P-worlds - worlds where the ants move in at time T. Call the set of such worlds P
C-worlds - worlds where God cares about the ants. Call the set C
D-worlds - worlds where Paul carries out his action. Call the set D
Let W be the set of all possible worlds. X is an arbitrary subset of possible worlds.
So the overall condition (not possible that both P and there is a Q-agent) the relevant possible worlds are all P-worlds. In the actual world Paul will not have mowed. So that is not a D-world, it is a C-world. There are three things we could have our necessity operator quantifying over possible worlds:
□(D(x,y,t) > ¬P(T)) = ∀w (w∉P) & (D(w,x,y,t) -> ¬P(w,T)) = true
where the ">" is a counterfactual conditional and "->" is a material conditional, and everything to the right of ∀w w∉P is understood to be in world w which is not a P-world. This reads ">" as counterfactual to the ants moving in. This reading would render all facts about the past non-necessary and can't be what Plantinga means.
□(D(x,y,t) > ¬P(T)) = ∀w (w∉C) & (D(w,x,y,t) -> ¬P(w,T)) = false
we can always find possible worlds where D(w,x,y,t) and P(w,T) range over all possibilities so this will come out as false, but I don't think it's what Plantinga intended.
□(D(x,y,t) > ¬P(T)) = ∀w (w∈D) & ¬P(w,T) = false
This makes most sense to me.
The overall condition is:
□ªP(T) <-> P(T) & ¬◇ [P(T) & ∃x∃y∃t R(x,y,t) □(D(x,y,t) > ¬P(T))]
Where R(x,y,t) just contains the other bits of the condition for a Q-agent.
R(x,y,t) = (t ≥ T) & S(x) & A(y) & B(x,y) & C(x,y,t)
So,
□ªP(T) <-> P(T) & ¬∃w ∃x∃y∃t ∀v (w∈P) & R(w,x,y,t) & (v∈D) & ¬P(v,T)
specialising to the ants example, Let p = Paul, m = mows and t = T1 > T
□ªP(T) <-> P(T) & ¬∃w (x∈P) & R(w,x,y,T1) &( ∀v (v∈X) & (D(v, p,m,T1) -> ¬P(v,T)))
So the accidental necessity of P(T) depends on what the set X is. If the set X is counterfactual to Paul not mowing his lawn, which seems right, the relevant set is X = A. So
□ªP(T) <-> P(T) & ¬∃w ∀v (w∈P) & (v∈A) & R(w,p,m,T1) & ¬P(v, T)
and we get P(T) being accidentally necessary. But it hangs on there being possible worlds where God doesn't care about the ants. If God cares about the ants in all possible worlds then the ants moving in a week ago is not accidentally necessary.
So what I'm getting from this is in order to protect accidental necessity rather than have his counterfactual interpreted in the nearest possible world where Paul mows his lawn, which is one where God cares about the ants and causes them not to have moved in, he adds the necessity operator so that one has to consider all possible worlds counter to the decision not to act. This means his strict conditional catches worlds where God doesn't care about the ants which saves accidental necessity in the face of an omniscient all-powerful entity. I'm really not convinced that step is justified.
Do you agree with how I'm interpreting his necessitated counterfactual?
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Plantinga doesn't seem to have considered the case where something that should not have accidental necessity could get it through his formulation. Suppose Mother Shipton left a prophesy as follows:
At end of ye yere two thousand and fifteen, ye playere of chesse knoune by tagge Depethawt shalt poisonned be by adversery most vengeful.So P(T) is that I'll be poisoned by an vengeful chess oppponent on New Years day 2016. T is some time before 1561. This should not be accidentally necessary. Further suppose the poisoner will poison my coffee and I drink it in the actual world. So P(T) is true.
I'm clearly a Q-agent. As I've read Plantinga's counterfactuals we have:
□ªP(T) <-> P(T) & ¬◇ (P(T) & R(b,d,t) & □(D(b,d,t) > ¬P(T))
R(b,d,t) means an agent b = Bruce (me) has an action (inaction) d = don't drink the coffee at time t = New Years day 2016, I think avoiding drinking the coffee is as basic an action as one could hope for and clearly I can do it. So far this isn't a problem. The possible worlds where I do drink coffee leave us with:
P = set of worlds where the proposition is true, I am poisoned.
