One can have a true belief arrived at from a false reason.
False premisses and an invalid form/inference can get you there. So what? It's irrelevant to the argument being made and you know it. — creativesoul
Gettier:
Secondly, 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...
Gettier:
...Smith is therefore completely justified in believing each of these three propositions...
I believe that John is a man because he is a bachelor.
Are you claiming that there is/are no other truth condition(s) and/or justificatory ground for your belief that John is a man? — creativesoul
Gettier states:
I shall begin by noting two points. First, in that sense of "justified" in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.
Secondly, 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.
Keeping these two points in mind I shall now present two cases in which the conditions stated in (a) are true for some proposition, though it is at the same time false that the person in question knows that proposition.
Gettier wrote:
Let us suppose that Smith has strong evidence for the following proposition:
(f) 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 placenames quite at random and constructs the following three propositions:
(g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) 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 (0, 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 he has strong evidence...
Gettier wrote:
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...
Gettier:
...Smith is therefore completely justified in believing each of these three propositions...
...S is justified in believing Q.
I believe that John is a bachelor. I believe that "John is a bachelor" is true. I believe that "John is a man" follows from "John is a bachelor". I believe that "John is a man" is true if "John is a bachelor" is true. I believe that "John is a man" is true because John is a bachelor.
John is a man but isn't a bachelor. So my belief that 1) ["John is a man" is true because John is a bachelor] is false, but my belief that 2) ["John is a man" is true] is true.
Smith's belief that 1) ["Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford] is false, but his belief that 2) ["Jones owns a Ford or Brown is in Barcelona" is true] is true.
Ignoring 2 doesn't make it go away.
S believes P, P entails Q, S deduces Q from P and accepts Q as a result of that deduction only gets us to belief that:((p v q) follows from (p)).
Therefore S does not yet believe that:((Q) is true) — creativesoul
One never gets to belief that:((p v q) is true). It stops at the former for reasons already argued for ad nauseum without subsequent refutation... — creativesoul
Gettier states:
I shall begin by noting two points. First, in that sense of "justified" in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.
Secondly, 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.
Keeping these two points in mind I shall now present two cases in which the conditions stated in (a) are true for some proposition, though it is at the same time false that the person in question knows that proposition.
Gettier wrote:
Let us suppose that Smith has strong evidence for the following proposition:
(f) 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 placenames quite at random and constructs the following three propositions:
(g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) 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 (0, 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 he has strong evidence...
Gettier wrote:
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...
Gettier:
...Smith is therefore completely justified in believing each of these three propositions...
...S is justified in believing Q.
1. p
2. p ⊨ p ∨ q
3. p ∨ q
This is a valid argument. Therefore the rational person who believes 1 and 2 will also believe 3. And Gettier states that Smith is a rational person and believes 3.
Your attempts to refute this are nonsense.
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