The Gettier Getaway: a Gettier Example

Here is a Gettier-type (per Gettier's "Is Justified True Belief Knowledge?") case I came up with:

A car speeds past you. Directly behind this car follows a speeding police cruiser with its siren on. The speeding cars, one after the other, round a corner and disappear from sight.

You believe on the basis of this incident that the driver of the speeding car is being pursued by the police, perhaps for a criminal act. You are justified in doing so. And in fact, the driver is being pursued by the police for a criminal act.

However, when you saw the driver, he was not trying to escape the police cruiser behind him but was in fact speeding back to his apartment because, after he had robbed a bank earlier that day, he remembered he had left his oven on. The police cruiser behind him was not chasing him but had actually been dispatched to go to the bank the driver had just robbed, in order to pursue the robber (the officer had no idea that that robber was right in front of her). This officer noticed that the car in front of her was speeding, but since she had more important crimes to worry about than traffic violations, she was not pursuing it at that moment.

(i) You believe that the driver is being pursued by the police.

(ii) It is true that the driver is being pursued by the police.

(iii) You are justified in believing the driver is being pursued by the police.

But because what you saw does not actually constitute evidence of his being pursued, you do not know that the driver is being pursued by the police.

This case is different in an important respect from both the first Gettier case and cases like the sheep case (qv. Chisholm) and the clock case (qv. Russell). In those cases, the major premise of the valid inference is a sound implication, but the minor premise is false.

First Gettier Case

(i) If Jones (who has ten coins in pocket) will get the job (p), the person who will get the job has ten coins in pocket (q). [p ⊃ q]

(ii) Jones will get the job. [p]

∴ The person who will get the job has ten coins in pocket. [q]

In fact, Jones will not get the job [~p], though the person who will get the job has ten coins in pocket. [q]

Thus, Smith has made a valid but unsound inference due to the minor premise being false.

Sheep Case

(i) If Roddy sees a sheep in the field (p), there is a sheep in field (q). [p ⊃ q]

(ii) Roddy sees a sheep in the field. [p]

∴ There is a sheep in the field. [q]

In fact, Roddy does not see a sheep in the field (he sees a sheep-like object) [~p], though there is a sheep in the field (that he does not see). [q]

Thus, Roddy has made a valid but unsound inference due to the minor premise being false.

Clock Case

(i) If the clock is working (p), the time it reads is the actual time (q). [p ⊃ q]

(ii) The clock is working. [p]

∴ The time it reads is the actual time. [q]

In fact, the clock is not working [~p], though the time it reads is the actual time (it just so happens). [q]

Thus, a valid but unsound inference has been made due to the minor premise being false.

Gettier Getaway Case

(i) If a speeding car is closely followed by a police car with its siren on (p), the driver of the speeding car is being pursued by the police (q). [p ⊃ q]

(ii) A speeding car is closely followed by a police car with its siren on. [p]

∴ The driver of the speeding car is being pursued by the police. [q]

In fact the speeding car is closely followed by a police car with its siren on [p], and the driver of the speeding car is being pursued by the police. [q]

Since, unlike the other cases, the minor premise in the Gettier getaway case is true, and you have made a valid inference, something else must have gone wrong. It is the major premise that is unsound. We find that [p ⊃ q] in this case is not necessarily true. It is false in some cases^*.

Major premise cases, I think, take us closer to the problem with the “no false lemmas” objection than minor premise cases because with them we see that to be Gettier-proof, the major premise must be necessarily true in all possible worlds, not just in almost all instances. This is a problem because this would seem to set too high a threshold for justification. How could one ever obtain certainty that one’s major premise is necessarily true in all possible worlds? And how many natural inferential bases would be ruled out due to not being necessarily true?

_____

*The garbage chute case (Sosa) is the most similar in this respect to the Gettier getaway, except that (i) the garbage chute case is inference-based instead of directly perceptual, as the would-be knowledge holder does not see the basement but only infers its state from partial evidence, and (ii) its consequent has to be made false [~q] in order to show that it can go wrong.

The Seventh Passenger: a Game Design Document

POLYSEMOUS POLYGRAPHY

Consider the sentence:

As Violet sat by the bank, after her trip over the spring, she saw the jam she had made for herself from the dates with her contemplative pupil.

This sentence contains at least 64 different narratives, depending on one of two meanings for the six words: bank, trip, spring, jam, dates, and pupil. (2^6 = 64) Every reading is coherent. 

As Violet sat by the bank (building or slope), after her trip (voyage or tumble) over the spring (season or aquifer), she saw the jam (problem or condiment) she had made for herself from the dates (trysts or fruit) with her contemplative pupil (student or inner-eye).