D = set of worlds where I drink coffee.
□ªP(T) <-> P(T) & ¬∃w ∀v (w∈P) & (v∉D) R(w,b,d,t) & ¬P(v,T)
R is true in all P-worlds, I can avoid drinking the coffee, but do. P(v,T) is false in worlds that are not D-worlds, as I avoid the coffee. So □ªP(T) correctly comes out false and mother Shipton's prophecy is not accidentally necessary.
In his ants example Plantinga has God intervening to stop the ants move in.
P = set of worlds where I am poisoned on 1/1/2016.
D = set of worlds where I drink the coffee.
S = set of worlds where they also poison my cake.
In the possible worlds w∈S they have a second route to poison me. They only poison my coffee in the actual world, so the actual world is not an S-world.
□ªP(T) <-> P(T) & ¬∃w ∀v (w∈P) & (v∉D) & R(b, d, t) & ¬P(v, T)
Because ∀v (v∉D), includes possible worlds where they poison my cake P(v,t) is true for some v∉D and so the prophecy comes out as accidentally necessary when it shouldn't.
This could mean I've not understood Plantinga's condition, but I think my poisoning example is not so different from his ants example. So I think to avoid making something that should be accidentally necessary not so he's allowed cases that shouldn't be accidentally necessary to become so.
Or more simply and sticking with Plantinga's original ants example. Suppose Nostrodamus had predicted that the ants would move into Paul's garden. The prediction cannot have the necessity of the past, I'm sure Plantinga didn't intend that, but it seems to piggy back on the accidental necessity of the ants moving in in Plantingas formulation. Since the rules for determining the prediction's accidental necessity are the same as for determining the ant's move's accidental necessity. So I think his adding a necessarily to (3) causes as many problems as it solves.
Originally posted by DeepThoughtWith free will it boils down to the trust we have with God who can see all
Or more simply and sticking with Plantinga's original ants example. Suppose Nostrodamus had predicted that the ants would move into Paul's garden. The prediction cannot have the necessity of the past, I'm sure Plantinga didn't intend that, but it seems to piggy back on the accidental necessity of the ants moving in in Plantingas formulation. Since the ...[text shortened]... tal necessity. So I think his adding a necessarily to (3) causes as many problems as it solves.
events at the same time in our universe past, present, and future. Does
He really have the ability to give and respect someone who wants to make
a choice He does not want? If He does love us all and some want to go to
Hell, and He allows that than that answer is yes. If He loves us what could
He do without forcing us to make a bad choice? He could make robots with
out choices, He could hold a gun to our head like our governments do when
they pass laws do or die, go to jail, lose money, land, and so on. What part
of free will is there when one is forced into obeying, it does not play out
well with ISIS reject Christianity or die, people die.
So you and I find ourselves in a universe where we can make good and
bad choices and if we make them we own them they are what we do, we
also say nasty things too. So if faith is required to give us real will, than
much of the complaints here are about something that is needed and we
could not do without to be a real human.
So God when talking to us about future events does so with the knowledge
of what is going to happen and not only that, but how we react! Being told
about something that is going to happen with no other way of knowing it
is also going to effect us in the present. Would those things happen if He
didn't tell us, I don't know, I just know that we are forewarned, and we can
do with that what we will as we do all things.
Originally posted by AgergIt could be such a deity creates a draft, information only, of what the universe will be like, there being at least 3 timelines, the timeline of the deity, and separate timelines for the draft and the timeline of the universe made real by the deity.
Wrt possibility 1, I agree ... it would indeed be like a movie reel laid out in front of [God] so [he] can see every frame at the same time. But the essential feature here is that the movie reel should not be known [b]prior to its creation (otherwise, as per my op, that would be predetermining our choices). From our perspective we can just go ahead ...[text shortened]... rse going about and fixing this timeline for God when he eventually gets round to looking at it.[/b]
It would mean the fact that our timeline started from zero at the creation of our universe, the deity has its own timeline outside ours. Creating our universe only starts a local clock.
