- #1
NickJ
- 36
- 0
The following claims each strike me as intuitively plausible:
I. For any event e, if e occurs that it is possible that the laws of nature made it the case that e occurs.
(This is supposed to capture the intuition that it is possible for every happening to be law-governed. The laws of nature making something the case is understood to be an event/happening, like more ordinary events such as eggs breaking and toast burning.)
II. For any event e, if the laws of nature make it the case that e occurs, then e occurs.
(This is supposed to capture the intuition that the operator "the laws of nature make it the case that" is factive.)
III. For any events e1 and e2, if the laws of nature make it the case that both e1 and e2 occur, then the laws of nature make it the case that e1 occurs and the laws of nature make it the case that e2 occurs.
(This is supposed to capture the intuition that the operator "the laws of nature make it the case that" distributes over conjunctions.)
IV. There is at least one event e such that e occurs at some point in the history, present, or future of the world and it is not the case that the laws of nature make it the case that e occurs.
(This is supposed to capture the intuition that not everything is in fact governed by a law -- e.g., some happenings are chancy.)
Question #1: Do people agree that these are each intuitively plausible?
Here's the problem: These four claims are jointly inconsistent.
1. Assume that E is the event of a happening/ event occurring but not being made the case by the laws of nature. (instance of IV)
2. Then it is possible that the laws of nature make it the case that E. (from 1 and I)
3. Go to the nearest possible world in which the laws of nature make it the case that an event occurs but the laws of nature do not make it the case that such an event occurs.
4. Then, in that world, the laws of nature make it the case that the event occurs; and the laws of nature make it the case that the laws of nature do not make that event occur. (from 3 and III)
5. Hence, the laws of nature make it the case that the event occurs; and the laws of nature do not make it the case that the event occurs. (from 4 and II on the rightmost-conjunct of 4). Contradiction.
6. So there is no such possible world as the one mentioned in #3: it's an impossibility for the laws of nature to make it the case that an event occurs but the laws of nature do not make it the case that such an event occurs.
7. In other words, it's an impossibility for the laws of nature to make it the case that E occurs.
8. This contradicts the result derived at line #2.
9. Therefore, by modus tollens on I, there is not at least one event e such that e occurs at some point in the history, present, or future of the world and it is not the case that the laws of nature make it the case that e occurs. This contradicts IV.
Question #2: Is this reasoning valid? If not, what are the flaws? If so, which claim (I - IV) is it most plausible to reject and why?
I. For any event e, if e occurs that it is possible that the laws of nature made it the case that e occurs.
(This is supposed to capture the intuition that it is possible for every happening to be law-governed. The laws of nature making something the case is understood to be an event/happening, like more ordinary events such as eggs breaking and toast burning.)
II. For any event e, if the laws of nature make it the case that e occurs, then e occurs.
(This is supposed to capture the intuition that the operator "the laws of nature make it the case that" is factive.)
III. For any events e1 and e2, if the laws of nature make it the case that both e1 and e2 occur, then the laws of nature make it the case that e1 occurs and the laws of nature make it the case that e2 occurs.
(This is supposed to capture the intuition that the operator "the laws of nature make it the case that" distributes over conjunctions.)
IV. There is at least one event e such that e occurs at some point in the history, present, or future of the world and it is not the case that the laws of nature make it the case that e occurs.
(This is supposed to capture the intuition that not everything is in fact governed by a law -- e.g., some happenings are chancy.)
Question #1: Do people agree that these are each intuitively plausible?
Here's the problem: These four claims are jointly inconsistent.
1. Assume that E is the event of a happening/ event occurring but not being made the case by the laws of nature. (instance of IV)
2. Then it is possible that the laws of nature make it the case that E. (from 1 and I)
3. Go to the nearest possible world in which the laws of nature make it the case that an event occurs but the laws of nature do not make it the case that such an event occurs.
4. Then, in that world, the laws of nature make it the case that the event occurs; and the laws of nature make it the case that the laws of nature do not make that event occur. (from 3 and III)
5. Hence, the laws of nature make it the case that the event occurs; and the laws of nature do not make it the case that the event occurs. (from 4 and II on the rightmost-conjunct of 4). Contradiction.
6. So there is no such possible world as the one mentioned in #3: it's an impossibility for the laws of nature to make it the case that an event occurs but the laws of nature do not make it the case that such an event occurs.
7. In other words, it's an impossibility for the laws of nature to make it the case that E occurs.
8. This contradicts the result derived at line #2.
9. Therefore, by modus tollens on I, there is not at least one event e such that e occurs at some point in the history, present, or future of the world and it is not the case that the laws of nature make it the case that e occurs. This contradicts IV.
Question #2: Is this reasoning valid? If not, what are the flaws? If so, which claim (I - IV) is it most plausible to reject and why?