Plantinga's Math Problem

[TT]

@mad_masala

I was doing this but lost my coin under some furniture.

Do you have a coin?

I have an app

[Leggat]

So, it seems the most rational position is a stoic agnosticism. I think, maybe.**

** yes, that’s the joke

[mad_masala]

An app that gives you the head.

Interesting.

[OysterOmelet]

@tando

just toss a coin 1000 times.

No that’s not gonna work.

[tando]

@Mick

toss a coin 1000 times and ask what are the odds it lands on heads 750 times ( or more ).

the problem is the same with the simple coin one.

[volv1992]

@TT

I have an app

Is it configurable to change the coin to a 20NT? Would then solve two threads on here simultaneously.

[TT]

@volv1992

Is it configurable to change the coin to a 20NT? Would then solve two threads on here simultaneously

The paid version of this app has more coins, mostly US (and two face from batman). No NT and no custom option, it seems

A different app might give the option, though. I just use this because sometimes a coin toss is an easy way to make a decision and I don’t always have a real one in the pocket

[Poundsand]

@OysterOmelet

If the probability that any one of your beliefs is true is .5, the probability that your cognitive faculties are reliable (.75 or more of your beliefs are true) is 10^-58. Show your work

That’s not what it’s saying. it’s saying if the probability any belief is .5, not 8f the probability of any one belief. Very different things.

@volv1992

My belief is that this is a load of shit.

My belief is oo posts many things from books that he doesn’t take the time to think critically about.

@Andrew

Don’t really get the point of this (and haven’t thought about it much), but the “27” bit is a citation. It should be 10^-58.

like this.

@OysterOmelet

I don’t know how you guys get 1000

and that. it says 1000 in your picture. not to mention, wtf is the difference between 75/100 and 750/1000 in probability, so who cares?

[Mick]

@Poundsand

wtf is the difference between 75/100 and 750/1000 in probability, so who cares?

If yu are measuring coin tosses, the probability of getting 75 heads out of 100 tries is massively higher than getting 750 heads out of 1000 tosses.

[OysterOmelet]

@Mick

If yu are measuring coin tosses, the probability of getting 75 heads out of 100 tries is massively higher than getting 750 heads out of 1000 tosses.

Yeah I originally got 5/16 as a wrong answer based on getting 3 out of 4.

[tempogain]

@OysterOmelet

Yeah I originally got 5/16 as a wrong answer based on getting 3 out of 4.

A wrong answer to what? I’m sure not the question in the OP.

[OysterOmelet]

@tempogain

@OysterOmelet

Yeah I originally got 5/16 as a wrong answer based on getting 3 out of 4.

A wrong answer to what? I’m sure not the question in the OP.

Yeah. Just do it 4 times and scale up.

[tempogain]

I guess Plantinga is trying to make some kind of point but not sure what. It seems obvious to me that if your beliefs have a .5 probability of being true as a rule, you have no hope of ever approaching .75 reliability.

[OysterOmelet]

@tempogain

I guess Plantinga is trying to make some kind of point but not sure what. It seems obvious to me that if your beliefs have a .5 probability of being true as a rule, you have no hope of ever approaching .75 reliability.

Yes, that’s exactly it. He defines reliable as .75 or better.

In addition to @Mick 's solution, this is how I computed it in Python.

import numpy as np
from scipy.stats import binom
k,n,p=750,1000,.5
answer=0
for i in range(k,n+1):
answer=answer+binom.pmf(i,n,p)

print(answer)
6.73812825301905e-59

This is how I originally tried to compute it.

There are 5 ways to get .75 or better.
TTTT
TTTF
TTFT
TFTT
FTTT

There 2^4=16 possible ways.

So the probability of getting .75 or better is 5/16.

[OysterOmelet]

Python only stores 16 places for floating point numbers. If you tried to use the cumulative density function, you’ll get a wrong answer.

1-binom.cdf(k,n,p)
Out[38]: 1.1102230246251565e-16

[Poundsand]

@OysterOmelet

Yes, that’s exactly it.

I think what TG is saying is “well, d’uh.” What’s the point? Yes, if you’re not any more right than a random coin flip on anything, you’re cognitive faculties aren’t reliable… and?

[tempogain]

Kind of, but I’m sure Plantinga must be going somewhere with it, and the OP was really purely about the math. I’d try to figure it out but it’s hard sledding reading him. I used to be more up for this kind of stuff but I’ve lost interest a little.

[OysterOmelet]

@tempogain

Kind of, but I’m sure Plantinga must be going somewhere with it, and the OP was really purely about the math. I’d try to figure it out but it’s hard sledding reading him. I used to be more up for this kind of stuff but I’ve lost interest a little.

He argued that if naturalism and evolution were both true, then our beliefs are indeed wrong half the time.

[Poundsand]

@OysterOmelet

He argued that if naturalism and evolution were both true, then our beliefs are indeed wrong half the time.

I’m assuming it’s not a direct ‘if x then y’ as you shorthanded above, so what does he base that argument on?

[TaipeiGuy2000]

The Self-Defeat of Naturalism: A Critical Comparison of Alvin Plantinga and...

“once one admits that one’s cognitive faculties are unreliable all of one’s beliefs are epistemically undermined, including one’s beliefs in naturalism and evolution”

Very interesting and I do not understand much of this. Perhaps the belief in naturalism is simply an evolutionary advantage.