PHIL120 Lecture Notes - Lecture 9: Metalanguage, Metalogic, Classical Logic

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Wednesday, September 26, 2018
The problem of the spy on the island is an example of what is known as a meta-problem. When looking
at a meta-problem we have to understand the requisite terms. The root word of metaphysics is meta,
which means the “after”, “about”, or “beyond”. Metaphysics itself is defined as ontology, or the theory
of beings and existence. Other terms within this field include:
Metalogic - the theory of logical systems and their properties
Metalanguage - language that is used to talk about another language, e.g. English, in this course,
will be used as a meta-language to discuss the formal language of classical logic
Meta-puzzles - these are puzzles in which information about the conclusion is given in the
description of the problem, e.g. what three word question could be asked to solve the problem?
Note that in some questions there’s only one answer which could elucidate the truth, not like other ones
where any answer provides a solution.
Let’s look at another problem from the Island of Knights and Knaves.
Abercrombie met two brothers on the island, Tak and Jal, one of whom was the island’s witch doctor. Jal
said that he was the witch doctor. He also claimed to be a knight, and accused Tak of being a knave.
Abercrombie then asked Tak, “Are you the witch doctor?”, to which he answered “yes” or “no”.
Abercrombie then knew who was the witch doctor. How?
Since Tak and Jal can be be knights or knaves, and only one them can be the witch doctor, we have four
different possibilities (2 x 2 x 1 = 4). To solve this problem we’ll be using a table in which Ja stands for Jal,
Ta for Tak, W? for Jal’s claim to be the witch doctor, and Con for the consistency of Jal’s claim that he is
a knight and Tak is a knave.
Ja
Ta
Con
W?
Answer
k
k
0
N/A
N/A
k
n
1
Ja
yes
n
k
1
Ta
yes
n
n
1
Ta
no
As you can see, there are only three possible answers that could have been given, but the only way that
Abercrombie could have figured out the identity of the witch doctor was if Tak answered his question
with, “no”. From here Abercrombie would know that Tak is the witch doctor, and both brothers are
knaves.
Now let’s move onto another island. Here the conditions are a bit different:
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Document Summary

The problem of the spy on the island is an example of what is known as a meta-problem . The root word of metaphysics is meta which means the after , about , or beyond . Metaphysics itself is defined as ontology, or the theory of beings and existence. The theory of logical systems and their properties will be used as a meta-language to discuss the formal language of classical logic. Language that is used to talk about another language, e. g. english, in this course, These are puzzles in which information about the conclusion is given in the. Note that in some questions there"s only one answer which could elucidate the truth, not like other ones where any answer provides a solution. Let"s look at another problem from the island of knights and knaves. Abercrombie met two brothers on the island, tak and jal, one of whom was the island"s witch doctor. Jal said that he was the witch doctor.

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