Some people deny the Law of Excluded Middle (LEM--for all p, p or not-p) because they are convinced it leads to fatalism. But they really shouldn't deny LEM.
Suppose Helga is convinced that utilitarianism is true. You offer Helga a reductio argument against utilitarianism on the assumption that the hedonistic theory of happiness holds and another reductio argument against utilitarianism on the assumption that the hedonistic theory of happiness does not hold. Helga accepts both reductios and comes to deny hedonistic utilitarianism and non-hedonistic utilitarianism, but continues to accept utilitarianism. Pressed on how Helga's new position squares with logic, Helga asserts that based on her belief that utilitarianism holds, and her new beliefs that if hedonism holds, utilitarianism is not true, and if hedonism doesn't hold, utilitarianism is not true, she has concluded that LEM does not hold. There seems to be something irrational about this. Surely, she should either find fault with at least one of the reductios or abandon her belief in utilitarianism. It is hard to imagine premsies whose plausibility should trump LEM.
Arguments the depend on LEM are not, I think, uncommon in philosophy. If Molinism is true, evil and the existence of God are compatible (by Plantinga's free will defense). If Molinism is not true, evil and the existence of God are compatible (by Adams' free will defense). Hence, evil and the existence of God are compatible. It is pretty likely that Helga uses LEM-based arguments in other contexts, and it is pretty likely that the defender of the Open Future who denies LEM also uses LEM in other contexts.
Could they both say that LEM applies in some contexts (e.g., non-normative ones in Helga's case, or in ones that do not involve the future in the freedom case) but not others? Yes. But once we denied the plausible view that LEM follows from the meaning of the words "or" and "not", and denied the general intuition that between p and not-p tertium non datur, it seems that we have undercut the grounds we could have for thinking LEM holds even in those contexts in which it is supposed to hold in. Besides, the defender of the Open Future who denies LEM presumably does so on the basis of something like a temporalized modal logic according to which if p already holds, then not-p is no longer possible. But surely the principles of classical non-temporal non-modal logic are more plausible and more deeply embedded in our thinking than those of temporalized modal logic.
Anyway, it seems much better to hold on to LEM, and just deny the principle that if not(will(p)), then will(not-p), where "will(p)" means p will hold. The principle that if not(will(p)), then will(not-p) is a dubious one if we see "will" as a modal-type operator, maybe akin to "would" except for being a one-place operator, and that is precisely how we will see "will" if we have presentist or growing-block intuitions. Moreover, it is a principle that is less central to our thinking than LEM, particularly because it applies only to our thinking about the future, while LEM applies to all our thinking. It seems clear to me that this is what the person impressed by the argument for logical fatalism should say, boldly holding that there is a fact of the matter whether Jones will mow the lawn tomorrow: it is false that Jones will mow the lawn tomorrow, just as it is false that he will fail to mow the lawn tomorrow. And God's omniscience will be unrestricted: he knows that it is false that Jones will mow the lawn and that it is false that he will not mow the lawn.
Of course, it's best to hold on to both LEM and if not(will(p)), then will(not-p).
31 comments:
Alex,
I think you’re exactly right – the open theist shouldn’t deny LEM. For some future contingency X, they should hold both that it’s false that it *will* happen and false that it *will not*.
The biggest challenge for this view is the following, I think, and I’m wondering if you’ve got any ideas on how the open theist could respond. Suppose I predict that X will happen, but that at the time of my prediction, the world is indeterminate with respect to X’s happening. So, according to this open theist, it’s false that X will happen (when I make the prediction). But suppose it turns out that X happens. Most are inclined to say, “Hey, you were right!”, i.e. that I said something true at the time of my prediction. But (on this view), not only did I not say something true (which would follow on the denial of LEM route), I said something *false*.
By the by, this problem is discussed in Alan Rhoda et al.’s recent article in Faith and Philosophy, “Open Theism, Omniscience, and the Nature of the Future.” They hold onto LEM, contra Hasker and other open theists.
I hadn't thought of that problem. Since I'm not an open theist, it's not a problem for me. :-)
But I should say that the problem does not seem that much more serious on the LEM-asserting than on the LEM-denying open theism. "Hey, you were right!" is incorrect if the prediction lacked truth value. It might be true that the error is lesser on the LEM-denying open theism, since then it's a matter of asserting a proposition that wasn't false, but had no truth value. But it's not even clear to me that that's a lesser error (is it a lesser error to speak nonsense than to speak what is false, for instance?).
