So, let the games begin.
Four games will be played in the following chapters. In these games the
concepts of truth, justification, and knowledge will be discussed as well as
the inference rule Modus Ponens and the epistemic principles of
conjunctive and deductive closure.
In chapter 2 Lewis Carroll’s famous article, "What the Tortoise said to Achilles,"
will be discussed. In Carroll’s article the
Tortoise wins over Achilles in a most special theoretical race: he seems
successfully demonstrate that Modus Ponens cannot be justified. My aim
is to show that there is an escape for Achilles from the Tortoise’s conclusion:
Achilles can argue that the Tortoise is unable to win and thus the Tortoise
fails to make any relevant point about the challenged logical principle.
In this way, Modus Ponens, and more generally first logical principles,
can be justified, at least in one special sense of the concept of
justification. I will present my reply go Carroll’s position in two
steps: first I will show that the Modus Ponens-skeptic fails to
challenge our reliance on Modus Ponens. She fails because she cannot
coherently claim her position: undermining Modus Ponens itself depends
upon the application of this rule. I will then consider the special game played
by the Tortoise and Achilles. Exploiting the dialogical setting, I will present
an Aristotelian “negative” demonstration for Modus Ponens.
Truth will be the central
concept of chapter 3. Verificationism is the doctrine stating that all truths
are knowable. This interpretation of the concept of truth seems especially
appropriate for epistemological purposes. Fitch’s knowability paradox, however,
teaches us that the verificationist claim (all truths are knowable) leads to
“epistemic collapse”, i.e. everything which is true is (actually) known.
First, I will examine the intuitionistic response to Fitch’s paradox, defended
primarily by Timothy Williamson. My main objection will be that an
intuitionistic answer cannot be extended to areas of empirical knowledge. I
will then introduce and analyze a solution that remains within the scope of
classical logic. This solution is based on the introduction of a truth operator
through which the shortcomings of the non-standard solution can be avoided.
Nevertheless, this solution still falls short of our expectations. Truth, as
defined by my truth operator, is not closed under the rule of
conjunction-introduction. I will conclude that verificationism, extending to
empirical areas, is defensible, though only at a rather great expense.
Verificationism tries to
connect directly the concepts of truth and knowledge. Epistemic theories
usually choose a longer, less direct connection: truth becomes one of
the necessary conditions for propositional knowledge. Another important
condition for knowledge is the justification of the putative knower’s true
beliefs. Justification will be the central concept of chapter 4. I will discuss
one important epistemic principle related to this concept: the connective
closure principle of justified true beliefs. This principle has recently been
challenged by several paradoxes. The lottery paradox reveals that the set of
the intuitively most appealing epistemic principles is inconsistent. According
to the paradox, we have to abandon at least one of these principles as either
the Conjunction or the Less-Than-Absolute-Certainty Principle. I will suggest a
solution which avoids the denial of these two principles. First, I will refine
the formal language such that not only lottery tickets but also their sets can
be considered. This technical modification, which is instrumental for my
solution, makes the relevant propositions simple and easily conceivable. Then
we turn to the central question of the paper: “What exactly can justify a
person’s beliefs about his lottery tickets?” The answer will show that in order
to resolve the paradox we have to modify the Generalization Principle, which
determines how justification can be transferred from one belief to others.
In the last chapter of Part 2 I will discuss Nozick’s theory of knowledge, inspired by Gettier’s famous counter-examples as well as by the many “post-Gettier” challenges to knowledge. To ensure the proper, non-accidental connection between facts and the knowledge about them, Nozick introduces a counterfactual analysis of belief states. If the epistemic agent’s belief “tracks” the truth and falsity of the corresponding proposition, i.e. his belief co-varies with the truth of this proposition, then the agent’s true belief amounts as knowledge. Otherwise it does not. One of the most important and famous outcomes of Nozick’s theory is the claim that knowledge is not closed under deduction. I will analyze Nozick’s theory arguing that it is both too strong and too weak. Nozick’s theory excludes situations which we intuitively judge as cases of knowledge while it acknowledges others which we intuitively would not. I will also argue against Nozick’s non-closure, pointing out that it can both lead to a special case of omniscience, and question convincing cases of empirical knowledge.