Title: oxford / 102 knr

Front: types of modality
Back: Modality (necessity + possibility) comes in different kinds:
1. Logical modality (P v ~P)
2. Metaphysical modality. This has no generally accepted definition, but is metaphysical possibility is generally taken to be the broadest kind of possibility short of logical possibility. (Nothing can be green all over and red all over. Nothing can travel faster than itself.)
3. Nomic or physical modality. (Nothing can travel faster than light. It’s a law of nature.)
4. Epistemic modality. (Fred cannot be the killer. The evidence shows that he’s innocent.)
5. Deontic modality. (You cannot promise to come and then stay at home. It’s wrong.)

Front: Nozick's tracking account of knowledge
Back: S knows p iff:
1. S believes P
2. P is true
3. If P were false, S would not believe P [sensitivity]
4. If P were true, S would believe P
(3) and (4) are counterfactual conditions. see: interpretations of counterfactuals.

Front: counterfactuals
Back: Think of the set of possible worlds, which can be more or less 'close' (~ similar) to the actual world:
* Stalnaker assumes ("limit") that there exists a closest possible world to each world. Lewis does not assume this.
* Stalnaker’s says that each world is at least as close to itself as any other is; Lewis’s makes the stronger claim
that each world is closer to itself than any other is.
Lewis:
P boxarrow Q at w iff either
P is true at no worlds
OR
There is some world, x where P is true, and at every world closer to w than x, P rightarrow Q.
Stalnaker:
P boxarrow Q at w iff for any world x, if x is the closest-to-w world where P is true, then Q is true at x.

Front: contextualism about knoweldge
Back: Epistemic Contextualism (EC) is roughly the view that
what is expressed by Alice when she says "S knows that P" depends partly on something in the context of Alice (the attributor).
Because what such an utterance expresses is context-dependent, so too is whether the knowledge attribution is true.
Features of the context that typically matter in an EC view:
* A's practical stake in the truth of p
* The prominence in A's situation of skeptical doubts about knowledge
We can give an analysis of EC in terms of Nozick's tracking account of knowledge, to the effect that
In counterfactual condition (3) "If P were not true, S would not believe P", context determines which possible worlds are to be considered to evaluate the counterfactual.

Front: sensitivity condition on knowledge
Back: If p were false, S would not believe that p.

Front: safety condition on knowledge
Back: If S were to believe that p, p would not be false.
e.g. In the close possible world where Merton college voted against admitting women, Alice would still believe p, but p would be false.

Front: Reliabilism about knowledge
Back: Simple K-Reliabilism:
S knows that p iff
    p is true;
    S believes that p;
    S’s belief that p was produced by a reliable cognitive process.

Front: Fission
Back: Hemispherectomy is considered a drastic but acceptable treatment for otherwise-inoperable brain tumors.
1. Hemispherectomy: We destroy L. The result is psychologially continuous with you.
2. Transplant: We destroy L, and transplant R. The one who received the transplant would be psychologically continuous with you.
3. Fission: We transplant both L and R, each into a different empty head.  The two recipients —call them Lefty and Righty—will each be psychologically continuous with you. However, lefty and right cannot be identical.
So psychological continuity != indentity
Should we care about identity or psychological continuity? Parfit: psychological continuity.

Front: indefinite and definite descriptions

Front: non-existent objects and definite descriptions
Back: People thought sentences involving definite descriptions of non-existent objects posed a puzzle.
(A) The present king of France is bald.
(A) does not seem to be true: if we consider all the bald things, the present King of France isn't among them. But if it is false, then one would expect that not(A), that is, "It is not the case that the present King of France is bald," or its logical equivalent, "The present King of France is not bald," is true. But this sentence doesn't seem to be true either: if we consider all the things that fail to be bald, the present King of France is not among them. We therefore seem to have a violation of the Law of Excluded Middle.
But (A) seems perfectly intelligible.
A sentence like "the present King of France", Russel suggested, isn't a referring expression. Rather, it is a definite description, i.e. it makes an existence claim.
Thus A can be formalised as:
(A_formal)∃x(Kx ∧ ∀y(Ky → x=y) ∧ Bx)
This reveals that "The PKoF is not bald" is ambiguous between
(notA_formal1) ¬∃x(Kx ∧ ∀y(Ky → x=y) ∧ Bx)
(notA_formal2) ∃x(Kx ∧ ∀y(Ky → x=y) ∧ ¬Bx)
A_formal, notA_formal1 and notA_formal2 all have a truth value. So we do not have a violation of the law of the excluded middle.

