Math Fun

Philosophy Forums Science, Technology, and Math
1421

This part, James. This is what you forgot. This time, as you go away, never admitting defeat, I’d like you to remember who’s going away, and who’s still here.

I’ve given you a syllogism, if it’s not a sound demonstration of the conclusion, then either point to the specific given (if it is valid and not sound) or the specific logical step (if it is invalid) that you think is wrong. I made it easy and numbered them for you. Make clear which are “the only problems” and we can go from there.

To nail anything, you have to get specific. You won’t see the problems with your position until you do more than wave your hands and speak in generalities and repeat rhetorical catch phrases like “turtles all the way down”. If you mean that the reasoning is circular, show that it is. Spell out your reasoning, clearly, directly, without sarcasm or sass. If you’re having trouble articulating it under those conditions, it’s a good bet that the reasoning was never actually there.

I say this because I’ve been wrong before, I’ve known the difficulty of making explicit a flawed position that I’d always accepted without close examination, and at times I’ve stubbornly refused to admit when my argument was vacuous. I even thought for a time that I was wrong on this logicians problem, but Phoneutria’s rebuttals, your lack of exposition, and my own attempts to articulate both your objections and my responses to them leave me pretty well convinced that the logic is sound – in part because of the very arguments you made showing that certain minds of argument would lead to infinite possibilities!

You’re absolutely free to walk away, but don’t pretend I’m engaging in bad faith or refusing to address the arguments you make whenever you’ve deigned to actually make them. And if you make new ones, or even try anew to express arguments you think you’ve already made for your position, I’ll keep offering rebuttals and rearticulating mine. I’m still here.

1422

You went away for 6 months without a word.

I did that already, not going to keep going on about it. Obviously it is one of those blind spots you choose to support.

Do you really want me to start bring sight to the blind?

And you will never prove anything until you actually eliminate all alternatives. The fact that you can only think of one possible solution to a problem doesn’t prove that yours is the only one. And in this kind of problem, if there is another possible solution, then yours isn’t a solution.

That is the part that you can never accept.

But thanks for playing. :sunglasses:

1423

There is no other solution that solves the problem with certainty.

1424

You haven’t proven that at all, but then if you had, you would have none that solve it with certainty.
That was my point.

1425

Proof is on my very fist post on this subject:

Colors you can see: finite set. Solution is certain.
Colors you can’t see: infinite set. Solution is speculative.

1426

Colors of socks that I wear - finite set.
Solution is certain.

Colors never imagined by anyone throughout human history = infinite.
Solution is speculative.

Just drop it. You guys haven’t a clue.

1427

your socks are not headbands included in the puzzle, which is obviously what I meant

colors visible in the puzzle are colors certainly included in the puzzle

don’t make me go durrr, durface

1428

No one need push a cart downhill.

Although possibly having nothing whatsoever to do with your color.

"Are you happy to see me?
I saw someone with a gun.
Therefore what’s in your pants must be a gun!!
Concealed weapon - CONVICTED!!!
What else could it be?!?! :confused: "

1429

Although possibly having nothing whatsoever to do with your color.
[/quote]
If they don’t the problem is not solvable.

[/quote]
There is an infinite set of things that could be hiding in your pants. Not solvable.

1430

One I accidentally learned today and solved it right away to my own surprise given how I haven’t done almost any math for more than a year, but it’s rather easy really.

How to arrange:

1a, 1b, 1c, 1d
2a, 2b, 2c, 2d
3a, 3b, 3c, 3d
4a, 4b, 4c, 4d

into a 4x4 square like above so that each row, column and the 2 diagonals contain one of each letters and one of each number.

1431

[tab]1a 4b 2c 3d
2d 3c 1b 4a
3b 2a 4d 1c
4c 1d 3a 2b[/tab]

1432

Between this post where I first offer the syllogism, and this post, where you claim you have already pointed to a specific, numbered premise or logical move that you find false or invalid, you make three posts, and in them, the only number you use is in the name “Ed3”, which is not a reference to a specific, numbered premise or logical move (you also use the word “nothing”, which could be charitably interpreted as a number, and would be the correct response to the request to point to what is wrong with the syllogism).

