Introduction
I wrote about the Gettier problems a few days ago. I’ve rethought my arguments against Gettier Case II. To say the least, my attempt then was an utter failure: I messed up my translations to inclusive and exclusive ORs, not realizing that my arguments then were contingent on the validity of those translations as such. However, now I’ll make the IOR and XOR argument again, but from an anti-OL philosophy position. It is likely that my undertaking here will, like my previous attack, result in ineffectual nonsense, but there may, nevertheless, be some merit in the arguments that follow.
How things might be said to be different this time around is that, now, I’ve come to realize my true motivation against the “problem” illustrated by Case II does not center on the internal “problem” of “logic qua knowledge.” I was thinking that I could attack the logic “from the inside” and show it to be incoherent as logic, and thus not applicable to knowledge. Now, my argument has more to do with idealized language and the reduction of language to logic for further unrelenting analytic philosophical analysis. When the analytics strong-arm language into the domain of logic, it seems that unfair argument against Platonic language speakers–as if existing; in effect, straw men–dictates, almost certainly, the direction of the analysis. I should say now, I’ll be wary of such traps the analytics set, while maintaining, I suppose, some kind of hope that the papers I read in the future do not become rote, nauseating, and boring.
Complaints aside, I should switch gears into making my point. Both inclusive and exclusive ORs turn out true on the truth table; however, it’s that semantically these propositions yield different results or have different contexts for usage. Essentially, I think that although OR propositions may be calculated to give true value-assignments, they are epistemically neutral when analyzing human knowledge. These propositions tend to have non-contextual natures in that they speak relevantly about a specific context in a broad sense, but are propositions which are context-limiting yet not internally context-denoting.
If nothing is denoted, not having a specific claim being made about a certain referent, the proposition analyzed cannot be treated as a propositional knowledge-claim. OR propositions usually come of the form A v B, whereas A might be the case or B might be the case. So stated, the case is not actually denoted; cases are given as a context (e.g. “I know about the weather. It can generally be this or that…but not a dragon egg”, etc), limiting the relevance of other cases to the knowledge claim.
On Gettier Case II
A v B is logically equivalent to -A->B.
(1) Jones owns a Ford or Brown is in Barcelona.
(1.1) If Jones does not own a Ford then Brown is in Barcelona.
(2) It is raining or it is snowing.
(2.1) If it is not raining then it is snowing.
Now if we look at OR propositions in this way (typically called the ‘arrow’ derived rule; I can prove it without other derived rules), the question is raised: Does the speaker know the value of the antecedent when he or she speaks it?
Suppose Smith were to say, “If Jones does not own a Ford, then Brown is in Barcelona.” Smith must find out if Jones really owns that Ford or not. It can’t simply be that Smith would think, as Gettier would like it, “Well, I see him drive a Ford all the time.”
By validly changing the way the statement is uttered, the semantic emphasis is altered. Thus, certain questions become relevant regarding Smith’s knowledge. This is my example. If Smith were to say “if [...] then [...],” he’d be making a claim typically about logical inference. However, Smith isn’t in the Gettier case. He’s just making a JTB knowledge-claim, presumably. But in the form of 1.1, if it is uttered that way (regardless of if it actually shows up in ordinary language, it’s logically equivalent! so unless we admit that logical inference presupposes idealized language, we can say it could possibly show up in language), then we’d ask Smith. Seeing as that there’s a consequential relationship between the antecedent and consequent, he’d probably feel obligated to at least determine the consequential nature of the proposition. We’d ask what’s the truth-value of the antecedent, a pressuring move. Moreover, in this sense of the proposition, he’d come to know that Brown’s being in Barcelona contingent upon his knowing that Jones owns a Ford.
Smith is not justified in believing that Jones owns in the case of thinking “If Jones owns a ford…” because the usage of “if” demands that an empirical investigation is taken with seriousness. Not only that, but Smith is further saying “If Jones does not own a Ford…” Posed as the logical equivalent conditional, for Smith to venture into “listing” inferred OR statements, what keeps us from asking, “Why not go further and check the truth value of the antecedent?”
Gettier seems to believe that “logically justified inference” is tantamount to “justified belief.” But we all know that we do not intuitively think in terms of logical inference alone. We impose logic on our thinking, not the other way around. Logic has nothing to gain from perpetuating its usage. Most of our lives, we think illogically.
Furthermore, so stated as the logically equivalent conditional, why, at all, would Smith think that Brown’s being in Barcelona is even contingently and consequentially relevant to Jones’ owning a Ford? They’re of different categories. (2) and (2.1) at least refer to the same thing, the weather. Typically, it doesn’t rain when it snows.
(3) Jones owns a Ford or Brown is in Barcelona, or Jones owns a Ford and Brown is in Barcelona. (IOR)
This is obviously epistemically unjustified. Smith just rattled off a list. So, he couldn’t possibly know A & B, even if it is an included OR. He wouldn’t even think of knowing it, only hypothesizing it. He would have no justification in believing an inclusive.
(4) Jones owns a Ford or Brown is in Barcelona, and it is not the case that Jones owns a Ford and Brown is in Barcelona. (XOR)
Again, why would he make any sort of and claim if he just rattled off a list of possibilities? He’d never possibly know them unless he checked. And he couldn’t be epistemically justified based on the inference because the list was just conjured up. If he thought of and at all, he’d ask himself, “Do I know this?” So he would have to increase the inner determining (to use Kant’s strength of will; think “strength of justification” to one’s self) ground of his justification. He’d have to raise the bar on what he’s justified in believing. Gettier seems to think he can just do it for the sake of argument…raise the bar to the maximal belief justification, regardless of the proposition’s phrasing and semantic persuasion. As if language is like the geometric figures the Cartesians believed they could impose upon Nature.
Analytic philosophers are committing the same mistake they accused, and probably still accuse, many of the metaphysicians before Kant (or really before the Vienna Circle). They’re importing nonexistent (linguistic) constructs that do not actually grasp anything real about the world.
I’ll rethink Gettier Case I and Gettier Cousin Case III later; I’ll further consider my overall attack on the unnatural “language” the analytics have been using for their expositions of philosophical discourse. Perhaps I’m completely off the mark.