Gettier Problem

hlss09 2012-01-28 21:41:19 UTC #1

Okay. So, I was asked if Gettier, in his paper Is Justified True Belief Knowledge, uses deduction in his Case II?

I noticed that in Case 2, Gettier lays out a disjunction. Basicallly, as far as I can see, Gettier lays out the propostion (f) that Jones owns a Ford, and propositions (g), (h), and (i) as 'tack on' statements.

The article says that Jones owns a Ford:

Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:

Either Jones owns a Ford, or Brown is in Boston.
Either Jones owns a Ford, or Brown is in Barcelona.
Either Jones owns a Ford, or Brown is in Brest-Litovsk.
Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (f), and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which be has strong evidence. Smith is therefore completely justified in believing each of these three propositions, Smith, of course, has no idea where Brown is.

But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.

So, according to the rule of disjunctions, only one half of the disjunction has to be true for the whole thing to be true. It doesn't matter that Smith is wrong in (f) that Jones owns a Ford, becasue by luck, Brown happens to be in Barcelona. That being said, is there a deduction at play?

I thought not. I thought that there is a deduction in the case 1, obviously. But, the more I look at this, the more I think that possibly Smith IS using deduction. The deduction rule, as Gettier outlines earlier:

for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.

So, perhaps...

(i) Smith is justified in believing that ((f) v (h))
(ii) (f) Jones owns a Ford entails ((f) v (h))
(iii) Smith deduces ((f) v (h)) from (f) Jones owns a Ford
(iv) Smith believes ((f) v (h)) as a result of this deduction

Is ^ correct, to any philo wizards out there? Is Smith/Gettier using a deduction in the Gettier case? I need help my peeps!

dshroy 2012-01-28 02:41:31 UTC #2

hlss09 wrote:
Okay. So, I was asked if Gettier, in his paper Is Justified True Belief Knowledge, uses deduction in his Case II?

I noticed that in Case 2, Gettier lays out a disjunction. Basicallly, as far as I can see, Gettier lays out the propostion (f) that Jones owns a Ford, and propositions (g), (h), and (i) as 'tack on' statements.

The article says that Jones owns a Ford:

Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:

Either Jones owns a Ford, or Brown is in Boston.
Either Jones owns a Ford, or Brown is in Barcelona.
Either Jones owns a Ford, or Brown is in Brest-Litovsk.
Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (f), and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which be has strong evidence. Smith is therefore completely justified in believing each of these three propositions, Smith, of course, has no idea where Brown is.

But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.

____________________

So, according to the rule of disjunctions, only one half of the disjunction has to be true for the whole thing to be true. It doesn't matter that Smith is wrong in (f) that Jones owns a Ford, becasue by luck, Brown happens to be in Barcelona. That being said, is there a deduction at play?

I thought not. I thought that there is a deduction in the case 1, obviously. But, the more I look at this, the more I think that possibly Smith IS using deduction. The deduction rule, as Gettier outlines earlier:

for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.

So, perhaps...

(i) Smith is justified in believing that ((f) v (h))
(ii) (f) Jones owns a Ford entails ((f) v (h))
(iii) Smith deduces ((f) v (h)) from (f) Jones owns a Ford
(iv) Smith believes ((f) v (h)) as a result of this deduction

Is ^ correct, to any philo wizards out there? Is Smith/Gettier using a deduction in the Gettier case? I need help my peeps!

Nards 2012-01-28 02:51:57 UTC #3

Ya I think Spock hacked into your T-Nation man.

alexus 2012-01-28 02:56:47 UTC #4

ahahahaha.

epistemology. don't miss it.

do i use 'deduction' (or perhaps some other step of inference?) to form the following beliefs or are they perhaps formed without some step of inference...

2 is greater than 1
3 is greater than 1
4 is greater than 1
5 is greater than 1
6 is greater than 1

(and so on??)

my point being...

the disjunctive rule says that from p you can infer either p or anything you like...

do i use 'deduction' (or perhaps some other step of inference?) to form the following beliefs or are they perhaps formed without some step of inference...

2 is greater than 1 or i am the king of the world
2 is greater than 1 or i am not the king of the world
2 is greater than 1 or getteriology is a Fucking Waste of Time lolz.

TigerTime 2012-01-28 03:19:16 UTC #5

Technically speaking, yes. He's using the model of deductive reasoning, but in real life we know that the type of car Jones owns doesn't define Brown's location and he's wrong to think otherwise. However, so long as he believes these conclusions follow from his premise, he is using Deductive reasoning.

Although, this is just my opinion. It's equally valid to say that the truth value of one's reasoning out-weighs the use of its model. In this case, since the conclusion doesn't follow from the premise by necessity, it cannot be deductive reasoning (or any kind of reasoning really, since it's such a silly belief). I just happen to believe deductive reasoning is a matter of attempt, rather than result. It's the key, rather than the opening lock.

Whoever asked you this is just fanning the flames of thought. The actual answer you come to doesn't matter, so long as you come to a conclusion you feel you can justify.

