Thursday, February 28, 2019

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:  

Wednesday, February 27, 2019

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.

Thursday, January 31, 2019

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