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Originally posted by KellyJayIt's not clear to me yet what the consequences of my argument are. What it means is that Plantinga's formulation of accidental necessity - the necessity of the past - gives things like the knowledge of an omniscient entity or the predictions of any soothsayer who is correct accidental necessity. It means that Plantinga's formulation doesn't do what he was expecting it to. There are a number of possible resolutions, the most obvious one is simply to rule out an omniscient, or at least presciently omniscient, entity - not one I imagine you'll accept. Alternatively it may be possible to find a resolution that preserves both the necessity of the past and free will in the face of an entity with prescient omniscience.
With free will it boils down to the trust we have with God who can see all
events at the same time in our universe past, present, and future. Does
He really have the ability to give and respect someone who wants to make
a choice He does not want? If He does love us all and some want to go to
Hell, and He allows that than that answer is yes. If He loves ...[text shortened]... , I just know that we are forewarned, and we can
do with that what we will as we do all things.
A resolution I think you'll be happier with would be to rule out a God who intervenes conditionally. If God is worried about the ants in Plantinga's example then he has to lead them away from Paul's garden (so they aren't destroyed if he mows) whether or not Paul is going to mow it a week after they move in. By doing this he can protect accidental necessity in the actual world, Paul's free will, and the ants.
That answer would solve one riddle of the Old Testament. If God knew that the Israelites would break the covenant what was the point in establishing it in the first place? This would seem to answer the question. God had to ignore his foreknowledge of the breaking of the covenant in order to preserve the Israelite's free will. It's enough that they were free not to break the covenant. It places limitations on how God can intervene in the world if he wants to preserve causality (the necessity of the past) and free will. This resolution does leave the necessity of the past contingent on God's benevolence, but that's the kind of thing you all seem to assume anyway.
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Just a quick question to DeepThought, what font and character encoding are you using in your browser as you set your arguments here?
Unfortunately, much of what you write wrt symbolic expressions doesn't render very well on my browser (unless squares (imbued with superscript 'a's) and diamonds ... happen to be logical notation I haven't come across yet)
Originally posted by AgergA square □ is the logical symbol for necessity so □P means necessarily P, in other words that P is true in all possible worlds. ◇P means possibly P, meaning there is a possible world where P is true. When unicode doesn't work you'll get a square with the unicode number in it. It's only if that happens that it hasn't rendered properly.
Just a quick question to DeepThought, what font and character encoding are you using in your browser as you set your arguments here?
Unfortunately, much of what you write wrt symbolic expressions doesn't render very well on my browser (unless squares/diamonds, greater than signs, and so on ... happen to be logical notation I haven't come across yet)
I'm using A -> B for the material conditional meaning If A is true then B is true.
I'm using A > B for a counterfactual conditional means if A were true then B would be true.
The material conditional is the familiar entity from logic with the following truth table:
A | B | A->B
---+---+--------
T | T | T
F | T | T
T | F | F
F | F | T
Where A and B are understood to be true or false in the actual world (the one we live in)
The counterfactual conditional (something I've only learnt about recently so don't rely on what I write here) does not assume that the arguments to it are true. For example "If I were in New York then I be in the U.S.". Is clearly true. I'm in England so the antecedent is false, but overall it makes sense. In possible world semantics it's translated as "In the nearest possible world where DeepThought is in New York then he is in the U.S.".
In his argument Plantinga uses a necessity operator (in all possible worlds) around a counterfactual conditional. I think he means in all possible worlds where the agent who could act does so.
I'm still wondering about my argument as I'm not entirely sure about it. There's a possible world where God hates the ants and smites them before they move in, which might mess up my argument about Nostrodamus.
To read more about modal logic, there's a Wikipedia page, but it's confusing. I'd recommend this page:
http://plato.stanford.edu/entries/logic-modal/
although it's not the easiest read ever it is clear. For what is meant by a possible world see:
http://plato.stanford.edu/entries/possible-worlds/
If you don't understand section 1 don't worry, just skip to section 2 which is still understandable even if you can't follow section 1. Their page on classical logic probably gives the information to understand section 1.
