What nobody has been willing to put into words is 1 nuance:
For a natural system like the human brain that is fairly stable, and to a large degree predictable, a person remarkably free from the determinism of natural causation would look:
Respectfully, I do not think this nuance has been overlooked. It’s been articulated in different words, but the idea that causal independence might be indistinguishable from randomness has certainly been said more than once, by multiple participants. That to speak of wholly undetermined acts as “willfull” or “under [the agent’s] control” would fail to capture usual intuitions associated with such language has also been clearly pointed out. The point itself is valid, but it is not the case that it had been overlooked until your voicing it just now.
Not really. True, if I eat only waffles tomorrow, I cannot have also eaten eggs. However, it remains the case that I could have eaten eggs. In that sense, there is more than one alternative.
Again, I am not conceiving of an omniscient being as one who can infallibly predict the future from present and past conditions. I am conceiving it as one who can directly apprehend the future in much the same way we can directly apprehend the present. This is a common conception of God: As a being who exists “outside of time”, meaning the past, present and future are all equally knowable and accessible to him. To that extent, then, such omniscience is metaphysically possible.
A consequence of this is that, if future events can be known by such a being, it is no more an argument against libertarian free will than is the fact that past events can be known by you and I.
If there is no causation in general, what use could free will possibly be, since choice necessarily involves causation by the choice of the chosen course of action? Yes, the prediction must be caused by the facts predicted; there must be some form of time travel, whether of material or information.
The subject must remain insulated from the prediction, or there could be a temporal paradox. If you have a choice between chalk or cheese, and I see that you will choose chalk and tell you so, you could decide to falsify my prediction by choosing cheese instead. In which case I would see that you will choose cheese and tell you so, and you could decide to falsify my prediction, and round and round we go. But that’s not a problem for libertarian free will, just for the integrity of time.
I’m not seeing the problem for libertarian free will in your subsequent scenario. I don’t see why any of this implies the subject’s choice causing everything or causation being in general transitive. Nor do I see a bullet that needs biting.
Perhaps I misread the conversation. I was under the impression that we were talking about conditions under which libertarian free will could or could not exist.
The conjecture that libertarian free will is less than entirely ruled out if retro-causation is permitted I propose requires that one first permit causation more generally. If you concur, then we can grant/assume causation and retro-causation for the sake of argument and consider how it would or would not permit free will given that which events occur is a matter of fact. Or, if you concur, we could dismiss causation for the sake of argument, and look for an argument as to how libertarian free will is possible given that infallible knowledge of events is possible without being causally produced. If you do not concur that retro-causation requires causation, then I’ll humbly ask for a clarification of how you mean each, just to see how the entailment does not hold.
What “use” libertarian free will has appears to me an entirely unrelated question, and that’s all I have to say on the subject at least until we make explicit that we wish to disengage with the topic already under discussion, and move on instead to the utility of libertarian free will with and without causation.
I’m not sure how to respond to this. You seem to just not entertain what is meant by infallibility here. Saying someone knows infallibly that the statement “You will eat waffles tomorrow” maps to the truth-value TRUE is a way of saying that there exists no possible world in which their knowledge of that specific mapping is incorrect. It is therefore not the case that there exists any possible world, wherein that statement maps to FALSE.
I would agree that retro-causation requires that causation exists, just as green frogs require that frogs exist, but that’s the only thing I understand of what you just said.
“Use” was perhaps the wrong word. But it seems to me that free will has no meaning unless it causes something, i.e. a choice. If causation doesn’t exist, free will can’t exist either.
I think Faizal is arguing along the lines of the Boethian view of divine time. From God’s perspective, the statement “You will eat waffles tomorrow” is meaningless, because there is no “tomorrow” for God. The statement that he believes would instead be “You eat waffles on 25 May 2024” which is not dependent on tensed language.
Likewise, God can know what your choices are without contradicting free will, because (for example) he knows the proposition “You freely choose to drink coffee rather than tea at 19:33:18 on 24 May 2024” to be true. He doesn’t know this to be true before the choice is made, because God views all events as an ever-constant present, and “before” has no significant meaning to him.
I don’t necessarily hold to a Boethian view of divine (a)temporality, nor do I think it solves the fundamental contradiction of LFW, but it does solve this ‘contradiction’.