Here is a slightly more worrying variant. Suppose I say: "It is not the case that Jones will mow the lawn." And then Jones mows the lawn. On the view in question, what I said was true when I said it. That's really weird. But maybe it's only really weird because we misread "It is not the case that Jones will mow the lawn" as "It is the case that Jones will not mow the lawn." And open theists tend to think that propositions change in truth value anyway, so maybe this shouldn't be too much of a worry.
Or maybe it should. Ultimately, I do think the best move is to reject all this weird stuff, and just stick to the eternity of truth. ;-)
Oh, here's another problem, another weirdness. Suppose Jones has mowed the lawn every Thursday. On the view I advocated for the open theist, it's appropriate to say: "In light of all the evidence, Jones will probably mow the lawn tomorrow, but it is false that Jones will mow the lawn tomorrow." And that's really weird, isn't it? But a variant of this example will also be a problem for the LEM-deniers, who then have to say how a proposition that lacks truth values can have probabilities.
Plantinga has refuted the logical problem of evil with a free will defense?
Plantinga's argument is just a 'saving the appearances' argument of the type used to show that logically the sun could go around the earth, even though the appearances of planets in the sky is not compatible with it.
'Saving the appearances' type defenses are not convincing.
Plantinga claims 1) God has created beings with free will that have never chosen evil (namely the angels in heaven) and also 2) God cannot create beings with free will that never choose evil.
Something has to give.
There are, of course, other holes in Plantinga's arguments.
For one thing, his claims about Molinism are a) trivially true and b) unhelpful to his cause.
Plantinga's defense is that even an all-powerful god cannot create people who always choose good, even though it is logically possible that such people exist, and it is Christian doctrine that god created beings with free will that never rebelled and were never thrown out of heaven.
Plantinga's argument is as follows :-
1) It is a fact about me that if placed in circumstances C1, I would choose good action GA1.
And if placed in circumstances C2, I would choose good action GA2, if placed in circumstances C3, I would choose evil action EA3 , etc etc.
There is a whole row of facts about what I would do in every conceivable set of circumstances. In some I choose good actions. In others I choose bad actions.
This set of facts is what Plantinga calls 'counterfactual truths' about me. Not even God can change them.
2) Different creatures have a different set of counterfactual truths to those I have in. Where I would choose good action GA200, when in circumstances C200, a different creature would choose evil action EA200 , when in circumstances C200.
3) God considers the vast range of possible creatures he could choose and the vast range of possible circumstances he could put them in.
4) Sadly, despite being able to choose exactly what creatures to make and exactly what circumstances to put them in, the 'counterfactual truths' about these creatures mean that every single one of them will choose an evil action in some set of circumstances that god can actualise.
That is Plantinga's argument.
It is just an extraordinary coincidence that the 'counterfactual truths' about every one of the virtually infinite number of possible creatures have this property, especially when Christians teach that god has created some angels which have never chosen evil.
An almost infinite number of creatures who each and every one just happen to have a counterfactual truth that leads to them choosing evil? How likely is that?
And, of course, Plantinga's claim is just wrong.
Can a god create almost identical twins - creatures that behave very similarly , except in a few circumstances?
The obvious and correct answer is 'yes.'.
If there is a set of counterfactual truths about what I will do in every circumstance that I meet in the actual world, then logically, there is a possible human being - a near-twin of mine - who behave almost identically to me, except on a few occasions.
On the occasions that I choose evil, this near-twin of mine chooses good.
As it is obviously clear that near-identical twins are possible, Plantinga's argument falls apart.
It is not even as though this near-identical twin has to have a set of 'counterfactual truths' that are always good. He does not have to have an angelic disposition.
He could choose evil in the circumstances in which I choose good.
Provided those circumstances never come to pass, no evil will occur.
God need no more actualise my near-twin being in those circumstances than he need actualise me being in those circumstances.
All god needs to do is create the near-identical twin of mine who chooses good when I choose evil, in the circumstances in which I actually do find myself.
The result would be that no evil is chosen.
So Plantinga's arguments are deeply flawed.
------------------------
But why is Plantinga's Molinism trivially true, and unhelpful to his case?