Sadly their page on counterfactuals isn't written yet. That site is a bit of a gold mine for people interested in this stuff.
After thinking about it some more, my objection doesn't work. Here is his condition for accidental necessity:
(42) p is accidentally necessary at t if and only if p is true at t and it is not possible both that p is true at t and that there exists an agent S and an action A such that (1) A is basic for S, (2) S has the power at t or later to perform A, and (3) necessarily if S were to perform A at t or later, then p would have been false.Plantinga is saying that P(T) is some proposition that is rooted at time T. So, for example, if I were to claim that the Labour party will win the next election, this coming May, then P(T) = "Labour will win the May 2015 election." and T = 21st March 2015. So P(T) is a proposition about the future made now. But Labour hasn't won yet (and unless they sharpen up their act a lot they won't). So P(T) isn't true in any meaningful sense. This is the problem with my counter-examples I'm relying on propositions made before their truth value is known. He talks about propositions strictly about the past. Predictions are made before the event and the formulation expects the event to have happened at or before the time of the proposition.
On Ockham's Way Out
Alvin Plantinga
Faith and Philosophy, Vol 3 No. 3, July 1986
The agent who can change the event is expected to do that after it has happened. This is the point of the example with Paul's mowing decision. God a week earlier knows that Paul is not going to mow his lawn and so lets his favourite ant colony move into Paul's garden. If Paul is going to mow his lawn then God will guide the chosen ants elsewhere. He introduces the necessity operation to ensure the ants moving in has the necessity of the past. It hangs on God not necessarily caring about the ants, but this does not mean that soothsayers can get around it, their propositions are about the future and don't have a truth value in the sense Plantinga means.
The way the logic works the accidental necessity is protected by the necessity operator around the counterfactual (3). But the proposition rooted in the past has to refer to something that happened before or at the same time, it can't refer to something in the future. So my counterexamples fail for this reason.
The only counterexamples that will spoil this involve time travellers, but if time travel is possible no events have the necessity of the past.
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Originally posted by DeepThoughtI think just because we cannot see the whys for an out comes and
It's not clear to me yet what the consequences of my argument are. What it means is that Plantinga's formulation of accidental necessity - the necessity of the past - gives things like the knowledge of an omniscient entity or the predictions of any soothsayer who is correct accidental necessity. It means that Plantinga's formulation doesn't do what he ...[text shortened]... ast contingent on God's benevolence, but that's the kind of thing you all seem to assume anyway.
understand how a thing has arrived with an omniscient being doesn't
mean that have to or even should rule one out.
I recall years ago I was talking with a friend about what if everything was
in a 2D universe not what we have now, those who lived there in this 2D
world would grasp all that was written or drawn on the board or paper, but
nothing not on it. We on the other hand could see the whole board/paper
and could add and subtract at will. Those in the 2D universe would be able
to follow us only as we drew or wrote on the board or paper. They would
know what was placed on it as soon as it was, but its knowledge would
always stop where the author left off.
Since it cannot grasp the author and could only understand it by what the
author left or did it would never really fully grasp any of the hows or whys
in its world.
With us God gives us the ability to choose, so we do, that does not mean
that all of our choices must be accepted or thought of as good? So when
God puts road blocks in our way preventing us from doing something like
gravity which stops us from just flapping our arms to fly. He does that to
put boundaries on us and we deal with it with our wills, as He does when
He says do this, or don't do that. We choose, but our choices are on us.
I feel like I'm missing some of what you are saying, and I'm willing to bet
that its me not you. If I'm missing your point, please forgive and try one
more time.
Originally posted by DeepThought"If God knew that the Israelites would break the covenant what was the point in establishing it in the first place?"
It's not clear to me yet what the consequences of my argument are. What it means is that Plantinga's formulation of accidental necessity - the necessity of the past - gives things like the knowledge of an omniscient entity or the predictions of any soothsayer who is correct accidental necessity. It means that Plantinga's formulation doesn't do what he ...[text shortened]... ast contingent on God's benevolence, but that's the kind of thing you all seem to assume anyway.
My personal opinion!
I think God is covering all of the bases with us.
We had no law but one don't eat of that one tree, failure.
