Relation between an argument and false premise on Knowledge

Question

If I argue something from a premise such as "It's raining where I wrote this question" which is contingent false, then is it true that I could argue or deduct anything?

For example, from the premise above, can I argue that "It is not the case that it's raining where I wrote this question"?

I asked similar question few days ago. But because of my poor English, the question was not clear enough.

What I really want to know is the following:

In Gettier counter-example, why the fact that the premise is contingent false proposition doesn't matter?

I thought that all the problem comes from the false premise. But my prof said to me that it doesn't matter at all, and the fact that the conclusion comes from the premises by inference rule is important.

But I need more explanation for this issue.

Answer 1

The point of gettier counterexamples is not really one about deducing things from false premises. however, it is essential for a gettier counter-example that the premise be false.

the gettier case is supposed to be a counter-example to the claim that knowledge is justified true belief. It is therefore constructed in such a way that the agent forms a belief which is justified by something apparently false - an example of this stage in the process is when I look in a dark room and mistake John for Smith and assert that Smith is in the room. However, a lucky coincidence then makes the conclusion true - Smith also happens to be in the room but out of my visual field.

Gettier then asks us whether this is an instance of knowledge or not. It would be, were knowledge just justified true belief, because the belief is true and justified (on some loose definition of justified). however, we seem to have a strong intution that it is not knowledge.

Hopefully, this clarifies why it is not essential that the initial premise be false for the Gettier case to work.

For a longer, more exhaustive, and probably clearer explanation of the above, I'd recommend a paper by Linda Zagzebski; the title is something like the inescapability of Gettier problems but I' sure that if you look among her papers you will be able to pinpoint the one I'm talking about immediately.

Answer 2

We can refer to the "basic" of Aristotelian science :

The notion of "valid argument" is as old as "formal logic" itself; see Aristotle's logic :

A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so [emphasis added]. (Prior Analytics I.2, 24b18-20)

The core of this definition is the notion of “resulting of necessity” . This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of “valid argument”.

In a nutshell, we can say that according to Aristotle, science, i.e. true knowledge, is what we can deduce from true premises with a valid argument :

For this reason, science requires more than mere deduction. Altogether, then, the currency of science is demonstration (apodeixis), where a demonstration is a deduction with premises revealing the causal structures of the world, set forth so as to capture what is necessary and to reveal what is better known and more intelligible by nature.

Gettier Problems arise from Gettier's critique of the Justified True Belief account of knowledge; according to this view,

A subject S knows that a proposition P is true if and only if:

(i) P is true, and

(ii) S believes that P is true, and

(iii) S is justified in believing that P is true.

Gettier's Case II is :

Smith has a justified belief that "Jones owns a Ford". Smith therefore (justifiably) concludes (by the rule of disjunction introduction) that "Jones owns a Ford, or Brown is in Barcelona", even though Smith has no knowledge whatsoever about the location of Brown.

In fact, Jones does not own a Ford, but by sheer coincidence, Brown really is in Barcelona. Thus, Smith had a belief that was true and justified, but not knowledge.

The justified true belief came about, as the result of entailment (the inference licensed by disjunction introduction) from justified false beliefs that "Jones owns a Ford".

The issue is that, according to JTB theory, the conclusion : "Jones owns a Ford, or Brown is in Barcelona" appear to be knowledge because it is true (item (i)) : it's a fact that Brown is in Barcelona, and it is believed by Smith (item (ii)) and is justified by a correct use of inference rules (item (iii)) :

Smith, when he believes, holds a justified true belief. However, is Smith's belief an instance of knowledge? Intuitively, Smith's belief cannot be nowledge; it is merely lucky that it is true.

In fact it is not "real" knowledge, as we can see applying A's point of view : it is deduced from a false premise.

But the issue regards the "belief" involved in the definition : today we know that A's point of view regarding the possibility of achieving "absolutely" certain first principles to be used as starting points for science and knowledge is difficult to maintain.

JTB is a tentative account of knowledge which try to address this issue.