Plantinga's Molinism is the claim that if a person is placed in a particular set of circumstances (which, of course, include the circumstance of there existing a god who infallibly knows what that person will freely choose), then a person will freely choose one particular way - namely the way that the all-knowing being knew he would freely choose.
But, of course, when Plantinga describes the circumstances in which people make free choices , he always leaves god out of the description.
This is because the dogma of libertarian free will means there are always 2 almost identical sets of circumstances in which we make a choice.
They differ only in the content of God's knowledge.
So if we choose evil in circumstances A, there is always an almost identical set of circumstances in which we choose good.
And this set of circumstances can be actualised.
Why?
Because the person's counterfactuals of freedom include the fact that he will freely choose good in all those circumstances where there exists a god who knows he will freely choose good.
Which trashes Plantinga's claim that there may not be *any* circumstances in which we choose good.
No wonder Plantinga never includes the content of God's knowledge when Plantinga describes the circumstances in which we choose.
Here is the proof that Molinism is true. In fact, it is trivially true.
What is Molinism?
In every conceivable set of circumstances, free agents like us will choose one particular way.
These free choices are out of God’s control.
In a particular set of circumstances , that agent will choose that way, and that is all there is to it. Nothing can God do about it.
How does this possibly work?
As an example, take two different sets of circumstances that I can conceive of.
1) I am sitting down to breakfast in an hotel at 8:30 am on 2/04/2007, and a waiter is asking me ‘Tea or Coffee’, and God has infallible knowledge that I will choose tea.
2) I am sitting down to breakfast in an hotel at 8:30 am on 2/04/2007, and a waiter is asking me ‘Tea or Coffee’, and God has infallible knowledge that I will choose coffee.
Clearly, I can conceive of both sets of circumstances, and they are both possible, and they are clearly different to each other.
We can apply Molinism to each set of circumstances, and see if the claim is true that a person will freely choose one particular way in each set of logically possible circumstances that could occur in a real world.
Molinism works perfectly here.
In the first, I will freely choose one particular way, just like Molinism said I would. I will choose tea.
In the second set of circumstances, Molinism is right again. I will choose one particular way. I will choose coffee.
Of course, my choices are different in the two sets of circumstances, but I’m sure people will agree that free agents will choose differently in different circumstances, and it cannot be denied that the 2 circumstances are different.
And Molinism is right once again that not even God can determine my choice in those 2 sets of circumstances. In set 1), I drink tea, and in set 2), I drink coffee, and there is nothing God can do to change the outcome of either set of circumstances.
And, of course, this is all God's middle knowledge as neither of those 2 circumstances were actual.
So how does this proof of Molinism even begin to show that God cannot actualise the circumstances in which I drink tea?
Obviously God can actualise either of those circumstances.
Plantinga has shown that if Molinism is true, it is logically possible that God and evil coexist. He has not shown that it is probable, or even that it has non-zero probability, but only that it is logically possible. The arguments you offer may show that this has tiny, maybe even zero, probability, but they do not show it is impossible. (Some zero probability events are logically possible. The probability that a coin tossed an infinite number of times will land heads each time is zero--as is any other sequence--but such an outcome is logically possible.) Since the logical problem of evil claims that it is not logically possible, the logical problem of evil is refuted.
Plantinga hasn't shown that at all, as can be seen by my analysis of his arguments.
Plantinga's argument boils down to the tautology that if the state of affairs that exists when somebody makes a free choice include an omniscient being who knows that that free choice will be an evil choice, then god cannot arrange that in those exact same circumstances, the person will freely choose good.
Well, this is true.
But how does such a tautology help Plantinga?
And there are the other holes in his arguments.
I'm not sure what you mean by 'small probability' Is there only a small probability that God can create either one of near-identical twins?
What is a 'logical' deduction?
Is it logical to conclude that almost everybody has two legs, based on the fact that our memory and senses tell us that almost everybody has two legs?
Is it possible to construct a 'saving the appearances' defense against the logical problem of legs to show that it is logically possible that we only have one leg, despite appearances to the contrary?
If the 'logical' problem of legs can be refuted, what should we call the leap from (1) I can see that people have two legs , to (2) It is a fact that people do have two legs?
Is (2) a logical inference from (1)?
If not, then what is the best describing word for such an inference?
