Earlier quoted context omitted.
If you have none how can you say they are specifically brown? You could say they are any color then which makes them being just 1 specific color not true. Your non-existent cats aren't brown, they are every color or even no color. Maybe even more accurately they aren't brown, they are an undefined color. I'm not really satisfied saying that the characteristics of something that doesn't exist can be anything. I am sat…
You are talking about the colloquial meaning of these words.
A liar who always lies says "All my hats are green."
331–340 of 419 posts
Re: A liar who always lies says "All my hats are green."
#332Earlier quoted context omitted.
Well, I think showing that it defies logical inference is quite relevant in the context of that thread being about translating typical English into first order logic to do logical inference.
I worry about sets and consideration of edge cases. Legal, programmatic, medical. Adhering to a convention that presupposes meaning and claim that interpretation is the only interpretation, cannot be resolved with repetition. I remain unconvinced.
Re: A liar who always lies says "All my hats are green."
#333Earlier quoted context omitted.
I regret opening this can of worms called Monty Hall. But anyway I'll link the relevant section from Wikipedia: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_... > The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door , or always offer a choice to switch, or even never open the door revealing the car. However, Savant mad…
Just be glad that you didn't go for the 2 envelopes problem which was her next. Vos Savant was wrong about that one, and few people like the real answer. The problem is that you're presented with two envelopes with 2 real numbers inside. You randomly select one, then look, and try to guess if you got the larger number. It doesn't seem like you can do better than even, but you can! Unfortunately everyone hates the ans…
Re: A liar who always lies says "All my hats are green."
#334Earlier quoted context omitted.
This is generally the case for the vast majority of puzzles, and it equally drives me mad in those areas where academics set "puzzles" and conclude that people's inabilty to "solve" them is some cognitive deficiency. I've rarely encountered a case where it is isnt an extreme lack of self-awareness in the questioner -- eg., being extremely overfit to language/notation/etc. localised to their own area of expertise.
Logic itself is a relatively new invention, and is symbolic itself. That is to say, logic is a map not the territory. That said, if someone can't fathom the most widely used symbolic languages humans use (math, logic, language, etc) they probably do have a cognitive deficit of some sort when compared to those who can.
If you are a primitive farmer abstract thinking isn't really useful to you. Everything you deal with in your life, except religion, can almost entirely be dealt with absolutes with little in the way of abstractions.
If it rains at the right time then you can have a good harvest. If the weather is bad then it sucks. If there is animals threatening your crops or herd you need to take steps to deal with them.
There is a lot of logic in dealing with these things. You have to know the seasons, know the stars, know the dirt, etc. You have to understand the life cycle and manipulate the behavior and biology of plants and animals at the right stages in their lives. Things have a logical sequence and there are direct consequences that are predictable from events and your actions.
Where as in modern society you have been conditioned to think in terms of hypothetical and abstractions through being exposed to testing your entire life.
You first need to know how test questions work before you are able to answer them accurately.
For a person who isn't exposed to this then the whole affair of asking hypotheticals and assuming imaginary situations with specific rules that don't actually apply to the present reality is very confusing.
They don't even understand the question. So, of course, they are going to suck at answering them.
And ultimately that is all IQ testing measures.. your ability to take tests.
Re: A liar who always lies says "All my hats are green."
#335One complication is that in typical English, if you say "All my hats....", you are simultaneously making an existence statement that you have at least one hat... but the usual formal logic "forall" quantifier does NOT presume existence. Here's a formal proof that "forall" has a "surprise" meaning for those not well-versed in formal logic: https://us.metamath.org/mpeuni/alimp-surprise.html I propose that when translat…
Perhaps. But what if someone asks you "are all your hats green?" Then the interpretation is not so clear.
Re: A liar who always lies says "All my hats are green."
#336Earlier quoted context omitted.
> All my hats....", you are simultaneously making an existence statement that you have at least one hat It does not. All my unicorns fly. There is no assumption that I have a unicorn. There is an assumption, based on the claim but it is not a fact. The puzzle also assumes that "my" implies there is some ownership (we'll take for granted "my" means "has" for simplicity), which is another quibble that unravels the whol…
I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic. The fact that we compact these edge cases into arbitrary truth values is just for ease of computing. This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclus…
Re: A liar who always lies says "All my hats are green."
#337Earlier quoted context omitted.
I regret opening this can of worms called Monty Hall. But anyway I'll link the relevant section from Wikipedia: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_... > The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door , or always offer a choice to switch, or even never open the door revealing the car. However, Savant mad…
Just be glad that you didn't go for the 2 envelopes problem which was her next. Vos Savant was wrong about that one, and few people like the real answer. The problem is that you're presented with two envelopes with 2 real numbers inside. You randomly select one, then look, and try to guess if you got the larger number. It doesn't seem like you can do better than even, but you can! Unfortunately everyone hates the ans…
Re: A liar who always lies says "All my hats are green."
#338Earlier quoted context omitted.
My favorite example is Monty Hall problem. "Smart" people often use it as the evidence of how bad general people are at probability. It really isn't. The problem is usually given in this form: > Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, s…
Perhaps it'll be more intuitive to you if you scale the number of doors up. If there are 100 doors, only one containing a car, you pick one, the host reveals 98/99 remaining doors as goats, it's obvious the correct choice is to switch. The correct answer is a mathematically provable probability. 1% chance you picked the right door, 99% chance the door was in the remaining pool, therefore 99% chance the last remaining…
Re: A liar who always lies says "All my hats are green."
#339Earlier quoted context omitted.
Just be glad that you didn't go for the 2 envelopes problem which was her next. Vos Savant was wrong about that one, and few people like the real answer. The problem is that you're presented with two envelopes with 2 real numbers inside. You randomly select one, then look, and try to guess if you got the larger number. It doesn't seem like you can do better than even, but you can! Unfortunately everyone hates the ans…
"Two Envelopes Problem" seems to be usaully referred to a very different problem: https://en.wikipedia.org/wiki/Two_envelopes_problem
This is one reason that probability theorists have learned to be more careful in stating the double money version to rule out the solution that I gave. But my version has been in the literature since, I believe the 1950s. Under, as I first encountered it, the same exact name. (I encountered it from Dr Laurie Snell at Dartmouth College in the mid 1990s.)
Re: A liar who always lies says "All my hats are green."
#340Earlier quoted context omitted.
The joke, loosely, is : A wife asks her programmer husband” on your way home, can you swing by the store and buy one carton of milk, and if they have eggs, get six?” It’s funnier and more relatable to programming if he comes home empty handed, crashes the car into the garage door, and says, with perfect alacrity, “six what?”
English is an interpreted language. We wouldn't have this problem if we can check for undefined references during compilation.