Is “Might” the Opposite of “Will Not”? Some Rough Thoughts

Rachel Held Evans has a nice Q & A with Greg Boyd where he is asked to explain features of his Open Theism. Among the parts that interested me is this excerpt.

Philosophers and theologians have often defined “divine omniscience” as “God’s knowledge of the truth value of all meaningful propositions.” I completely agree with this. Unfortunately, they typically assumed that propositions about what “will” and “will not” occur exhaust the field of meaningful propositions about the future.  They thus concluded that God eternal knows all that will and will not take place and that there is nothing else for God to know.  

This is a mistake, however, because propositions about what “might and might not” take place are also meaningful, and God must therefore know the truth value of these. Moreover, the opposite of “might” is “will not,” and the opposite of “might not” is “will.”  So, if a “might and might not” proposition is true, then the corresponding propositions about what “will” and “will not” take place are both false. For example, if its true that “Greg might and might not buy a blue Honda in 2016,” then its false that “Greg will (certainly) buy a blue Honda in 2016” and false that “Greg will (certainly) not buy a blue Honda in 2016.” So too, if it ever becomes true that “Greg will (certainly) buy a blue Honda in 2016” or true that “Greg will (certainly) not buy a blue Honda in 2016,” then it will be false that “Greg might and might not buy a blue Honda in 2016.”  And since God knows the truth value of all propositions, God would know precisely when it is true that I “might and might not” buy this car and when it becomes true that I either “will” or “will not.”  God thus faces a partly open future.

This is controversial. Why assume that statements about what “might” happen contradict those about “will not”?  It seems this sort of statement is meaningful too: “I could run through the streets naked in the next 5 minutes, but I will not. The “could” here expresses the possibility of those (terrible) states of affairs, and the “will not” expresses that they shall not come to pass, owing to my rational choice. There is nothing contradictory about saying this sort of thing, but the semantic analysis Boyd gives of “might” would make it so. Thus, we have reason to doubt his analysis. Continue reading

On Counting (countable) Infinite Sets

Computability and LogicThis is an especially vivid illustration from the third edition of Boolos and Jeffrey’s Computability and Logic:

If a set is enumerable, Zeus can enumerate it in one second by writing out an infinite list faster and faster. He spends 1/2 second writing the first entry in the list; 1/4 second writing the second entry; 1/8 second writing the third; and in general, he writes each entry in half the time he spent on its predecessor. At no point during the one second interval has he written out the whole list, but when one second has passed, the list is compete!

Pg. 14.

Are Environmentalism & Animal Liberationism Incompatible?

An argument:

  1. One can be an environmentalist and an animal liberationist (premise for reductio).

  2. If animals ought to be protected from being killed (because they can feel pain, ect.) then the natural environments in which their lives are at risk ought to be reformed or eliminated (from liberationism).

  3. The natural environments in which their lives are at risk ought to not be reformed nor eliminated (from environmentalism).

  4. Therefore, it is not the case that one can be both an environmentalist and an animal liberationist (from 1, 2, 3).

  5. Therefore, one can only be an an environmentalist or only an animal liberationist (or neither) (from 4).

This sort of argument was spelled out in greater detail by Mark Sagoff, and it is an interesting one. Given their criteria of value (the ability to feel pain gives one moral status), animal liberationists ought to intervene in ecologies where sentient creatures are naturally harmed. That is to say, there is no good reason for letting such animals die in their natural habitats; indeed, one seems required to act for the same reason  that requires one to protect children from grizzly bears–suffering ought to be prevented. Conversely, an environmentalists, who primarily values things like wilderness or biodiversity, has reasons not to protect animals in the wild (unless they are endangered): these environmental goods take precedence over the interests and welfare of animals. Thus, it seems environmentalists are interested in preserving states of affairs that, for many animals, are nasty, brutish, and short.

It’s not clear to me if Sagoff personally believes this, but he seems aware that this sort of argument constitutes a reductio of the animal liberationists position. I tend to agree with this… what does Peter Singer think of lions, tigers, and bears? If anything, premise two seems to be the most vulnerable, and it would be prudent to revise it to say “animals under our care ought to be protected from being killed…” But some justification for circumscribing the animal kingdom this way needs to be given, and it isn’t obvious that it will be compatible with the primary values of animal liberationism.

Is Certainty Necessary for Knowledge?

The answer is “no.” Consider the argument from Jason Stanley’s Knowledge and Certainty:

“If knowing a proposition requires that proposition to be true, we would expect (7) to sound like an assertion of a trivial conceptual truth and (8) to sound like an assertion of an obvious falsity:

“(7) Everything anyone knows is true.
“(8) There is something someone knows that isn’t true.

“(7) is obviously true, and (8) obviously false. Similarly, if knowing a proposition requires believing that proposition, then we should expect (9) to be a trivial truth and (10) to be obviously false:

“(9) Everything someone knows she believes.
“(10) There is something someone knows that she doesn’t believe.

“Finally, if knowing a proposition requires having evidence for that proposition, we would expect (11) to sound like a trivial truth and (12) to sound obviously false:

“(11) If someone knows something, she has a reason to believe it.
“(12) There is something someone knows that she doesn’t have any reason to believe.