'(Some zero probability events are logically possible. The probability that a coin tossed an infinite number of times will land heads each time is zero--as is any other sequence--but such an outcome is logically possible.)'
Is it logically possible for an actual infinite number of coin tosses to occur?
Steven writes,
An almost infinite number of creatures who each and every one just happen to have a counterfactual truth that leads to them choosing evil? How likely is that?
What does likelihood have to do with the argument? Nothing that I can see. Plantinga's argument depends only on it being possible that every creatable essence is TWD. It does not depend on it being likely. Further, his claim is perfectly consistent with God's having in fact created angels that never go wrong. That is a contingent fact about angels, not an essential property of them, at least on a Christian view (after all Christians believe that angels can and did go wrong). There is a problem with Plantinga's argument, I think, but it's much more subtle. The argument depends on the truth of certain backtracking counterfactuals. But backtrackers are generally not true. But that's another story.
Hi Alex,
Pressed on how Helga's new position squares with logic, Helga asserts that based on her belief that utilitarianism holds, and her new beliefs that if hedonism holds, utilitarianism is not true, and if hedonism doesn't hold, utilitarianism is not true, she has concluded that LEM does not hold.
I'm not sure Helga has to give up LEM. She can accept your reductio, adhere to LEM, and deny that there are only two truth-values. She can say that what you've shown is that utilitarianism is, at best, indefinitely true. LEM is consistent with that. You can force her to give up LEM only if you add that bivalence is also true.
Like most other mathematicians, I have no problems with actual infinites.
To show that it is logically possible that God and evil coexist, it suffices to describe logically possible circumstances in which God exists and at least one evil occurs.
As for the near-identical twin, Plantinga will grant you the logical possibility of such a twin, but what he won't grant you is that such a twin could coexist with the actual set of conditionals of free will that God finds. Plantinga's God doesn't set the conditionals of free will, so if such a twin couldn't coexist with the actual set of conditionals of free will, God can't create such a twin.
Mike:
I guess in general what Helga would have to do is to subscribe to some logic on which the following inference is invalid:
if q, then p
if ~q, then p
---------------
p
She can do this one of two ways (well, more than that if she wants to go really radical and deny modus ponens, but let's suppose she doesn't). Either she can deny LEM, or she can hold on to LEM but deny the following rule of inference:
if q, then p
if r, then p
-------------------
if q or r, then p
(LEM plus this rule of inference would yield the inference that she denies).
I am out of my depth here. Is there a plausible logic that denies bivalence, holds on to LEM, but renders invalid the above rule of inference? Maybe. In any case, I think the same points will apply--when such an obvious rule of inference is denied to save a position, we've gone where we shouldn't go.
Like most other mathematicians, I have no problems with actual infinites.
To show that it is logically possible that God and evil coexist, it suffices to describe logically possible circumstances in which God exists and at least one evil occurs.
As for the near-identical twin, Plantinga will grant you the logical possibility of such a twin, but what he won't grant you is that such a twin could coexist with the actual set of conditionals of free will that God finds. Plantinga's God doesn't set the conditionals of free will, so if such a twin couldn't coexist with the actual set of conditionals of free will, God can't create such a twin.
'Plantinga's argument depends only on it being possible that every creatable essence is TWD.'
If there are beings that do not choose evil, then how can it be possible that all beings choose evil?
Is the claim 'It is possible all sheep are white' consistent with the claim 'Some sheep are not white'?
And, of course, I already showed that even if every creature suffers from TWD, then God can easily create a near-identical twin of me, who does evil in some of the circumstances where I choose good, provided this near-identical twin chooses good in the occasions which actually do arise in my life.
And Plantinga's argument boils down to no more than that God cannot actualise a word in which a person chooses good in a particular set of circumstances - those circumstances include an omniscient being , who knows that the person will freely choose evil.
Conversely, if the state of affairs which exists when we make a free choice include an omniscient being who knows that we will freely choose good....
Well, I'll let you work out our counterfactuals of freedom in those circumstances.
Molinism is trivially true, which is why Plantinga always omits his alleged god when he describes the state of affairs which exists at each moment we make a choice.
Really, his claim is that this state of affairs is not even logically possible, let alone actualisible :-
1) We have a free choice between good and evil and there exists an omniscient being who knows that we will freely choose good.
