# Barry Arrington and Company: Does A=A?

This is a little test of reasoning ability. I would prefer that for the first few days, only ID advocates post answers. These questions, and the underlying reasoning, are widely discussed on the internet, so you may have encountered them. If you have, I would appreciate knowing that fact. Also, for those who have seen them before, I would like to know how you did the first time you encountered them.

If anyone spots a typo or logical error, I’d appreciate hearing about is so it can be corrected.

The answers I’m looking for are in three parts:

First — yes or no — can the puzzles be solved by reason, assuming ordinary knowledge of the vocabulary. There are no tricks or unusual meanings involved.

Third, the provide the reasoning or proof.

Uncommon Descent frequently invokes logic and reason. this is a challenge to anyone who posts at UD. Feel free to post your answers on this thread or at UD.

Here are the questions:

1. [The original editor has been sacked. Re-Edited to straighten out the mess: The price of a cheeseburger is \$2.20, the price of a plain hamburger plus the price of the added cheese.] A plain hamburger costs two dollars more than the added cheese. How much does a plain hamburger cost?

2. In Elbonia, one person in ten thousand has Ebola. A new test is so good that anyone who is infected will test positive. But three percent of uninfected people will also test positive. John, a citizen of Elbonia tests positive. What is the probability that John has Ebola?

3. I have a deck of picture cards. They have automobiles on one side and living things on the other side. I have looked through them, and I think they follow the following rule: if a card has a GM automobile on one side, it will have an animal on the other side. After shuffling, I deal out four cards.

Cat, Ford, Petunia, Chevy

What cards must I turn over to test my hypothesis?

4. William is tweeting Betty, but Betty is tweeting John. William is in love, but John is not. Is a person in love tweeting a person who is not in love?

5. Elbonia has invented a treatment for Psoriasis. During a recent blind test, of the patients who were given the treatment 197 improved and 95 did not.

Of the patients who were given a placebo, 45 improved and 20 did not.

Is the treatment effective?

## 237 thoughts on “Barry Arrington and Company: Does A=A?”

1. TristanMiller:
I solved the first question almost immediately but only because I recognized it as a version of a famous attribute substitution problem.

These problems are not correlated with IQ style intelligence. I think you can learn to solve them. I think people who challenge mainstream math and physics should find them rather easy. That was my only point.

2. I think people who challenge mainstream math and physics should find them rather easy.

I would expect rather the opposite. 😉

3. petrushka: These problems are not correlated with IQ style intelligence. I think you can learn to solve them. I think people who challenge mainstream math and physics should find them rather easy. That was my only point.

I understand your point, and attribute substitution has really nothing to do with IQ. I think it likely heavily underlies the IDer/Creationist psyche, which is why they might have a difficult time with these challenges.

[P]eople are not accustomed to thinking hard, and are often content to trust a plausible judgment that comes to mind.
~ Daniel Kahneman

4. tristan,

Then what explains the materialist/Darwinist whackos difficult time with these challenges?

And what explains your inability to notice?

5. phoodoo: Then what explains the materialist/Darwinist whackos difficult time with these challenges?

I’d expect you and yours to be all over it with all the free time you must have, what with nothing happening in ID.

6. Since this thread is not active anymore, I’ll close out my comments. My purpose in joining these debates is to educate myself. I am interested in any lines of reasoning that I don’t understand, or which make testable claims. I would also be interested in anyon on the ID side who shows evidence of being able to reason about evidence.

So far, the pickings have been pretty slim. When I started, 15 years ago, I knew next to nothing about biology. Now I know almost next to nothing, but I can follow the reasoning on both sides.

There are people like Byres and Gary Gaulin, who require no response. I see no point in debating them. Then there are people like gpuccio, whose argument is a bit more subtle, and requires some rebuttal. There is Behe and the folks who argue Behe’s claims. That argument requires evidence and rebuttal.Even Larry Moran respects Behe’s argument as one that requires rebuttal.

Then there are cranks and self-deluded experts who have mastered bafflegab and technical jargon. Since I have only a layman’s understanding of relativity and quantum theory, I cannot refute them. And I don’t like to rely entirely on argument from authority.

So my argument at the moment is that these people have learned to parrot crank theories, but cannot actually reason themselves. Hence the test.

I took some small personal risk by reworking the puzzles. I made at least one goof, which is embarrassing. I changed the language so it would not be easy to google the problems.

Regarding my goof, I consider that a meta test, and said as much in my OP. I asked for corrections. It is one thing to solve logic puzzles. Perhaps a larger thing to realize a puzzle is badly worded and to have the confidence to say so.

I also required responders to show their work. Show the line of reasoning. This requirement was intended to weed out bluffers and blowhards like phoodoo.

These kinds of simple logical problems seem to baffle ID advocates, which is interesting, because they seem enamored of math and logic. They often lecture on the subjects.