Call this Oulipian method of composition Polysemous Polygraphy.

"A Trap for the Curious," an Animated Short

Genius Loci drawings 3

Genius Loci drawings 2

Genius Loci drawings 1

This Old Genius Loci .2

Illustrated Verse (in progress)

Branching Timeline Time Travel Analysis

Legislation, printed

Legislation, a Card Game (complete print & play version)

Representative Cards for Legislation

Reality Is Impossible

Things that are true are not possibly true. They are just true!

Likewise, things that are false are not possibly false. They are just false!

If something is necessarily true, then it is true, which means that it is not possibly true. And if something is necessarily false, then it is false, which means that it is not possibly false.

Yet Alethic Modal Logic tells us that something being necessarily true just means that it is not possibly not true.

Does this definition, or pair of definitions for Necessity N and Possibility P, [(Na = -P-a) & (Pa = -N-a)], make sense, given our two Reality Principles, (1) [(a > -Pa) & (-a > -P-a)] and (2) [(Na > a) & (N-a > -a)]?

Let's see:  

False by Definition

With the Liar Statement—i.e. “This statement is false,” which we can translate as “p = this statement (p) is false = (p = ~p)”— the definition of p is false, not p itself. What does it mean for a definition to be false? It means that it is formally invalid.  This in turn means that it is not permitted within our logic to use a definition of this form. Note that the statement of a definition implies the statement that it defines, but it is not identical to the statement it defines. I.e. Def. p > (p = -p).

Conjecture: ∀p [(Def. p > (p = -p)) > -(Def. p)]          (1)

Def. q > ( q = -q)                                  S

Def. q                                   S

q = -q                                MP

q                                  S

-q                                ES

q & -q                        CONJ

-q                                      IP

q                                      ES

q & -q                             CONJ

-(Def. q)                                            IP

(Def. q > (q = -q)) > -(Def. q)                    CP

∀p [(Def. p > (p = -p)) > -(Def. p)]                       UG

(1), QED                                                     

We might say that all statements of self-reference involve such a definition statement implicitly because every self-reference statement necessarily requires a self-stipulation, which is of course a type of stipulation, i.e. a definition. However, some self-referential statements, e.g. “This statement is a written statement,” i.e. “p = this statement (p) is a written statement (w) = (p = w),” involve a valid form of definition, Def. p > (p = w), such that the definition is not false. 

In any case, the above proves that the Liar Statement is falsidical and not a real antinomic paradox.

Rules of Social Media

Legislation: a Card Game

Legislation

E.B. Nelson, 1.31.19 (c)

A Card Game for 3 to 8 Players

Components:

16 Representative cards; 81 Bill cards; Pro and Con Pledge Token sets numbered for players 1-8; Agenda Point Tokens

Rules:

You play as an elected Representative of Congress. Your goal is to get as many Bills that promote your Agenda passed as you can over the course of the legislative Session, while blocking all Bills that are detrimental to your Agenda.

You first draw a Representative to play as from the Representative Deck. The Representative Deck must be constructed according to the number of players so that there is an even distribution of Representatives per Agendas (see the Deck list below).

Next, shuffle the deck of 81 Bills and deal 9 face down to each player. You will look at these cards but conceal them from the other players.

On the first turn, players decide which of their cards they wish to keep, if any, and which they wish to discard. Discard into your own Discard Pile in front of you.

On the second turn, players draw the number of cards needed to make a full hand of 9 from any of the other players’ Discard Piles and/or the remaining Deck. On each subsequent turn, at the beginning of your turn, you can discard into your Discard Pile one card and pick up one card from any of the other piles, or you can choose not to discard.

On the third turn, place 3 Bills in front of you face up that you wish to place On Deck for future votes. Once you place a card On Deck, you cannot discard and replace it. It must eventually be voted on.

On the fourth turn, you seek Pledges to vote on your Bills from the other players. You do this by bargaining with each of them by offering to trade cards you have in your hand, to make Pledges on their Bills, or to make anti-Pledges on their opponent’s Bills. Pledges made by you and the other players are final only when your turn ends.

