Math and Logic Errors

[fidel]

Better hit the first one, it gets tougher after that.

Next Play, Centurion Man. Don't hang your head.

[Mal]

I liked Al. But I always got the impression he was more of an intuition kind of guy than an analytics kind of guy.

No doubt, but I would be interested to see if there are numbers to back up or contradict this particular intuition. It may just be confirmation bias from his coaching days, where maybe he got really frustrated to see one of his players miss two in a row, and then he blocked out instances where they'd miss the first and make the second.

On the other hand, it is a game played by humans, influenced by their emotions. I recall from my playing days that, at least in my mind, there was an ignominy attached to missing both free throws and coming away from the gift of having been fouled empty handed. I didn't think about that, however, unless and until I missed the first shot. Which meant that I placed a higher amount of stress on myself to make my second attempt after a miss than after a make, which may or may not have affected results.

I wouldn't be surprised if McGuire was right, and that the reason is when a player's just made a free throw their confidence rises and they don't feel as much pressure to make the second shot (or fear of missing) because they've already produced points on this trip to the line. That's dangerously close to the "hot hand" theory, so I don't want to put too much into it, but the trial is different than field goal attempts, which are spaced minutes apart, come from different places on the floor, and are against different types of defensive contesting. The physical circumstances of free throws on a single trip to the line are consistent from one to the next, and the repeating is more or less immediate.

[OldPhiKap]

Next Play, Centurion Man. Don't hang your head.

Is he one of those Millenials I always hear about?

[Acymetric]

Is he one of those Millenials I always hear about?

Even worse...Centennials.

[Reddevil]

I liked Al. But I always got the impression he was more of an intuition kind of guy than an analytics kind of guy.

I think you are right. Al was the first guy I heard say that if the first one rattles in, the next one will be a swish. I have no analysis to back it up, but it seems to be true. It is amazing to me how often this happens.

[killerleft]

I think you are right. Al was the first guy I heard say that if the first one rattles in, the next one will be a swish. I have no analysis to back it up, but it seems to be true. It is amazing to me how often this happens.

Worry no more. It's the Hot Hand. Short version.

[Bostondevil]

Listened to a discussion of rational thinking on NPR yesterday.

Example question to determine if you are a rational thinker.

A baseball and bat together cost $1.10. If the bat costs $1 more than the ball, what does the ball cost?






My first thought was - a lot of people are going to get that wrong until they take a second to think about it because it's not what feels like the obvious answer. Then I figured out the math. Apparently I am a rational thinker.

[Matches]

Listened to a discussion of rational thinking on NPR yesterday.

Example question to determine if you are a rational thinker.

A baseball and bat together cost $1.10. If the bat costs $1 more than the ball, what does the ball cost?

5 cents. But LOTS of people will say 10. Something about the question wires the brain that way.

[BLPOG]

Here's a category of logic error that drives me nuts: when someone attempts to call out another person or argument for invoking a logical fallacy, formal or informal, but does so incorrectly.

I think the fallacy that I see referred to incorrectly at the highest rate is the "No True Scotsman" informal fallacy. It is, somewhat unfortunately, also referred to as appeal to purity. I say "unfortunately" because that characterization places too much emphasis on the superficial characteristics of the fallacy rather than the underlying flaw, which tends to exacerbate the misusage of the phrase.

People tend to fling it about whenever someone brings up a test for membership in set in which the membership consists of people and the test consists of certain behaviors or beliefs. Alice might say, "Only Duke alumni can be real Blue Devils fans! Non-alumni just aren't." Bob might reply, "That's a No True Scotsman fallacy!"

That's wrong. The mere fact that someone is applying a test for membership isn't fallacious; even if the test is wrong, and even if it invokes an idea of purity or results in a very narrowly defined set. The entire field of logic is, in some sense, used to make distinctions in set membership.

Let's revise the example. Once again, Alice says, "Only Duke alumni can be real Blue Devils fans!" Bob replies, "That's not true. Mike Krzyzewski never enrolled at Duke, but he's real fan." Alice replies, "Obviously, team members themselves count, and coaches are members of the team. So the point stands - all those non-alumni can't be real fans."

In this case, Alice has committed the fallacy. In the example I've constructed, she expands the test for membership rather than contracting it as in the usual appeal to purity formulation (which is a further reason why "appeal to purity" is a bad term for the mistake). The fallacy lies in changing one of the argument's premises while still trying to achieve the same strength, rhetorically or logically, of the conclusion. It is similar to moving the goalposts, although it might be better thought of a shifting the starting line. The sign of the change (increasing or decreasing scope) isn't really important, nor is the fact that we're usually talking about groups of people.

[HereBeforeCoachK]

Here's a category of logic error that drives me nuts: when someone attempts to call out another person or argument for invoking a logical fallacy, formal or informal, but does so incorrectly.

I think the fallacy that I see referred to incorrectly at the highest rate is the "No True Scotsman" informal fallacy. It is, somewhat unfortunately, also referred to as appeal to purity. I say "unfortunately" because that characterization places too much emphasis on the superficial characteristics of the fallacy rather than the underlying flaw, which tends to exacerbate the misusage of the phrase.

