This is a very simple problem, but unfortunately it seems very difficult for most people to get correct. The typical result is that approximately 7% of the testers get the correct answer.
Problem 2:
Now consider the same problem with the inclusion of rule #2 and with the additional truth that rule #1 & rule #2 are mutually exclusive (that is, they cannot both be true at the same time).
Rule #2, "If a card has "K" on one side, then it will have a "3" on
the other side."
Question 2. Which cards and only which cards do you need to turn over
to verify rule #1 & rule #2?
Answer: You need to turn over the "D" card to make sure that there is nothing other than a "3" there that would refute rule #1, and you need to turn over the "K" card to make sure that there is nothing other than a "3" there that would refute rule #2, and you would need to turn over the "7" to make sure that there is no "D" or "K" that would refute either rule 1 or rule 2.
Again, the "3" card is irrelevant. The "D" card either has a "3" on the other side of it or it doesn't. The result will either refute rule 1 or tend to confirm it. Likewise, the "K" either has a "3" on the other side or it doesn't. The "7" either has a "D" or "K" on the other side or it doesn't, therefore if the rules are not refuted by the cards that can refute the rules then the rules must be true.
Question 3: If you turned over card "3" only and you find a "K", would
this refute rule #1?
Answer: No. You can still turn over the "K" card and find a "9" or turn over the "7" card and find a "K", so since rule 2 isn't proven true, then rule 1 is not excluded simply because they cannot both be true.
Question 4: If you turned over the "D" and found a "3" and turned over the "3" and found a "D", would this
refute rule #2?
Answer: No, you can still turn over the "7" and find a "D" which means that rule 1 is not proven true so that does not eliminate rule 2 from being true.
Question 5: How many rules can be refuted at any given instance?
Answer: Two. The "D" can have a non-"3" on the other side, as can the "K" card. (And the "7" can refute either as well).
Question 6: If rule #1 is refuted, does this mean that rule #2 is true?
Answer: No. Rules 1 & 2 are mutually exclusive and therefore cannot both be true, but they can both be false. (They are contrary, not contradictory. "Contradictory" would means that one of the two, but not both, must be true. "It is raining; it is not raining" is an example of contradictory because it is subject to the tautology "It is either raining or it isn't").
Question 7: If a rule is shown in two ways to be true and in one way to be false, what does this mean regarding that rule?
Answer: It means that it is refuted. I can see a thousand naturally black ravens and one naturally blue raven and the idea that all ravens are naturally black would be refuted. "True and false" ARE NOT SYMMETRIC CONSIDERATIONS. The idea that 'true and false' implies symmetry is a common misunderstanding. This means that all scientific laws and theories as they apply to future events (and are thus inductive) cannot be conclusively proven true, they can only be regionally confirmed true until someone finds a "card" that refutes the rule (in this case a scientific law or theory). The refutation is conclusive, which means that the scientific law or theory goes from being inductively confirmed true to deductively concluded false.
Relativists, postmodernists, and phenomenologists tend to make much more adu about this "uncertainty" than is actually warranted. Some "uncertainty" is less trivial than others. The chance that 2 + 2 = 4 might be refuted or that 'A = A' might be refuted is so trivial as to be laughable.
Question 8: By simply seeing the upside face of the "3" card (and not knowing what is on the other side), what does this tell us about rules 1 & 2?
Answer: It doesn't tell us anything about rules 1 & 2. This is why affirming the consequent in a material conditional is not deductively valid. This is why determining that an argument's conclusion is 'true' cannot prove true that argument's premises. A valid argument can have a false premise and a true conclusion (the conclusion can be true by accident).
Question 9: What does the "3" card metaphorically correspond to?
Answer: The "3" card represents EVERY "complexity" and "fine tuned universe" and "single cells seem designed" and "standing slack-jawed gawking at the universe"
so-called argument any theist, spiritualist, mystic-minded supernaturalist ever devised. It represents every "confirming the consequent" illogic that has ever been proposed that is supposed to have meaning but doesn't.
Theists often create a sort of converse thinking that is logically invalid. In other words, they think that "If X then Z" is the same as "If Z then X" when actually the counterfactual to "If X then Z" is "If not-Z, then not-X". (This is why the answer to problem 1 was "D" and "7". Rule 1 states that "If "D" is on one side then "3" is on the other side of the card". The counterfactual to this is "If there a non-"3" on one side, then there is a non-"D" on the other side". When a rule is true, the counterfactual will be true too.)
They think that affirming the consequent is meaningful and deductive.
They think that interpreting existence as a "conclusion" of "creation" or "design" as an effect qualifies them to presume a non-demonstrable premise of 'god' or 'creator' or "intelligent designer" as true. They think that an argument's conclusion can prove true that argument's premise. Theists are illogical and typically think poorly.
Question 10: What does the "7" represent?
Answer: The "7" card represents the refutability of meaningful questions. (the "D" and the "K" can refute as well of course.)
The seven is a counterintuitive means of refuting though, which is an important psychological and logical lesson and makes this "lesson" worth while.
The "4-card problem" is deductive because it is a closed set, but most considerations in the 'real world' are inductive open sets. What if this problem was the "perhaps unlimited number of cards" problem?
Question 11: How would this (open set) condition affect the problems we are considering? How would it affect the meaning of "D", "K", "3" & "7"?
Answer: It wouldn't affect the "3" at all. All the possibility of finding more "3" does for us is give more opportunities to find more "black ravens" because the "3" cannot refute either rule 1 or rule 2. Possible 'other' "D", "K" and "7" cards represent more opportunities for even 1 rule refuting card to pop up. In the real (inductive) world, we cannot rule out a "7" popping up when you least expect it. For instance the 'black raven' example I've been using is commonly used to describe induction, but people used to give 'white swans' as an example of the same thing until someone discovered naturally black swans in China.
Question 12: How does this logically relate to considerations of abiogenesis & creationism/ID?
What if abiogenesis was "D" and creationism/ID was "K"?
Answer: It would mean that if abiogenesis (or evolution theory or the Big Bang...) were false, it would not make creationism true. It means that they can both be false. "I don't know, therefore "K" made "3" is illogical.
Question 13: What does the above results tell us about ID "complexity" or "fine turned universe" arguments or creationism "evidence" by Paul's method of looking around and seeing the "complex" world?
Answer: It means that they have no reasonable argument at all because these arguments are logically flawed. They are looking at a "3" conclusion and presuming that this proves true their "K" 'god'/creator premise. The sad thing is that they can't show us a "K" card or even prove that it can even possibly exist. Christians describe the "K" card as supernatural. It is invalid to suggest that a "designer, a "creator" or a 'god' is a "more probable" answer than "naturalistic" means if they can't even show that their supernatural suggestion (or otherwise "designer") is even POSSIBLE (meaning it has a more than 0% probability of existing).
The Vampire
LOGOS
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