But it is a logically possible state of affairs, and it you very, very carefully examine that logically possible state of affairs, you can deduce what our counterfactual of freedom would be, if that state of affairs ever obtained in the actual world.
'As for the near-identical twin, Plantinga will grant you the logical possibility of such a twin, but what he won't grant you is that such a twin could coexist with the actual set of conditionals of free will that God finds'
But the definition of that twin is that the twin has that actual set of conditionals.
And all beings have whatever counterfactuals of freedom that God needs.
Both of these states of affairs are logically possible (granted libertarian free will).
1) I have a choice between good and evil and there exists an omniscient being (not necessarily god) who knows I will freely choose good.
2) I have a choice between good and evil and there exists an omniscient being (not necessarily god) who knows I will freely choose evil.
Both states of affairs are logically possible.
Molinism is the doctrine that if you describe every state of affairs that is logically possible, then a being with libertarian free will chooses one particular way in each logically possible state of affairs.
Examine 1) and 2) and you will see that Molinism is true.
So there is a logically possible state of affairs where the being's counterfactual of freedom is that he will choose good.
Steven, for my money, these posts are way too long. I'll comment on the first two things you say,
If there are beings that do not choose evil, then how can it be possible that all beings choose evil?
You are confusing what IS the case with what MIGHT BE the case. The fact that some beings ACTUALLY do not choose evil entails nothing about whether they MIGHT choose evil.
Is the claim 'It is possible all sheep are white' consistent with the claim 'Some sheep are not white'?
Yes, of course it is.
Alex,
Supervaluation logics (of vagueness) deny bivalence and retain LEM. My guess (though I'd have to check it out) is that they invalidate your inference.
MIKE
The fact that some beings ACTUALLY do not choose evil entails nothing about whether they MIGHT choose evil.
CARR
SO Plantinga's TWS is a claim that a being MIGHT choose evil?
TWD is the claim that there is no fact of the matter about what the being would choose?
Perhaps you might want some background reading on the subject.
CARR
Is the claim 'It is possible all sheep are white' consistent with the claim 'Some sheep are not white'?
MIKE
Yes, of course it is.
CARR
Amazing.
How can that be?
How can Plantinga ever claim it is possible that all sheep are white, if he can see with his own eyes that some sheep are not white?
Presumably, a unipedalist would claim that it is possible that all human beings only have one leg, even if some human beings do have two legs.
And, of course, thanks to Plantinga, we simply deny that the statement 'Almost all human beings have two legs' is a LOGICAL inference from the fact that our evidence and senses tells us that Homo sapiens is a bipedal species.
MIKE
The fact that some beings ACTUALLY do not choose evil entails nothing about whether they MIGHT choose evil.
CARR
For some reason an omniscient God keeps being dropped from defense of the claim that evil refutes the prescence of an all-good, all-loving, all-powerful, all-knowing being.
If I asked God whether the Angel Gabriel will ever do evil, God will say no.
If an all-knowing God creates a being that he infallibly knows will never do evil in the world that was created, what sense does it make to say that that being might do evil in the world that was created?
Isn't God's knowledge infallible enough for you?
Of course, Plantinga claims that if God creates a being that he infallibly knows will never do evil in the world that was created, then that being will do evil on at least one occasion.......
ALEXANDER
'On the view I advocated for the open theist, it's appropriate to say: "In light of all the evidence, Jones will probably mow the lawn tomorrow, but it is false that Jones will mow the lawn tomorrow."
CARR
I'm confused.
Is that similar in structure to claiming 'All sheep will possibly be white tomorrow, but it is false that all sheep will be white tomorrow'?
No, it's more like claiming that probably all sheep will be white tomorrow, but it is not the case that they will be white tomorrow.
Steven, you write,
...Amazing. How can that be?
How can Plantinga ever claim it is possible that all sheep are white, if he can see with his own eyes that some sheep are not white?
I think you might have in mind epistemic possibility when you use 'possiblity'. Under some notions of epistemic possibility it is not possible that we discover that all sheep are white, given that we know that some are not. But Plantinga is clearly not using 'possiblity' that way. What AP has in mind is broad logical possiblity. And certainly it is broadly logically possible that all sheep are white, even granting that some sheep are in fact not white. It simply means that there is a possible world (a possible, non-actual world, that is) in which all sheep are white.