So, looks like no, you didn’t already do that.

Arbiter, I tried your problem but gave up quickly. I cheated and looked at James answer, I’d be curious to know what your respective processes were
[tab]It does look there is a pattern. There are only four cyclic permutations (don’t know if that’s the right term, but I mean, if the numbers were wrapped around a cylinder, there would only be two patterns of them). Two patterns are used horizontally, and two vertically.

I was looking for that king of thing, but couldn’t find it and I then was just guessing. Arbiter, you said it was your first instinct? Why?[/tab]

1433

Which made this part:

…wrong^^^

Carl, do you agree with this statement?

1434

JSS and Carleas, regarding my puzzle, my answer is actually different from James’s

I began by making this:

1a 3b
2b 4a
1d 3c
2c 4d

Half of the possible combinations into the 2 diagonals. Then you simply fill in the holes, and the result:

1a 4c 2d 3b
3d 2b 4a 1c
4b 1d 3c 2a
2c 3a 1b 4d

1435

James,
First, that premise is something you granted here:

The key point being, you’ve explicitly agreed that an infinite set renders the problem unsolvable. And now you’re saying that that premise, the “common ground” that prompted me to offer the syllogism, is actually your only problem with the syllogism? That looks a lot like bad faith. Were you wrong when you accepted that premise, or are you wrong now when you are rejecting it?

Second, I did a second syllogism, showing that it isn’t affected by the assumption that some logicians take other premises.

Third, I offered yet another syllogism, which addresses your concerns with the reasoning in the Blue Eye problem (because once we accept that each logician’s headband is one of the colors they can see, the Master Logician problem becomes the Blue Eye problem). And that’s the syllogism you haven’t addressed, even though it is new and it is squarely in response to your worry that some other better logician might have a better way to leave the island earlier.

The beauty of specificity, James, is that it makes this kind of sloppiness obvious. When you spell out your reasoning, when you don’t resort to sarcasm, we can see what, if anything, there is to your argument.

Arbiter,
I think that first one probably got messed up when the software truncated white space, and should have looked like this:
1a _ _ 3b
_ 2b 4a _
_ 1d 3c _
2c _ _ 4d

There have to be a lot of correct answers. Each number can be shuffled without breaking the solution (so that e.g. 1 becomes 2, 2, becomes three, three becomes 4, and 4 becomes 1), and each letter can be shuffled the same way. That’s at least 4! x 4! possible answers, assuming there is only one pattern that those different letter and number mappings are being placed onto.

1436

Carl, one of the reasons that you are blind to solutions is that you refuse to see the questions being asked:

And in anticipation of your next 10 responses:

Then we can discuss your errors (again).

AoC’s puzzle:
[tab]First, you can work with merely the numbers and forget the letters (to be added in later).

Then you know that across each row, the numbers have to change but cannot be replicated down any column. So to begin that, I simply flipped the first column:
1 4
2 3
3 2
4 1

Then the next column must be vertically unique while ensuring no horizontal replication. So for that, I just flipped the first two pairs in the first column:
1 _ 2
2 _ 1
3 _ 4
4 _ 3

Then I had to flip one of the remaining pairs of numbers while still avoiding any replication:
1 _ _ 3
2 _ _ 4
3 _ _ 1
4 _ _ 2

Finally, I had to add in the letters. The letters being a transposition of the numbers allowed for me to just flip the entire letter set solution 90 degrees and superimpose them onto the numbers.

a b c d
d c b a
b a d c
c b a b

superimposed into:

1a 4b 2c 3d
2d 3c 1b 4a
3b 2a 4d 1c
4c 1d 3a 2b[/tab]

1437

gaaaghhh spoilers in tabs bitches i havent looked at this yet

1438

Prove that unicorns don’t exist.

1439

Oh, another spoiler regarding my puzzle

[tab]it was initially showed to me with cards, with suits and colors instead of numbers and letters.[/tab]

1440

That was pretty much my point in saying that the puzzle isn’t actually solvable by logic alone (although perhaps if you’re really good).

AoC,
[tab]it was initially showed to me with cards, with suits and colors instead of numbers and letters.

^^That would make separating the numbers from the suits a little harder.[/tab]