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This is seriously messing up with my head. What is wrong with the response? The following generated by GPT4 seems reasonable to me Based on the given informat

This is seriously messing up with my head. What is wrong with the response? The following generated by GPT4 seems reasonable to me Based on the given information, we can use logical reasoning to determine if it rained today. The statement "If it rains today, I will drive home" can be represented as: Rains → Drive Home However, you mentioned that you did not drive home, which means the second part of the statement is false: ¬Drive Home In this case, we cannot definitively conclude whether it rained today or not. It is possible that it did not rain, or it rained, but you chose another mode of transportation for some reason.

spuz 3y ago
It messed with my head a lot as well. The answer is that it's not possible for ¬Drive Home AND Rains to be true. This is because if Rains were true, then due to the first implication, Drive Home must also be true. Therefore, if ¬Drive Home is true, then Rains must be false.
rayiner 3y ago
If the statement is true, the contrapositive is true: if !Drive Home -> !Rain. So provided with the fact that I didn’t drive home, you can infer it didn’t rain.
- PartiallyTyped 3y ago
  Your interpretation is wrong then. We have that rain -> drive home; here is the truth table. rain | drive | rain->drive home false| drive | true true | drive | drive Thus, the statement could be true, if you have driven home, but you did not provide such information. Just because something is on the right hand side of an implication doesn't make it true. The statement A=>B is true iff A is false, or A is true and B is true at the same time. Or alternatively, (not rain) || drive home rain | not rain | drive home | (not rain) || drive home true | false | true | true true | false | false | false false| true | true | true false| true | false | true So it is entirely possible to not have rained, and not to have driven home. The contrapositive is !drive home -> !rain (drive home) | rain | !(drive home) | !rain | !(drive home) -> !rain true | false| false | true | true true | true | false | false | true false | false| true | true | true false | true | true | false | false Thus whether the statement is true depends entirely on whether it rained; but you can not infer that as both options yield a true statement. This whole thread and chain is affirming the consequent. > In propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room"). > Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes. https://en.wikipedia.org/wiki/Affirming_the_consequent https://en.wikipedia.org/wiki/Affirming_the_consequent
  - jallen_dot_dev 3y ago
    Wouldn't that only be affirming the consequent if it were the following?: > If it rains, I drive home. I drove home. Therefore, it rained. <-- logical fallacy Because, for example, you could've driven home for some other reason. But that wasn't the statement. > If it rains, I drive home. I didn't drive home. Therefore, it didn't rain. How could it possibly have rained without violating the statement "If it rains, I drive home." given you didn't drive home?
    - PartiallyTyped 3y ago
      Ugh I messed up last night. GP is correct.
  - PartiallyTyped 3y ago
    This is false. I messed up last night when writing this. Sorry.

spuz 3y ago

It messed with my head a lot as well. The answer is that it's not possible for ¬Drive Home AND Rains to be true. This is because if Rains were true, then due to the first implication, Drive Home must also be true. Therefore, if ¬Drive Home is true, then Rains must be false.

rayiner 3y ago

If the statement is true, the contrapositive is true: if !Drive Home -> !Rain. So provided with the fact that I didn’t drive home, you can infer it didn’t rain.

PartiallyTyped 3y ago
Your interpretation is wrong then. We have that rain -> drive home; here is the truth table. rain | drive | rain->drive home false| drive | true true | drive | drive Thus, the statement could be true, if you have driven home, but you did not provide such information. Just because something is on the right hand side of an implication doesn't make it true. The statement A=>B is true iff A is false, or A is true and B is true at the same time. Or alternatively, (not rain) || drive home rain | not rain | drive home | (not rain) || drive home true | false | true | true true | false | false | false false| true | true | true false| true | false | true So it is entirely possible to not have rained, and not to have driven home. The contrapositive is !drive home -> !rain (drive home) | rain | !(drive home) | !rain | !(drive home) -> !rain true | false| false | true | true true | true | false | false | true false | false| true | true | true false | true | true | false | false Thus whether the statement is true depends entirely on whether it rained; but you can not infer that as both options yield a true statement. This whole thread and chain is affirming the consequent. > In propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room"). > Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes. https://en.wikipedia.org/wiki/Affirming_the_consequent https://en.wikipedia.org/wiki/Affirming_the_consequent
- jallen_dot_dev 3y ago
  Wouldn't that only be affirming the consequent if it were the following?: > If it rains, I drive home. I drove home. Therefore, it rained. <-- logical fallacy Because, for example, you could've driven home for some other reason. But that wasn't the statement. > If it rains, I drive home. I didn't drive home. Therefore, it didn't rain. How could it possibly have rained without violating the statement "If it rains, I drive home." given you didn't drive home?
  - PartiallyTyped 3y ago
    Ugh I messed up last night. GP is correct.
- PartiallyTyped 3y ago
  This is false. I messed up last night when writing this. Sorry.