Nards 2012-01-28 03:26:57 UTC #6

T Nation...What a country!

biglifter 2012-01-28 03:48:17 UTC #7

I pick things up and put them down.

SkyzykS 2012-01-28 04:22:04 UTC #8

Nope. And here's why.

alexus 2012-01-28 05:30:36 UTC #9

alexus 2012-01-28 05:40:41 UTC #10

smith is justified in believing that jones owns a Ford (we are asked to grant this and I don't think too many people have problems with this.

The 'Disjunction' rule is a bit harder (unless one has done a bit of formal logic). I'm opposed to trying to teach Gettier to students who haven't studied formal logic for the simple reason that all of a sudden a lot of background is required...

the disjunction rule:

Let us take the proposition 'jones owns a Ford' and let the variable p stand in its place. p could be true or p could be false. of course we know that while smith is justified in believing that p is true p is actually false - but for now forget about that.

It will help a lot if I can draw a truth table.

that just says that p could be true (it is in the first world / row) and p could be false (it is in the second world / row).

now we need another variable to stand in for a different proposition. this proposition again, needs to be one that could be either true or false. just for fun let q= Brown is in Barcelona.

now we want the truth table to capture all the possibilities with respect to the truth / falsity of p and q:
p q
T T
F T
T F
F F

since there are two propositions (p, q) there are 4 possible combinations of truth values. The first column / world is a world in which p is true and q is true. the second column / world is a world in which p is false and q is true.

(bonus marks - which world do we live in?? bonus bonus marks - which world does smith believe we live in??)

now we are ready to stipulate / describe the logical rule 'disjunction'. a disjunction is roughly (not exactly) equivalent to the english expression 'or' or 'either one or the other or both'. the symbol we use is v. so pvq is (roughly) 'either p is true or q is true or both are true' or, alternatively (equivalently) 'p and q are not both false'. roughly isn't good enough. we now want to know precisely when pvq is true, and precisely when pvq is false.

ready?

p q pvq
T T T
T F T
F T T
F F F

the disjunction 'pvq' is true in the first world (the case where p is true and q is true). it is true in the second world where the first disjunct is true (where jones owns a ford) and the second disjunct is false (where brown is not in barcelona). it is true in the third world where the first disjunct is false (where jones doesn't own a ford) and the second disjunct is true (where brown is in barcelona). it isn't true (is false) ONLY WHEN both disjunct aren't true (are false).

why?

BY DEFINITION. that is just the way it is. it might sound odd / strange. whatever. if you think that is bad wait till you get to the paradoxes of material implication. it actually isn't so bad... lets try and get into the spirit of it: what is required for the expression 'either one thing is true or the other thing is true or both things are true' to be true? why, for one or the other or both of those things to be true... or for both of them not to be false...

so... disjunction. a valid deductive inference.

back to gettier...

we are asked to grant that smith is justified in believing that jones owns a ford. okay. we are also told that it is false that jones owns a ford, BUT THAT DOESN'T MATTER. the point is that he is justified in believing that jones owns a ford.

the justified belief that jones owns a ford isn't a candidate for knowledge, of course, because the belief is false. but that doesn't matter. gettier isn't trying to persuade us that it is a candidate for knowledge.

smith knows his logic. and he knows that if p is true then the truth value of q is irrelevant to the truth of a claim of the form pvq (because only one disjunct need be true). so... cause he is a little tricky like that he takes a claim he (wrongly oops) believes to be true (jones owns a ford) and gets a little funky and infers that either jones owns a ford or brown is in barcelona. i'm pretty sure he doesn't stupidly believe that the kind of car jones drives impacts on the location of brown - it is more that he believes that the first claim is true and that is all that matters for the disjunctive rule to be applied.

so in other words... he takes a claim that he is justified in believing to be true and he applied a rule that he is justified in believing to be valid in order to arrive at the claim 'either jones owns a ford or brown is in barcelona'. he seems justified in believing the latter to be true, yeah?? and he is right - the latter is true.

he knew that.

suck it up.

alexus 2012-01-28 05:41:39 UTC #11

of course people think there is something dodgey. perhaps something along the line of 'you can't infer truths from falsehoods'.

but that is crap.

paradox of material implication:

from a false premiss i can infer anything i like!!

Vicomte 2012-01-28 05:42:14 UTC #12

What the fuck?

Is this what people do in college?

I'll tell you a little something I learned when I was a young boy with an inquiring mind and lots of free time:

Sometimes a thing is so smart it's gone full circle back to completely fucking retarded.

^Exhibit A for the prosecution.

alexus 2012-01-28 05:44:37 UTC #13

bitch of a question btw. my commiseration's.

Vicomte 2012-01-28 05:44:43 UTC #14

Except for the false premise.