Perhaps I was uncautious to continue in the use of “tomorrow”. Though I think my argument holds even without the tensed (and in slightly more formal) language:
Let A be the proposition that some state of affairs a is assumed at some time t. Libertarian free will requires that, if A holding is a matter of an act of volition, there must exist at least one possible world where A holds, and at least one possible world where it does not – for only then can one choose which of them to render the actual world when the time comes, as perceived from within time. If A is known by an entity P infallibly, then it is the case that A is believed by P in all possible worlds, but it is not the case that there exists a possible world where P is incorrect about their belief that A holds. Therefore, there exists no possible world where A does not hold. Because the existence of at least one such world is a necessary condition for the existence of libertarian free will regarding A, however, libertarian free will regarding A, is precluded. If there exists a being who knows all propositions linking states of affairs to points in time, then libertarian free will is (by iteration on the argument so far) precluded regarding all such propositions.
This would seem to be a flaw in your argument, possibly due to a strange definition of “infallibly”. I don’t see why it wouldn’t work that A is believed by P in those worlds in which A is true and not-A is believed by P in those worlds in which A is false.
I would also disagree with your definition of infallible belief. An infallible belief is one which certainly corresponds to reality, not one which is true in all possible worlds. There is a possible world where I don’t exist, but that doesn’t mean that God’s belief that I exist is fallible.
Indeed, I was expecting this sort of objection when formalizing my argument. There is however a reason I stuck with my definition. First, let’s lay them out with some precision. Again, I am foregoing sufficiency criteria, because for the sake of the argument at hand it does not matter whether we can conclude that a being has the knowledge, but rather we seek to investigate the consequences of the premise that it does. It is therefore enough to specify what knowledge entails, but not what entails knowledge. In that sense, here is my definition, and the suggested alternative, in that order:
Definition 1: Entity P is said to “infallibly know” proposition A only if in every possible world W: P believes A in W and A holds in W.
Definition 2: Entity P is said to “infallibly know” proposition A only if in every possible world W: P believes A in W if A holds in W, and P believes non-A in W if non-A holds in W.
Now, this may come down to a matter of personal intuition. Consider, however:
If we say that P knows A, this usually entails P believing A, and that A is true. When we want instead to express that P is correct in its belief without ourselves committing to voicing one, we say something like “What P believes about the truthfulness of A does match the truthfulness of A”.
To me it seems counter-intuitive to say that adding infallibility forces us into the latter meaning, as per Def. 2. If “P infallibly knows A” only means that P is correct about A in all possible worlds, then the statement “P infallibly knows A” is equivalent to the statement “P infallibly knows non-A”. An alternative formulation of the problem is that under Def. 2 there can be a world where the statement “P infallibly knows A and A is false” holds. Plainly said, by Def. 2, “infallible knowledge” is not a subcategory of “knowledge” anymore.
Under Def. 1, “infallible knowledge” is a form of “knowledge”, but what we pay for that inclusion is that “infallible knowledge” can only apply to necessary statements.
Obviously, since definitions are a matter of convention, I have no argument for why one is objectively better or worse than another. I personally find it more intuitive to define infallible knowledge as a kind of knowledge which can only apply to a subset of all considerable propositions, than as something that applies ot all considerable propositions but is not really a kind of knowledge.
If we take knowledge as “justified true belief” then the phrase “P infallibly knows A” cannot speak to the truth of A but instead indicates that the justification for the belief is itself infallible. Which is different from both your alternatives.
I don’t think it generally implies that ~A is impossible in the sense of possible world semantics, any more than the truth of any statement makes its negation impossible in that sense.
How is this different from both my alternatives? Either “P infallibly knows A” implies that “P knows A” or it does not. If it does, and knowledge is justified true belief, then “P infallibly knows A” implies “P knows A”, which in turn implies A. If it does not, then there exists a possible world where “P infallibly knows A” is true and A is false.
You are suggesting definitions that looks something like this:
Definition 3: Entity P is said to “infallibly know” proposition A only if in every possible world W: P has an adequate justification to believe A.
Definition 4: Entity P is said to “infallibly know” proposition A only if in every possible world W: P has an adequate justification in W for P’s opinion in W on the truthfulness of A in W.
Definition 5: Entity P is said to “infallibly know” proposition A only if in every possible world W: P has an adequate justification in W to believe A in W if A holds in W or to believe non-A in W if A does not hold in W.
None of these definitions entail A being true or false in any one particular world, that much I concede. However, let us now assume that “P infallilbly knows A” by any of these definitions. Because infallible knowledge only means having infallible justification (either for the truth of the statement or for one’s own belief about such, or for a correct belief concerning the statement), there now exists one or more possible world for each of the following scenarios:
Which ever ‘infallible knowledge means infallible access to justification’ definition we go with, there remains one or more possible world W, where the statement “P infallibly knows A” holds, but “P knows A” does not.