People tend to fling it about whenever someone brings up a test for membership in set in which the membership consists of people and the test consists of certain behaviors or beliefs. Alice might say, "Only Duke alumni can be real Blue Devils fans! Non-alumni just aren't." Bob might reply, "That's a No True Scotsman fallacy!"

That's wrong. The mere fact that someone is applying a test for membership isn't fallacious; even if the test is wrong, and even if it invokes an idea of purity or results in a very narrowly defined set. The entire field of logic is, in some sense, used to make distinctions in set membership.

Let's revise the example. Once again, Alice says, "Only Duke alumni can be real Blue Devils fans!" Bob replies, "That's not true. Mike Krzyzewski never enrolled at Duke, but he's real fan." Alice replies, "Obviously, team members themselves count, and coaches are members of the team. So the point stands - all those non-alumni can't be real fans."

In this case, Alice has committed the fallacy. In the example I've constructed, she expands the test for membership rather than contracting it as in the usual appeal to purity formulation (which is a further reason why "appeal to purity" is a bad term for the mistake). The fallacy lies in changing one of the argument's premises while still trying to achieve the same strength, rhetorically or logically, of the conclusion. It is similar to moving the goalposts, although it might be better thought of a shifting the starting line. The sign of the change (increasing or decreasing scope) isn't really important, nor is the fact that we're usually talking about groups of people.

The basis of logic is much like math...if/then....if A is bigger than B and B is bigger than C, then A is bigger than C. It's really a lost skill on society on the whole to my observation.

But the biggest bust of all is how so many people use, or fall for, flawed analogies. Drives me crazy.

[crimsondevil]

Let's revise the example. Once again, Alice says, "Only Duke alumni can be real Blue Devils fans!" Bob replies, "That's not true. Mike Krzyzewski never enrolled at Duke, but he's real fan." Alice replies, "Obviously, team members themselves count, and coaches are members of the team. So the point stands - all those non-alumni can't be real fans."

In this case, Alice has committed the fallacy. In the example I've constructed, she expands the test for membership rather than contracting it as in the usual appeal to purity formulation (which is a further reason why "appeal to purity" is a bad term for the mistake). The fallacy lies in changing one of the argument's premises while still trying to achieve the same strength, rhetorically or logically, of the conclusion. It is similar to moving the goalposts, although it might be better thought of a shifting the starting line. The sign of the change (increasing or decreasing scope) isn't really important, nor is the fact that we're usually talking about groups of people.

You could say the membership being contracted is non-alumni to make it fit the usual construction better ("Coach K is not a true non-alum").

Alice could just avoid the fallacy with a phrase I'm not fond of: "Coach K is the exception that proves the rule."

[OldPhiKap]

UNC sucks.
Vacuums suck.

UNC is a vacuum.


Intellectually, true. Literally, not really.

[Indoor66]

Literally, not really.

Are you sure?

[HereBeforeCoachK]

You could say the membership being contracted is non-alumni to make it fit the usual construction better ("Coach K is not a true non-alum").

Alice could just avoid the fallacy with a phrase I'm not fond of: "Coach K is the exception that proves the rule."

Or one could say that a true Duke fan realizes that any limitation of true fandom to a (relatively) tiny student population, and thus a tiny alum population is, destructive.

[Jeffrey]

Are you sure?

Absolutely, society benefits from vacuums.

[BLPOG]

You could say the membership being contracted is non-alumni to make it fit the usual construction better ("Coach K is not a true non-alum").

Alice could just avoid the fallacy with a phrase I'm not fond of: "Coach K is the exception that proves the rule."

The "exception that proves the rule" phrase is nearly always misused. People use it as a cliche to trivialize a counterexample. Guess what? The counterexample doesn't just disappear in a puff of smoke.

The proper usage of the phrase is in noting that a specific exception that one has made is an indication that a rule exists; one wouldn't have to make an exception if one didn't first have the rule. The proof is not of the truth of the content of a rule but rather its existence.

Example: The medical hardship redshirt option (or whatever the proper term is) so long as the player has played fewer than a certain percentage of games that season. It is an exception that, by its existence, shows the existence of a rule that normally eliminates the redshirt option once someone plays any minutes at all.

There are circumstances in which a general rule might not be formally or explicitly stated and therefore the exception is useful to infer its existence.

[OldPhiKap]

Nature abhors a vacuum.
Society benefits from a vacuum.

QED, nature abhors society.

[HereBeforeCoachK]

Nature abhors a vacuum.
Society benefits from a vacuum.

QED, nature abhors society.

HAH, not so fast...you see...

Because if nature did NOT abhor a vacuum....
...vacuums would not exit.
QED that nature does not abhor society....

[camion]

HAH, not so fast...you see...

Because if nature did NOT abhor a vacuum...
...vacuums would not exit.
QED that nature does not abhor society...

QUE? Society does not exit.

[OldPhiKap]

Time is money.
Time is the name of a song on Dark Side of the Moon.

QED, Money is also the name of a song on DSotM.

(Boy, this kind of logic will give you Brain Damage).