Front: a priori
Back: Three attempts to precisify "a priori"
1. A proposition is a priori iff its truth-value can be known independently of any sensory experiences.
2. A proposition is a priori iff its truth-value can be known independently of any facts about the actual world.
3. More formally:
Usually when we utter P at world w we mean "P, considering w as actual". But with 2D semantics, we can also express the more general notion "P, considering v as actual" where v is some other world. We may evaluate propositions at pairs of worlds (world considered actual, described world). P is true at (v,w) iff P truly describes w when v is considered as actual. The usual conception of truth at w is truth at (w,w). We may now define a prioricity in a way that distinguishes it from necessity.
P is a priori iff P is true at (w,w) for all w
2D semantics distinguishes 2 kinds of necessity.
Nec_1: P is necessary (when uttered in w) iff P is true at (v,v) for all v
Nec_2: P is necessary when uttered in w iff P is true at (w, v) for all v
A prioricity concides with Nec_1, but not with Nec_2.
Other fields (not shown on cards):
notes: sider terminology:
Nec_1 = Deep Necessity
Nec_2 = Shallow necessity

Front: analytic proposition
Back: Aproposition is analytic iff it is possible to know its truth-value by knowing its meaning alone. Otherwise, it is synthetic.
A more formal attempt: A proposition is analytic iff it is possible to turn it into a tautology by synonym-substitution.

Front: The new riddle of induction stated
Back: Suppose that at time t we have observed many emeralds to be green and no emeralds to be any other color. We thus have evidence statements:
Emerald a is green, emerald b is green, etc.
and these statements support the generalization:
All emeralds are green.
Now define the predicate “grue” to apply to all things observed before time t just in case they are green and to other things just in case they are blue. Then we have also the evidence statements
Emerald a is grue, emerald b is grue, etc.
Hence the same observations support incompatible hypotheses about emeralds to be observed after t; that they are green and that they are blue.

Front: open texture
Back: Open texture is the idea that however tightly we think we define an empirical predicate, there always remains a set of (possibly remote) possibilities under which there would be no right answer to the question of whether it applies.
It is not the same as vagueness, since in actual situations the application of the term may be quite un-vague.
For example, the term ‘mother’ is not vague, but its open texture is revealed if through technological advance differences open up between the mother that produces the ovum, the mother that carries the foetus to term, and the mother that rears the baby. It will then be fruitless to pursue the question of which is the ‘real’ mother, since the term is not adapted to giving a decision in the new circumstances.

Front: lottery
Back: The threshold view of belief simpliciter: "it is rational to believe something simpliciter iff it is rational to believe it with a probability p>y."
The lottery case purports to show that the threshold view is false.
1 Let the threshold y required for belief be any real number less than 1. For example, let y = 0.99.
2 Now imagine a fair lottery with 100 tickets
3 It is rational for you to have 0.99 confidence that ticket #1 will not win, 0.99 confidence that ticket #2 will not win, and so on for each of the other tickets. According to the [threshold view], this implies that it is rational for you to believe each of these propositions.
4 Assuming that rational belief is closed under conjunction, it is also rational for you to believe that (ticket #1 will not win and ticket #2 will not win . . . and ticket #100 will not win)” (Foley 1992).
5 However, this is a contradiction with your belief that the lottery is fair, i.e., that exactly one ticket will win the lottery.
6 Thus y cannot be 0.99. The same conclusion can be reached for any probability y<1: simply create a lottery with (2-y)/(1-y) tickets, and argue as before. Thus the threshold cannot be any less than 1.

Front: de re and de dicto
Back: The sentence "The president of the United States is male" becomes ambiguous if we apply modal operators to it. Specifically, is this sentence necessarily true?
[latex]
$\Box Mt$ [de re reading] \\
$\Box \forall x (Px \rightarrow Mx)$ [de dicto reading] \\
Where the extension of $P$ at this world is the singleton containing $t$.
[/latex]
It could mean: "Donald Trump is male" or "The person holding the Presidency is male".
In the first case, Donald Trump is picked out in every possible world, while in the second case, the POTUS is picked out in every possible world.
Thus the first sentence (de re) is arguably necessary, while the second (de dicto) is not.
De dicto necessity is philosophically uncontroversial, whereas de re necessity requires a meaningful transworld counterpart relation.

Front: a sceptical argument
Back: sceptical arguments take this form:
P1: If I know P, then I know not-BIV
P2: I do not know not-BIV
C: I do not know P
Where P is some ordinary proposition and BIV is a sceptical scenario.