That would be Holmes's old saw about eliminating the impossible, no?

alexus 2012-01-28 05:50:30 UTC #15

thats brilliant that.

kinda like how how
psychology ain't anything over and above chemistry
and chemistry ain't anything over and above physics
and physics requires an observer
which (arguably) brings us back to mind.

alexus 2012-01-28 06:01:42 UTC #16

i'm not sure. all i know is that material implication (backwards c) is defined such that anything follows from a false premiss.

so...

if the moon is made of green cheese then i'm a monkeys unkle' is true. and of course it is also similarly true that if the moon is made of green cheese then i'm not a monkeys unkle. similarly anything follows from a contradiction (since contradictions are necessarily false - false in all possible worlds / rows).

i did some of this stuff in college. it was okay. i think it gives philosophy a bit of a bad name. gettier has given epistemology (study of knowledge) a bit of a bad name from within philosophy, too. most people don't like him very much... very technical / logical / anal... set off a whole process (somewhat affectionately referred to as getteriology) of offering a different criterion for converting a juicy tasty beef (justified true belief) into knowledge... then a counter example... then a criterion... then a counter-example.

philosophy has more to offer definitely.
the rest of college for sure.

but it is kinda cool. was for me anyway. felt like understanding came and went... not quite as good as a perfect squat but pretty close sometimes.

alexus 2012-01-28 06:03:02 UTC #17

re your paper.
just do your best, son.

alexus 2012-01-28 06:27:58 UTC #18

it is revising up better

I thought not. I thought that there is a deduction in the case 1, obviously. But, the more I look at this, the more I think that possibly Smith IS using deduction. The deduction rule, as Gettier outlines earlier:

for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.

So, perhaps...

P=Jones owns a ford
Q=either jones owns a ford or brown is in barcelona

(i) Smith is justified in believing that (jones owns a ford) P
(ii) Jones owns a Ford entails (either jones owns a ford or brown is in barcelona) P entails Q
(iii) Smith deduces 2 from 1 (s deduces Q from P)
(iv) Smith believes 2 as a result of this deduction (Q accepted as result).

so S is justified in believing Q. Q is true. smith KNOWS it (iff the JTB theory is correct).

Why would you think Smith ISN'T using deduction?? ***
deduction... what better form of justification could there be??

Vicomte 2012-01-28 06:12:31 UTC #19

alexus wrote:

Vicomte wrote:

alexus wrote:
of course people think there is something dodgey. perhaps something along the line of 'you can't infer truths from falsehoods'.

but that is crap.

paradox of material implication:

from a false premiss i can infer anything i like!!

Except for the false premise.

That would be Holmes's old saw about eliminating the impossible, no?

i'm not sure. all i know is that material implication (backwards c) is defined such that anything follows from a false premiss.

so...

if the moon is made of green cheese then i'm a monkeys unkle' is true. and of course it is also similarly true that if the moon is made of green cheese then i'm not a monkeys unkle. similarly anything follows from a contradiction (since contradictions are necessarily false - false in all possible worlds / rows).

i did some of this stuff in college. it was okay. i think it gives philosophy a bit of a bad name. gettier has given epistemology (study of knowledge) a bit of a bad name from within philosophy, too. most people don't like him very much... very technical / logical / anal... set off a whole process (somewhat affectionately referred to as getteriology) of offering a different criterion for converting a juicy tasty beef (justified true belief) into knowledge... then a counter example... then a criterion... then a counter-example.

philosophy has more to offer definitely.
the rest of college for sure.

but it is kinda cool. was for me anyway. felt like understanding came and went... not quite as good as a perfect squat but pretty close sometimes.

I have absolutely no idea what you meant.

None at all.

Are you saying a false premise hold no sort of sway over the following 'proof' (or whatever these things are called in this situation?

'Cause it seems to me, that if the premise is false, then we can at least rule out the false premise, if nothing else.

I'm just trying to understand the rules of this thing.

hlss09 2012-01-28 07:11:43 UTC #20

Alexus, I love you. I'm going to PM you BTW. But yeah. I've taken intro logic. Class I'm in is writing on various philosohpical subjects. We write a paper every week. lol. This week is on epistemology. I understand the concept of truth tabels. Wittgenstein, right? I also understand disjunctions. I just think it's werid that "smith" claims he's somewhere as a disjunct to something else that he's justified in believing.

I guess then I coiuld say that 2+2=4 or dogs can break dance. I mean, by definition this disjunction is true, b/c 2+2 is true and I'm justified in believing it. But, what if I KNOW that dogs CAN'T break dance?

It's one thing to deduce something on a false premise, but another to intentinally place a disjunct that you know to be false, correct, or not?

As far as the false premise argument: Gettier talks about a guy in a park. The guy sees a dog standing in the park, and says to himself "there's a dog in the park." He's obviously justified in this belief - he sees a dog, etc. He is justfiied. But, as it turns out, that dog is actually a robotic hologram. Additionally, however, there IS a dog behind a tree, out of the man's line of sight. So, his belief that there's a dog in the park is technically TRUE, but it's based on a deduction that relies on a falsehood. This example disproves that knowledge can result from a falsehood...