“An assertion of (11) certainly seems true, and (12) seems false. If it is intuitively obvious that knowledge requires subjective certainty, we should expect (13) and (14) to seem like banal truths and (15) to seem obviously false:

“(13) I’m certain of everything I know.
“(14) Everyone is certain of everything she knows.
“(15) There are some things I know, of which I’m only fairly certain.

“However, (13) and (14), unlike (7), (9), and (11), do not sound like banal truths. An utterance of (15) also does not share the obvious sense of falsity of (8), (10), and (12). Similarly, if knowledge requires epistemic certainty, we should expect (16) to be a banal truth, on a par with (7) and (9), and we should expect (17) to seem clearly false, on a par with (8), (10), and (12):

“(16) Everything I know is certain to be true.
“(17) There are some things I know, which are only fairly certain to be
true.

“But (16) does not seem like a banal truth, and (17) seems perfectly in order.”

From page 4 (37). Here’s more:

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Why No 5K to Save the Zygotes?

In the manner of explaining why she lost faith in the pro-life movement, Libby Anne says this sort of argument made an impression on her:

Due to hormone imbalances, genetic anomalies, and a number of unknown factors, between 50 percent and 75 percent of embryos fail to implant in the uterus and are passed with the monthly menstrual flow. If we agree with pro-life advocates that every embryo is as morally valuable as an adult human, this means that more than half of humans immediately die. This fact provides pro-life advocates with an opportunity to follow through on their convictions. Surely, a moral response to a pandemic of this magnitude would be to rally the scientific community to devote the vast majority of its efforts to better understanding why this happens and trying to stop it. Yet the same pro-life leaders who declare that every embryo is morally equivalent to a fully developed child have done nothing to advocate such research. … Even if medicine could save only 10 percent of these embryos — and we don’t know because no one has cared enough to ask — it would be saving more lives than curing HIV, diabetes, and malaria combined. One could say that this massive loss of human life is natural, and therefore, humans are under no obligation to end it. But it is not clear why the same argument could not be used to justify complacency in the face of AIDS, cancer, heart disease, and other natural causes of human death.

The above paragraph is from Jonathan Dudley’s Broken Words: The Abuse of Science and Faith in American Politics. I think this is an interesting argument; it can be stated more formally like this:

[1] If the pro-life movement were morally consistent, it would advocate for research to mitigate the loss of human life naturally lost in the womb [premise].

[2] The pro-life movement fails to do this [premise].

[3] Therefore, pro-life movement is morally inconsistent [MT 1, 2].

Suppose this is right. Then the pro-life movement should make an effort to advocate for research to be morally consistent. But so what? That just says something about what the pro-life movement fails to do; it doesn’t say anything about the truth of what the pro-life movement believes about the human embryo, which is what ultimately matters.

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Molinism and the Grounding Objection

Since I am attracted to the theory of middle knowledge (Molinism) as a way of reconciling God’s providence/foreknowledge and human freedom, I face the primary objection to the theory: the grounding objection. The grounding objection can be stated like this:

According to the argument, there appears to be no good answer to the question of what grounds the truth of counterfactuals of creaturely freedom. They cannot be grounded in God because determinism would follow—the necessity of God’s being or His will would transfer to the counterfactuals. Additionally, the prevolitional character of middle knowledge speaks against grounding counterfactuals of creaturely freedom in the will of God.

First, what is a counterfactual of creaturely freedom (CCF)? They are statements that take the form “If it were the case that x was in circumstances C, then X would perform action A.” The classic CCF Molina liked to discuss was Peter’s denial, which might be styled like so: “If it were the case that Peter was in the circumstances described by Luke 22:54-56, then Peter would deny Christ” (call this P).

Second, Molina believed that God knew the truth value of P, “before” God created the world. But how? If Peter’s choice is not causally determined by God or physical substances in creation, then it seems that there nothing that makes P true. It seems that their needs to be something that exists to determine the fact of the matter. A professor of mine spells this ‘truth-maker assumption’ out more formally:

(TA): Necessarily, for any proposition p, if p is contingently true then there are some xs such that, necessarily, if the xs exist then p is true (Crisp, 2007:90).

But why believe (TA)? After all, there is nothing that exists that grounds the truth value of the claim, “There are no unicorns.” Perhaps a reply would be that there exists a null set of states of affairs in which unicorns are a constituent, and the existence of this null set is what grounds the truth of the claim “There are no unicorns.” Perhaps, then, sets of states of affairs do the work.

Nonetheless, it seems that the Molinist has a way out. My reading of Alfred Freddoso and Thomas Flint deploys the following strategy that reasons from cases we are likely to judge to be true. The enumerated points state the necessary and sufficient conditions of what it takes for a truth claim to be grounded.

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A Correction to a Penal Substitution Syllogism

I came across this syllogism by Tom Schreiner in his chapter on penal substitution in the IVP 4 views book on the atonement. It goes like this:

[1] One must obey the law perfectly to be saved.

[2] No one keeps the law perfectly.