That’s pretty much all I have to say on the subject.

7. Ok, I’ll bite.
1: \$2.10
2: 3%
3: Petunia and Chevy. If petunia has chevy on the back, the theory is falsified. If the chevy has something other than an animal, the theory is falsified.
4: We don’t know.
5: No.

8. Welcome, Bruce. Yes things have gone a little quiet here. If some of those 500 comments at UD contained some new developments in ID there might be something to perk our interest. As it is, I suspect we’ve become sceptical of that happening.

9. Ok, I’ll bite.
1: \$2.10
2: 3%
3: Petunia and Chevy. If petunia has chevy on the back, the theory is falsified. If the chevy has something other than an animal, the theory is falsified.
4: We don’t know.
5: No.

The puzzles and their solutions were addressed in previous posts.

Number 2 is not 3%.
Number 4 has a solution.

10. Also, for #5, “No” is an inappropriate answer to the question “Is the treatment effective?”

11. DNA_Jock:
Also, for #5,“No” is an inappropriate answer to the question “Is the treatment effective?”

Not demonstrated effective?

The question could be worded more carefully, but that might give it away.

12. #2 is not 3% — well, 1 in 10,000 actually have ebola, that would be about 0.01%. 3% give false positive. You might argue that the correct answer is 3.01%, however that would assume that the margin of error on the 3% has sufficient resolution to account for the latter — a bit of a mathematically correct stretchy.

On 4, what is the answer?

13. From a previous post:

Betty is either in love or not in love (stipulated)
If Betty is in love, then Betty is a person in love tweeting John, who is not in love.
If Betty is not in love, then William is a person in love tweeting Betty, who is not in love.

14. DNA_Jock:
Also, for #5,“No” is an inappropriate answer to the question “Is the treatment effective?”

Let me see:
The ratio of those who responded to the treatment: 197 / 95 = 2.07
The ratio of those who responded to placibo: 45 / 20 = 2.25
Therefore more people responded positively to the placebo than to the treatment. What part of “not effective” do we have trouble with?

15. petrushka: The puzzles and their solutions were addressed in previous posts.

Number 2 is not 3%.
Number 4 has a solution.

Sorry, you are right on number 2. The answer is about 1 in (10,000 * .03) aprox = 1 in 300.

Hmmm, you’re right on #4 too. If Betty is in love, she meets the criteria as she tweets John. If she is not in love, then William meets the criteria when tweeting her. As long as “in love” is a true boolean (‘not sure it is) then the answer is 1.

‘Pays to be doing boring work when solving logic problems.

16. I’ve learned a lot about the wording of puzzles. Some of the ambiguity is mine. Some is inherited from my source.

17. The more interesting fact is that there is a right answer. If we were to locate intelligent life on another planet they would produce the same answers, or be wrong, yes?

18. brucefast: Let me see:
The ratio of those who responded to the treatment: 197 / 95 = 2.07
The ratio of those who responded to placibo: 45 / 20 = 2.25
Therefore more people responded positively to the placebo than to the treatment.What part of “not effective” do we have trouble with?

To put it simply, the trial has too few patients to rule out a moderate benefit for the treatment.
It’s ‘sampling error’; to illustrate:
When I modeled the treatment as having a 66% response rate, and the placebo 60% (that’s a 15% reduction in the number of non-responders – the kind of effect size that oncologists would recognize as clinically significant), then the treatment looked as bad as the data observed (or worse) in over 12% of the trials. So, based on the numbers given, you cannot rule out (at p=.05) the possibility that the drug is somewhat effective.

If I push the response rate all the way up to 72%, then trials as bad as this one become unlikely – only ~2% look this bad. So you could reasonably say that the drug probably isn’t highly effective. But before cancelling the development program, you might want to run a larger trial.
An appropriate answer to the question would be “We cannot reject the null (that the drug has no effect)”. Or, in layman’s terms, “Can’t tell”.
“No” is an inappropriate response, because it implies a certainty that just isn’t there.

19. A = A

True if one accepts the standard meaning. I accept it.

But consider this would mean that is supposedly equivalent

|=|

But one could say that looks like a TIE fighter. 🙂

But consider some computer language

nyval = not myval

or

A = not A

http://stackoverflow.com/questions/17168046/python-how-to-negate-value-if-true-return-false-if-false-return-true

Where is the contradiction in “A= not A”. A software developer will not interpret that even as an assertion of truth or falsehood, but the contents of variable A are negated.

In such case these symbols don’t even make an assertion that is either true or false.

If one doesn’t appreciate the problem of attaching meaning to symbology, one doesn’t understand the problem in formal logic it created around the time of Bertrand Russel, Alfred Whitehead, and Kurt Gödel.