Front: a gettier case
Back: Suppose King's college has recently voted to admit women by a just barely sufficient majority. The boy's choir is singing in the chapel when a visitor (who is not aware of the vote) hears their voices from the main quad and remarks: "King's college must have admitted women". Asked for a justification, she says: "I hear their high-pitched voices". Her belief is true and justified. But we would not call it knowledge. Her justification is not of the right kind. She just got lucky.

Front: no false lemmas
Back: No False lemmas: JTB+X where
X = S’s belief that p is not inferred from any falsehood.
In Gettier’s cases, the justified true belief is inferred from a justified false belief. So this condition explains why it isn’t knowledge.

Front: barn county
Back: The landscape next to the road is peppered with barn-facades: structures that from the road look exactly like barns. Suppose Henry is driving along the road.
Now suppose that Henry happens to be looking at the one and only real barn in the county. His belief is true, and Henry has no reason to suspect that he is the victim of organized deception, it is justified. But since its truth is the result of luck, it is exceedingly plausible to judge that Henry’s belief is not an instance of knowledge.
Yet the no-false-lemmas condition is met in this case. His belief is not the result of any inference from a falsehood.
Depending on how the case is set up, the sensitivity condition may also be met. Suppose the particular location Henry is examining is not one that would have been suitable for the erecting of a barn façade. If there had been no barn, Henry would not believe there is a barn.

Front: Gettier overview
Back: JTB+X
Gettier -> No false lemmas -> Barn country -> Sensitivity -> Barn Country II -> Safety
TB+Y
Tracking account ⊆ K-realiabilism
Beyond the analysis of Knowledge
Zagzebski (1994) and Sturgeon (1993) point out that unless the safety of the belief or the reliability of the cognitive process are taken to literally guarantee truth, cases of epistemic luck can always be constructed. Abandon one-size-fits-all analysis and let the stringency of the condition vary according to context

Front: internalism and externalism
Back: Internalists about justification think that whether a belief is justified depends wholly on states in some sense internal to the subject. Externalists about justification think that factors external to the subject can be relevant for justification; for example, process reliabilists think that justified beliefs are those which are formed by a cognitive process which tends to produce a high proportion of true beliefs relative to false ones.
gettier's original case is aimed at internalists

Front: epistemic closure under known entailment
Back: Kowledge is closed under known entailment iff
K: If, while knowing p, S believes q because S knows that p entails q, then S knows q.

Front: closure and the tracking account
Back: Suppose you are at a zoo standing in front of a cage marked ‘zebra’; and you truly believe zeb, that the animal in the cage is a zebra.
Zeb entails not-mule: it is not the case that the animal in the cage is a cleverly disguised mule rather than a zebra. 'Zeb entails not-mule' is a necessary proposition, you know it.
If not-mule were false, you would still have zebra-in-a-cage visual percepts, and you would still believe not-mule. So according to the tracking account you do not know not-mule.
[Contextualists may still reply that this argument fails to distinguish between different senses of know. The closure principle is correct, contextualists say, so long as it is understood to operate within given contexts, not across contexts.]

Front: lewis' analysis of modality
Back: Lewis is a reductionist about modality. He wants to explain modality in non-modal terms.
According to lewis:
Necessarily, P iff in every world, P.
Lewis' view contains two claims:
1. Using a possible worlds semantics: analysing modality in terms of quantification over possible worlds
2. Being a realist about possible worlds: calling them just worlds.
Part (2) is what allows Lewis' account to be reductionist.

Front: conceptions of possible worlds
Back: Realism
1. Possible worlds exist -- they are just as real as our world;
2. Possible worlds are the same sort of things as our world -- they differ in content, not in kind;
3. Possible worlds cannot be reduced to something more basic -- they are irreducible entities in their own right.
Abtractionism
Possible worlds are abtract entities describing total ways things could be. Adams (1974), for example, defines possible worlds to be consistent sets of propositions that are total in the sense of containing, for every proposition p, either p or its negation
Combinatorialism
Takes possible worlds to be recombinations, or rearrangements, of certain metaphysical simples. Both the nature of simples and the nature of recombination vary from theory to theory.