On the fifth turn, choose one of your three Bills On Deck and put it to a vote. Everyone votes, and the vote is “Yay,” “Nay,” or “Abstain.” Representatives can choose to betray their Pledges by voting against their Pledged or anti-Pledged votes or by abstaining, but if they do so, whether once or multiple times on a Vote round, they must skip the next Pledge turn entirely, neither seeking Pledges nor making any (although players can still Pledge on their On Deck Bills per bargains with other players). A Bill pass if it has a positive vote total; otherwise it fails. A “Yay” counts as 1, a “Nay” counts as -1, and an “Abstain” counts as 0. If your Bill passes, you gain the Agenda Points listed for your Agenda on the Bill, as do the other players with that Agenda, and others lose points as listed. Place passed Bills in the Passed Bills Pile. If the Bill does not pass, place it in the Failed Bills Pile. Finally, replace the empty On Deck spot with a new face up Bill.

Next is a Pledge round again, followed by another Vote round, and so on. The game ends when all players run out of Bills in their hands and On Deck, i.e. after 9 votes for each player (optional: players can have hands of 6 instead for a shorter game).

Some cards also have Special Effects if they pass, and Representatives each have a Special Effect they cannot enact once per game. Follow the rules for these Effects as described. The winner is the player with the highest Agenda Point total at the end of the Session.   

Representatives (two of each type):

Single Agenda:

1. Social Progressive
2. Social Conservative
3. Fiscal Progressive
4. Fiscal Conservative

Dual Agenda:

1. Social Progressive, Fiscal Progressive
2. Social Progressive, Fiscal Conservative
3. Social Conservative, Fiscal Conservative
4. Social Conservative, Fiscal Progressive

Representative Deck Builds per Number of Players:

Where X= Social Progressive, Y= Social Conservative

Where X= Social Conservative, Y= Social Progressive

Where A= Fiscal Progressive, B= Fiscal Conservative

Where A= Fiscal Conservative, B= Fiscal Progressive

3 Players: X, A, YB

4 Players: All single or all dual

5 Players: XA, YB, XB, Y, A

6 Players: X, Y, A, B, XA, YB

7 Players: XA, XB, YA, YB, X, Y, A

8 Players: All

Bill Deck Chart:

Bill	Agenda Points Scored if Passed per Representative Agenda
# & Name	Social Progressive	Social Conservative	Fiscal Progressive	Fiscal Conservative
1	+1	+1	+1	+1
2	+1	+1	+1	-1
3	+1	+1	+1	0
4	+1	+1	-1	+1
5	+1	+1	-1	-1
6	+1	+1	-1	0
7	+1	+1	0	+1
8	+1	+1	0	-1
9	+1	+1	0	0
10	+1	-1	+1	+1
11	+1	-1	+1	-1
12	+1	-1	+1	0
13	+1	-1	-1	+1
14	+1	-1	-1	-1
15	+1	-1	-1	0
16	+1	-1	0	+1
17	+1	-1	0	-1
18	+1	-1	0	0
19	+1	0	+1	+1
20	+1	0	+1	-1
21	+1	0	+1	0
22	+1	0	-1	+1
23	+1	0	-1	-1
24	+1	0	-1	0
25	+1	0	0	+1
26	+1	0	0	-1
27	+1	0	0	0
28	-1	+1	+1	+1
29	-1	+1	+1	-1
30	-1	+1	+1	0
31	-1	+1	-1	+1
32	-1	+1	-1	-1
33	-1	+1	-1	0
34	-1	+1	0	+1
35	-1	+1	0	-1
36	-1	+1	0	0
37	-1	-1	+1	+1
38	-1	-1	+1	-1
39	-1	-1	+1	0
40	-1	-1	-1	+1
41	-1	-1	-1	-1
42	-1	-1	-1	0
43	-1	-1	0	+1
44	-1	-1	0	-1
45	-1	-1	0	0
46	-1	0	+1	+1
47	-1	0	+1	-1
48	-1	0	+1	0
49	-1	0	-1	+1
50	-1	0	-1	-1
51	-1	0	-1	0
52	-1	0	0	+1
53	-1	0	0	-1
54	-1	0	0	0
55	0	+1	+1	+1
56	0	+1	+1	-1
57	0	+1	+1	0
58	0	+1	-1	+1
59	0	+1	-1	-1
60	0	+1	-1	0
61	0	+1	0	+1
62	0	+1	0	-1
63	0	+1	0	0
64	0	-1	+1	+1
65	0	-1	+1	-1
66	0	-1	+1	0
67	0	-1	-1	+1
68	0	-1	-1	-1
69	0	-1	-1	0
70	0	-1	0	+1
71	0	-1	0	-1
72	0	-1	0	0
73	0	0	+1	+1
74	0	0	+1	-1
75	0	0	+1	0
76	0	0	-1	+1
77	0	0	-1	-1
78	0	0	-1	0
79	0	0	0	+1
80	0	0	0	-1
81	0	0	0	0