We were left on our own for awhile, failure.
We were given a law where if we obeyed than good things, failure.
Now God has setup grace through Jesus Christ where all the heavy lifting
for our righteousness is now through Jesus Christ not us, success for those
in Christ.
The law in my opinion was given because if we could have been right with
God through it, that'd been good, but instead it only showed us because the
law was good how bad we really are. Example don't lust, so after we lust
we see the sin in us.
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Originally posted by DeepThoughtI've been intrigued by this discussion, mostly because I don't know why it would present a problem for anyone. You said:
If someone is selfish and greedy it does not, of itself, mean that they are not also scrupulously honest. The difficulty with your point about free will is that it is rather coarse grained. I don't think any of us disregard the idea that we make our own decisions, but do we make them in the manner of clockwork, or in some less deterministic way? The n ...[text shortened]... er, we are not yet there. We are still trying to work out what the necessity of the past means.
Omniscience is an attribute which has been claimed as a property of God. If that is the case it is reasonable to ask what the implications are for free will.
Omniscience is as you say a property of God, but it's not a property of man. Free will (at least from mans point of view) suffers from no contradictory implications. So any concern with free will and omniscience would naturally have to rest with how it relates to an omniscient being. But I frankly don't see how Gods omniscience could in anyway interfere with a mans ability to make free will choices. Omniscience doesn't necessarily imply control, because O is about knowing (an action) and FW is about choosing (an action).
Foreknowledge would mean God already knows what will happen, however knowing an action does not directly translate into causing an action. If I know what I will do and then do it then there is a connection between knowing and action under those circumstances, even though it wouldn't involve foreknowledge. But an omniscient being knowing what I will do before I know what I will do is entirely different. It may seem bizarre and difficult to understand... I certainly don't understand omniscience, but I still can't see where coexistence of omniscience (in God) and free will (in man) would necessarily contradict or come in conflict with one another.
I should stop now, and sum this up before I get too lost in it and end up confusing myself:
Just because God knows what I will do does not mean he causes me to do it.
Originally posted by lemon limeThat is what this thread is about. Does foreknowledge imply causation by the knower, or alternatively, does foreknowledge actually rule out causation by an agent.
Foreknowledge would mean God already knows what will happen, however knowing an action does not directly translate into causing an action.
I say that at a minimum, it rules out ultimate causation by an agent - depending of course on how you define causation.
Of course it doesn't bother me all that much because I am not particularly attached to free will defined as 'the ability to act randomly'. I am perfectly comfortable with free will that is compatible with a deterministic universe - although I am not attached to determinism either.
Originally posted by twhiteheadI am not particularly attached to free will defined as 'the ability to act randomly'.
That is what this thread is about. Does foreknowledge imply causation by the knower, or alternatively, does foreknowledge actually rule out causation by an agent.
I say that at a minimum, it rules out ultimate causation by an agent - depending of course on how you define causation.
Of course it doesn't bother me all that much because I am not particul ...[text shortened]... is compatible with a deterministic universe - although I am not attached to determinism either.
Neither am I, because I've always assumed random acts are exclusively attributable to inanimate objects... because inanimate objects don't have the ability to exercise free will. But I'm not particularly attached to the idea of randomness as a valid concept either. Something may appear to be random if no discernible or predictable pattern can be found, but I think I'm safe in saying that for every action there is always a cause, whether that cause can be identified or not.
Even so, I suppose it's possible that someone might be able to prove (without a doubt) that something can happen for no reason whatsoever. I should know better than to predict that something can't happen, because a little over 10 years ago I was talking with a computer expert and we both agreed that quantum computing was a pipe dream... it wasn't a practical idea worth exploring because there were too many problems to overcome. Well, so much for that prediction. I don't know if near absolute zero conditions are still needed to make it work or not, but sure enough a workable quantum chip was developed. And just recently I've seen that a significant improvement was made in quantum chip computing...
I'm just blathering on and on randomly now, so there's no need to take note of anything I'm saying at this point... although, there might be a discernible pattern here that could coalesce into something later on... ?
later on
Nope... just random thoughts is all... maybe something will turn up tomorrow morning. 😴