Much as layed out in less structured form before, our choice here is between only three options:
It differs in that it addresses “infallibility” without bringing in possible worlds.
Neither is correct.
Try this:
If “P infallibly knows A” then P believes A and P has an infallible justification for believing A.
It does not imply that P knows A in all possible worlds - or even in all possible worlds where A is true. It certainly does not imply that P infallibly knows ~A in any possible world
(If A may be absolutely proven in some - but not all - cases A would be infallibly known when the proof succeeded. But if the proof failed it would not be proof of ~A)
I disagree - infallible knowledge - like knowledge - carries an implication of truth, but not necessary truth. 2 is likely true for humans but only because of the difficulty of finding an infallible justification.
Not true in any reasonable sense. You’re trying to sum P over all possible worlds, but neither statement applies to all possible worlds. The correct statement would be "P infallibly knows either A or not-A, depending on what world P is in. (And I have to say that all this formalism obfuscates more than it clarifies.)
That formulation would seem to be wrong and contradictory to definition 2 as well as definition 1. So I’m not getting your argument at all.
This again comes down to intuitions, I’m afraid. To me, the term “infallible” connotes a statement about the (im)possibility of failure. I would not try to attempt formalizing this without the modal logic toolkit. If J is an “infallible justification”, then either it is a “justification” that does not fail in any possible world, or it is not a “justification” but something else entirely.
Definitions 3-5 offer a handful interpretations of the former sort, but if you wish to suggest something else yet, and argue that it captures what a reasonable user of the English language would typically mean to express by using these words, by all means, please do.
This is fair. I was attempting to formalize, specifically “infallibly knows”. What you are suggesting is something more akin to “P is infallible in P’s knowledge regarding A, and also P knows the truth-value of A”. This would be yet another definition, namely one that equates “infallibly knowing” with (something akin to) “being infallible and also knowing”. Indeed, my conclusion would not follow under a definition like this.
My point is that knowing A already entails the truth of A, and infallibly knowing A adds nothing to that. I don’t see how modal logic is either necessary or useful in this case. There is no possible world where P infallibly knows A and A is not true. But the same is true if P simply knows A. Infallible knowledge and knowledge are exactly the same from that perspective.
If we run a few rounds of a Miller-Rabin primality test we can be certain that a number which fails is not prime but if it passes we can’t know for sure that it IS prime. So we could infallibly know that a number is not prime in the possible worlds where it failed the test, but we wouldn’t in possible worlds where the number passed the tests or the tests were not run.
You have entirely lost me.
I am not familiar with the term “Boethian”. But, yes, that is exactly what I mean.
IOW, if I had waffles for breakfast on Tuesday morning, an omniscient being would know that I had waffles for breakfast on Tuesday morning. And if I didn’t have waffles for breakfast on Tuesday morning, an omniscient being would know that I didn’t have waffles for breakfast on Tuesday morning.
That seems just fine to me. I would agree with that definition. What is the problem?
Hmm. “Definition 2 : Entity P is said to ‘infallibly know’ proposition A only if in every possible world W: P believes A in W if A holds in W, and P believes non-A in W if non-A holds in W” (emphasis added) .
Doesn’t the last phrase contradict what you just claimed?
100%
If so, I do not see how.
Suppose P infallibly knows A. The definition specifies that infallibly knowing is a statement about all possible worlds, namely that P believes what ever is true about A in all possible worlds. Therefore, if we assume that P believes what ever is true in all possible worlds, then they believe that A is false in one possible world W, wherein A is false.
It is only a contradiction, if we say that “infallibly knowing that A holds” implies “knowing A holds”, but by Def. 2 it does not. That was my entire point. That if we define infallibly knowing in a way that still permits for the infallibly known statement itself to be false in some possible worlds, then that costs us the ability to infer knowing from infallible knowing, which… well, for lack of a better argument, feels weird.
One could, of course, construct one (arguably somewhat artificial) remedy for this, in this way:
Definition 6: Entity P is said to ‘infallibly know’ proposition A only if A is true, and in all possible worlds W: P in W has knowledge of the truth-value of A in W.
This is, basically, Definition 2 + a stipulation that A is true in the world whence the statement is made. This satisfies the possibility for A to be false, maintains P’s knowledge about A in all possible worlds. The price paid for this, is that now the statement “P infallibly knows A” can only be true in worlds where A holds. In a world where it does not, they may know that it does not hold, but they cannot have infallible knowledge of A’s truth-value, because we have defined infallible knowledge as including the truth of the proposition in question. They can, however, know that not-A in such worlds, interestingly enough.
Now that I think about it, perhaps this is a more sensible interpretation than I figured so far… 