PHI 220 Symbolic Logic
© 2025 Gary Mar with Haya, Gabriel, Jessica, Yutong
Chapter 1, Strategic Hints
6.54 My propositions serve as elucidations in the following way: anyone who
understands me eventually recognizes them as nonsensical, when he has used them—
as steps—to climb beyond them. (He must, so to speak, throw away the ladder after
he has climbed up it.
— LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus [1921]
In the Game of Deductive Logic, we may distinguish between the official rules of the game (the recursive
definition of a derivation) and the strategic hints (the rules of thumb for playing the game well). These hints
include both tactics for exploiting the power of our playing pieces or premises and strategy that enables you
to conduct the entire deduction based on a sound plan laid out in advance.
Always begin by showing the HINT 0. Begin by showing the __________________ (but you needn’t
conclusion (and never show a show a _____________).
______________).
HINT 1. To show a conditional → , use CD, i.e., assume the
____________ and either derive (or show) the ______________ .
1. Show → n, CD 1. Show → 3, CD
To show a conditional use CD
2. Assume (CD) 2. Assume (CD)
. 3. Show
.
.
n.
HINT 2. Unless some other strategy is immediately obvious, use ID
(i.e., assume an _________________ of what you want to show and
To show anything else, use ID.
derive any __________________ i.e., and ~ in any order (and in
the same box).
1. Show j, k, ID 1. Show ~ j, k, ID
Whenever you obtain a boxed 2. ~ Assume (ID) 2. Assume (ID)
contradiction you can box and .
cancel by ID. .
.
j. j. ~
.
. (any contradiction)
k. ~ k.
Enter your “playing pieces” or HINT 3. Enter _________________ after you’ve entered any useful
premises after all useful ___________________, which can only be entered immediately after
assumptions are entered. an uncancelled ‘Show’ line.
1
© 2025 Gary Mar with Haya, Gabriel, Jessica, Yutong
Chapter 1, Strategic Hints
6.54 My propositions serve as elucidations in the following way: anyone who
understands me eventually recognizes them as nonsensical, when he has used them—
as steps—to climb beyond them. (He must, so to speak, throw away the ladder after
he has climbed up it.
— LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus [1921]
In the Game of Deductive Logic, we may distinguish between the official rules of the game (the recursive
definition of a derivation) and the strategic hints (the rules of thumb for playing the game well). These hints
include both tactics for exploiting the power of our playing pieces or premises and strategy that enables you
to conduct the entire deduction based on a sound plan laid out in advance.
Always begin by showing the HINT 0. Begin by showing the __________________ (but you needn’t
conclusion (and never show a show a _____________).
______________).
HINT 1. To show a conditional → , use CD, i.e., assume the
____________ and either derive (or show) the ______________ .
1. Show → n, CD 1. Show → 3, CD
To show a conditional use CD
2. Assume (CD) 2. Assume (CD)
. 3. Show
.
.
n.
HINT 2. Unless some other strategy is immediately obvious, use ID
(i.e., assume an _________________ of what you want to show and
To show anything else, use ID.
derive any __________________ i.e., and ~ in any order (and in
the same box).
1. Show j, k, ID 1. Show ~ j, k, ID
Whenever you obtain a boxed 2. ~ Assume (ID) 2. Assume (ID)
contradiction you can box and .
cancel by ID. .
.
j. j. ~
.
. (any contradiction)
k. ~ k.
Enter your “playing pieces” or HINT 3. Enter _________________ after you’ve entered any useful
premises after all useful ___________________, which can only be entered immediately after
assumptions are entered. an uncancelled ‘Show’ line.
1