Front: the golden triangle

Front: instance confirmation
Back: Hempel's instance confirmation

Front: paradox of the ravens

Front: bayesianism and the paradox of the ravens

Front: grue
Back: Suppose we define a predicate “grue” in the following way. An object is “grue” when it is green before time t and blue after time t.
Goodman considers a thought experiment in which we observe a bunch of green emeralds before time t. We could describe our results by saying all the observed emeralds are green and infer that all emeralds are green. But equally, we could describe the same results by saying that all observed emeralds are grue, and infer (using the same rule) that all emeralds are grue.
Inter-definability:
We can define the predicate bleen, which applies to things that are blue before time t and things that are green after time t. Now ‘green’ can be defined in a time-dependent manner too: things are green iff they are grue before t and bleen after t. If we start with blue and green, bleen and grue are defined using a temporal term; but if we start with grue and bleen, it is green and blue which are defined using a temporal term.

Front: hume and goodman
Back: Hume: Can induction be given a rational justification?
Goodman: Even it it cannot be justified, can we give a non-arbitrary distinction between predicates for which induction works and predicates for which it does not?

Front: hume's problem of induction

Front: the gettier intuition
Back: Accidentally true beliefs cannot be knowledge

Front: readings of the problem of induction
Back: We want to ground inferences like:
* If X is observed to be Y many times, then we should expect all Xs to be Y
Using degress of belief allows us to sharpen the question. We should increase our credence that all Xs are Y...
Absolutely: [the principle of inference]
* If X is observed to be Y many times, then we should increase our absolute credence that all Xs are Y, and reduce our credence in some other hypothesis
Relative to gruesome hypotheses [the principle of uniformity]
* [informal version] If X is observed to be Y many times, then we should increase our credence that all Xs are Y, relative to our credence in a hypothesis like "all Xs observed before time t are Y, others are not Y"
* [bayesian version] Use a prior distribution which places more probability mass on simple hypotheses like "all Xs are Y" and less weight on gruesome ones like "all Xs observed before time t are Y, others are not Y".
For each of these princples, we can distinguish:
* justifying it
* specifying it non-question-beggingly
This leaves four problems. Specifying the principle of inference is trivial, so there are three problems.
1. Justifying the principle of inference:
Can there be a justification for any instance of reasoning from particular examples to a universal conclusion? e.g. if I observe a black raven, what justifies increasing my absolute credence that all ravens are black?
This would be Hume's problem on an uncharitable reading.
The answer: Bayesian conditionalisation justifies this. Conditionalisation has strong support from a pragmatic self-defeat test, dutch books.
2. Justifying the principle of uniformity
The most charitable reading of Hume's problem.
Bayesian reading: justifying a simple prior
Generally agreed to be impossible.
3. Specifying the principle of uniformity
Goodman's problem.
Bayesian reading: specifying a simple prior
At first you think it's easy.
Because of inter-definability, it is not easy.
Solmonoff induction allows us to make progress, but ultimately is still language-dependent.

Front: chisolm's paradox
Back: Chisholm’s Paradox and bare identities
One such argument, adapted from Chisholm 1967, goes as follows. Taking Adam and Noah in the actual world as our examples (and pretending, for the sake of the example, that the biblical characters are real people), then, on the plausible assumption that not all of their properties are essential to them, it seems that there is a possible world in which Adam is a little more like the actual Noah than he actually was, and Noah a little more like the actual Adam than he actually was. But if there is such a world, then it seems that there should be a further world in which Adam is yet more like the actual Noah, and Noah yet more like the actual Adam. Proceeding in this way, it looks as if we may arrive ultimately at a possible world that is exactly like the actual world, except that Adam and Noah have ‘switched roles’ (plus any further differences that follow logically from this, such as the fact that in the ‘role-switching’ world Eve is the consort of a man who plays the Adam role, but is in fact Noah). But if this can happen with Adam and Noah, then it seems that it could happen with any two actual individuals. For example, it looks as if there will be a possible world that is a duplicate of the actual world except for the fact that in this world you play the role that Queen Victoria plays in the actual world, and she plays the role that you play in the actual world (cf. Chisholm 1967, p. 83 in 1979). But this may seem intolerable. Is it really the case that Queen Victoria could have had all your actual properties (except for identity with you) while you had all of hers (except for identity with her)?

Front: kripke's examples
Back: 1. Contingent a priori: The length one meter is instantiated by S (at time t_0)
2. Necessary a posteriori: Hesperus = Phosphorus
1. ‘one meter’ is a rigid designator for the length one meter. ‘The length of S (at time t_0)’ is, on the other hand, a non-rigid designator for one meter; in this world it designates one meter but in other worlds, those in which S is heated or cooled, ‘the length of S (at time t_0)’ designates other lengths.
2. Because of the rigid designation of the names it contains, ‘Hesperus = Phosphorus’ is necessarily true. Since empirical work on the part of astronomers was required to determine that the statement is true, we seem to have an illustration of necessary, a posteriori truth.