' It simply means that there is a possible world (a possible, non-actual world, that is) in which all sheep are white.'
So there is a possible non-actual world in which all beings are depraved, but it is not this world, where an alleged Heaven allegedly contains non-depraved beings?
So how does that help Plantinga refute the problem of evil?
Plantinga could defend the problem of evil, if we were in a different world?
Why not simply claim 'It is logically possible there is a defense against the problem of evil?'
The defense doesn't have to exist in our actual world, and apparently all Christians need is a logical possibility , and they are happy.
So why not simply claim 'It is logically possible there is a defense against the problem of evil?'
And , lo and behold, the problem of evil has been refuted.
So there is a possible non-actual world in which all beings are depraved, but it is not this world, where an alleged Heaven allegedly contains non-depraved beings? So how does that help Plantinga refute the problem of evil?
You've got to recall that Plantinga is responding to the logical problem of evil (not the evidential or probabilistic problem of evil). According to the logical problem of evil it is broadly logically impossible that God should exist along with any instance of evil. But to say that that is impossible is just to say that there is no possible world in which this occurs. That is the claim of those who defend the logical problem of evil, in particular John Mackie. In order to refute such a view, Plantinga need only show that there is such a possible, non-actual world. So, that's how it helps to point up that there is such a possible world.
So Plantinga claims that God actually has created beings that are not depraved, and that it is possible that all beings are depraved in all worlds that actually exist.
A bit like claiming that because there is a possible (non-actual) world in which all sheep are white, then possibly all sheep are white in all worlds which can be actualised.
Plantinga talks about 'reliable cognitive faculties'.
Are my cognitive faculties reliable if I claim that it is not possible that the Yankees won the World Series this year, because another team won it?
Presumably not , as there is a logically possible world in which the Yankees won the World Series....
I repeat my earlier question.
What should we call the leap from (1) I can see that almost everybody has two legs , to (2) It is a fact that almost everybody has two legs?
Is (2) a logical inference from (1)?
If not, then what is the best describing word for such an inference?
My English needs improvement. I cannot call the leap from (1) to (2) a logical inference, so I must call it a -blank- inference.
But what word goes in the -blank-?
Should I use the word 'rational'?
And why doesn't Plantinga simply claim 'It is logically possible there is a defense against the problem of evil?'
Why is that not , in itself, a defense against the logical problem of evil?
'According to the logical problem of evil it is broadly logically impossible that God should exist along with any instance of evil. But to say that that is impossible is just to say that there is no possible world in which this occurs.'
Doesn't Plantinga claim that God is a necessary being who is maximally good in all possible worlds?
In which case, doesn't Plantinga have to show that God and evil can co-exist in *all* possible worlds, not just one possible world?
Doesn't Plantinga claim that God is a necessary being who is maximally good in all possible worlds?
Yes
In which case, doesn't Plantinga have to show that God and evil can co-exist in *all* possible worlds, not just one possible world?
No, not to answer the logical problem of evil.
Steven,
The inference from your (1) to your (2) is a logically strict inference, because on the standard way of using the word "see", if one can see something, it is true, just as when we say someone knows something, we imply that the thing known is true. If by "see", however, you mean something weaker like "have an apparent perception" (which is compatible with hallucination), then the inference from (1) to (2) is probabilistic--if (1) holds, (2) is very likely.
'The inference from your (1) to your (2) is a logically strict inference, because on the standard way of using the word "see", if one can see something, it is true, just as when we say someone knows something, we imply that the thing known is true. '
If I see a bent stick in the water, I know that it is bent?
All seeing is 'apparent perception'.
A unipedalist would simply scoff at the idea of a 'probabilistic' inference.
http://ai.clm.org/articles/plantinga_advice.html
To use Plantinga's methods, what if there were 10 to the power 13 turps of evidence that people had two legs?
What would that prove? Nothing.
I have a properly basic belief that I have one leg, and no amount of evidence will convince me that everybody else has two legs (rather than a prosthetic leg)
Plantinga's defense against the logical problem of evil is the doomsday device of Christian apologetics, taking all rational thought with it.
And it doesn't even work, as , by definition, Molinism is a mere tautology.
Mike:
I don't think supervaluation helps get out of the argument for fatalism. Denying bivalence won't help if one holds on to LEM, because it is only LEM that the argument for fatalism needs.
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