[3] Therefore, those who rely on the works of the law to be saved stand under God’s curse.

But this is invalid. Here’s how the first two premises look more formally

[1] Necessarily, for any x, if x obeys the law perfectly, then x will be saved.

[2] There is no x such that x obeys the law perfectly.

It does not follow from these two premises that [3] those who rely on the works of the law to be saved stand under God’s curse. For if someone were to rely on it and obey it perfectly, they would be saved. That is just what premise [1] claims. Instead, the argument should look like this:

[1*] Anyone will be saved who obeys the law perfectly.

[2] No one keeps the law perfectly.

[3*] Therefore, no one will be saved.

Nonetheless, [3*] is not equivalent with

[3] Those who rely on the works of the law to be saved stand under God’s curse.

For it is not the case that

[4] No one will be saved if and only if those who rely on the works of the law to be saved stand under God’s curse.

Premise [4] is a conjunction of which one of the conjuncts contains:

[5] If those who rely on the works of the law to be saved stand under God’s curse, then no one will be saved.

And [5], according to Galatians, is obviously false. The antecedent is true and the consequent is false, because there are some who are saved by virtue of faith in Christ. Perhaps what is needed to get to make [3] equivalent with [3*] is another premise that states, “If everyone relies on the works of the law to be saved and not on Christ, then no one will be saved.” That would do the trick, but then that seems to be precisely what Paul is arguing for, so to assume this premise would make the argument circular. But at least it would not be invalid (circular arguments are true after all).

UPDATE: A Correction to “A Correction to a Penal Substitution Syllogism”

In the text above, I contended that the the first premise read like this:

[1] Necessarily, for any x, if x obeys the law perfectly, then x will be saved.

But I was wrong. After reading it more carefully, it actually reads like this:

[1] Necessarily for any x, x is saved only if x obeys the law perfectly.

Premise [2] is still right:

[2] There is no x such that x obeys the law perfectly.

Thus, it still doesn’t follow that

[3] Those who rely on the works of the law to be saved stand under God’s curse.

All that follows is

[3*] No one is saved (that is, there is no x such that x is saved).

And I still think it is right to say that [3*] is not equivalent with [3], but upon further reflection I don’t see how to make [3*] equivalent with [3], so I retract the rest of what I say in the original post.

An Elegant Argument for the Compatibility of Divine Foreknowledge and Human Freedom

I came across this in a paper by Ted Warfield and I thought it was an elegant proof for the claim that God’s foreknowledge of the future is compatible with human freedom. The argument goes like this:

  1. Plantinga will freely climb Mount Rushmore in 2000 AD.
  2. It was true in 50 AD that Plantinga will climb Mount Rushmore in 2000 AD.
  3. God exists in all possible worlds and is omniscient in all possible worlds.
  4. God knew in 50 AD that Plantinga will climb Mount Rushmore in 2000 AD.

If premise [3] is true, then premise [2] is logically equivalent with premise [4]. And it follows that if [3] is true, then [4] is compatible with [1]. Thus there is a view of God and omniscience on which divine foreknowledge and human freedom are compatible.

The upshot: the necessity of the past (or ‘accidental necessity’ as it is sometimes called) does not nullify Plantinga’s freedom (even in the libertarian sense) to choose to climb Mount Rushmore in 2000 AD.

An Argument for Personhood from Conception

An argument for full human personhood from the moment of conception:

  1. An adult human being is the end result of the continuous growth of the organism from conception.
  2. At no point, from conception to adulthood, is there a change in the essential nature of the fetus from non-person to person.
  3. Therefore, one is a person from the point of conception onward.

Adapted from Moral Choices by Scott Rae.

A Response to Theological Fatalism

I had the privilege of taking a class with William Lane Craig on divine omniscience this past January and he had us respond to this argument by the Open Theist philosopher William Hasker:

  1. It is now true that Clarence will have a cheese omelet for breakfast tomorrow. (Premise)
  2. It is impossible that God should at any time believe what is false, or fail to believe anything that is true. (Premise: divine omniscience)
  3. God has always believed that Clarence will have a cheese omelet tomorrow. (From 1, 2)
  4. If God has always believed a certain thing, it is not in anyone’s power to bring it about that God has not always believed that thing. (Premise: the unalterability of the past)
  5. Therefore, it is not in Clarence’s power to bring it about that God has not always believed that he would have a cheese omelet for breakfast. (From 3, 4)
  6. It is not possible for it to be true both that God has always believed that Clarence would have a cheese omelet for breakfast, and that he does not in fact have one. (from 2)
  7. Therefore, it is not in Clarence’s power to refrain from having a cheese omelet for breakfast tomorrow. (From 5, 6) So Clarence’s eating the omelet tomorrow is not an act of free choice. (From the definition of free will.)

One can find it in both Hasker’s God, Time, and Knowledge and his contribution to The Openness of God. Interestingly enough, this is popular with some Calvinists who cite it as a simple logical refutation of the Arminian theory of simple foreknowledge. But I think it’s too simple. It should be noted that my response is largely an adaptation of what I learned in Dr. Craig’s class.

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