The problem is meaning is not self-evident. The computer language example shows the meaning of the symbols:

A = A

Is not fixed, but language dependent. As I’ve shown, in the Phython language:

A = not A

is a valid construct. Of course I know what those self-evidentialists are claiming, but the problem is the meaning of the symbols below:

A = not A

is not self evident.

Pointless discussion.

The above is not sophistry but has bearing on Computer Science and the construction of formal languages.

The problem is a system of symbols cannot disambiguate the meaning of the symbols. Hence, if even in something like formal logic, things aren’t “self evident”, why try to extrapolate a dubiuos idea of “self-evidence” to all reality. Even if “self-evidence” exists, it’s moot since we are fallible and aren’t entitled to always being correct.

We know the truth because of God’s grace, not because the truth is “self-evident”.

21. A bit unfair, I think. BA surely is talking about comparison, not assignment.

Yes, but the point is, the meaning of the symbols is not self-evident. If one is having a philosophical discussion and the meaning of symbols is not self-evident, then it’s pointless to argue with the non-self-evident symbols of human language (or any language) the claim “there exists self-evident truths”.

The claim, even if true, cannot be defended with non-self-evident language, and is moot even if true. Ergo, the promotion of the idea is useless.

I accept “A equals A”. Big deal. Self-evident? I don’t care.

22. Some of us just can’t break the habit of misinterpreting other people’s meaning.

I kind of miss the C programming language, where you could say things like
++i = j– ;
And worse.

No ambiguity between comparison and assignment.

23. stcordova: The problem is meaning is not self-evident. The computer language example shows the meaning of the symbols:

A = A

Is not fixed, but language dependent. As I’ve shown, in the Phython language:

A = not A

is a valid construct. Of course I know what those self-evidentialists are claiming, but the problem is the meaning of the symbols below:

A = not A

is not self evident.

Worth a laugh. Thanks Sal. Proving Barry’s point.

NOT A is not equal to A else assigning the result of evaluating the expression back to A would be utterly redundant.

That’s why you don’t find compute code littered with expressions like this:
A=A
B=B
c=c
d=d

Even python programmers can grasp self evident truths.

24. Mung: Sal’s point may not be deep, but he is correct.

In many programming languages A = not A is a valid statement.

25. Proving Barry’s point.

A equaling A wasn’t what was being debated. Funny to watch you rail against something I wasn’t debating and then congratulate yourself knocking an argument down that you invented and attributed to me, but which I didn’t make.

If I wrote

“C = C” an organic chemist might throw a fit, because this would be better:

That’s because symbolic statements like: “C=C” are not self-evidently true, and as I pointed out, it isn’t self evidently true because without context we don’t know if we are talking mathematical tautologies or if we are talking how carbon would bond to other carbons.

Even in programming languages:

C=C

does not mean the same thing as

C=C

in math literature.

In fact, “C = C” in a programming language would likely be a semantic error!

26. Salvador, you do realize, don’t you, that A=A is just a symbolic way to express the law of identity? It’s not meant to be taken literally.

http://www.importanceofphilosophy.com/Metaphysics_Identity.html

Funny to watch you rail against something I wasn’t debating and then congratulate yourself knocking an argument down that you invented and attributed to me, but which I didn’t make.

That’s exactly what you were doing to Barry.

27. Gee Mung, you had to explain it to me. Since you had to explain it to me, does that mean it wasn’t self evident. 🙄

One other thing, is the meaning of “self-evident” self-evident, or do you have to explain what self-evident means? 🙂 So you encounter a 2 year old, is the meaning of “self-evident” self-evident to him?

If you have to explain it, then the meaning of “self-evident” isn’t self-evident. Therefore if the meaning of “self-evident” isn’t self-evident, one has to question the reliability of making claims that anything in general is self-evident.

Lot’s of people accept A equals A. Big deal. “Self-evident?” What do you mean by “self-evident”? If people have to learn what “self-evident” means, does that mean the notion of “self-evident” is itself is not self-evident?

28. petrushka,

I kind of miss the C programming language, where you could say things like
++i = j– ;
And worse.

That’s not legal C code. You can get away with a lot in C, but not quite that much.

There’s already an implicit assignment on the left-hand side, so a second assignment isn’t allowed. On the right hand side, “-” as a unary operator has to come before the variable, not after.

29. There are a number of ways that something can be self-evident. In ordinary language, we say that something obvious is self-evident. Philosophically, however, further distinctions must be made. In modern philosophy, something is self-evident when understanding what it means immediately results in knowing that it is true. In Aristotelian philosophy, another meaning of self-evident was used. There are four different ways of understanding self evidence – logical, indubitable, undeniable and impractical.
….
http://simplyphilosophy.org/self-evident-truths/

Oh my Science! The meaning of self-evident may not be self-evident!

So if someone says, “this is self-evident”, the assertion may still be debatable since the definition of “self-evident” is not itself self evident.

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