This chapter is almost unnecessary for those to whom the translation of every day speech into truth-functional schemata is common-sensical. If this describes you and you are cramming for an exam, feel free to omit this reading.
Logical inferences get us from premises to conclusions in a very certain manner if done properly. But the premises and conclusions are not themselves grounded in logic. This is why it's important to understanding how to translate everyday language into logical language. This involves identifying and isolating each distinct statement in a piece of rhetoric and proceeding to substitute literals for them. It also requires the ability to identify the nature of the relationships between each of the statements in order to form schemata. Without performing these steps properly it is impossible to correctly test for logical implications.
Chapter one contains examples of how negation can be notated logically. And conjunction only requires reflection for its various every day forms to be understood (think of "and", "although", "but", etc.). Use of one of these forms over the other may provide extraneous interpretative tips about the speaker's disposition or beliefs, but cannot have any bearing on the truth or falsity of the claim itself.
Phrases like "if p then q", "p only if q", "q if p", "q provided that p", and "q in case p", all translate to the truth-functional "If then".
"P only if q" is different than the biconditional "p if and only if q".
"Unless" translates to "v", the logical symbol representing alternation.
A central principle to the absolutely imperative art of translating words into symbols is to assure that you do not assign more than one interpretation to the same expression. "Violation of this principle was known traditionally as the fallacy of equivocation" (p. 56).
Though translating vocabulary into logical terms may come with little effort to some, the broader task at hand may be more involved. When sentences begin to agglutinate and the semantics of words and phrases are contingent on others, translation of day to day rhetoric into schemata requires additional levels of critical thinking.
[Note: I will henceforth use "***" to mark sections that I intend to return to and annotate at a later time.]
***
There are three phases to paraphrasing statements logically:
1. The translation of words into symbols.
2. Rephrasing clauses to avoid the fallacy of equivocation.
3. Organizing paraphrased clauses correctly in order to form a whole compound.
It's usually best to look for the big picture of a statement first, then work your way inward.
***
Logical inferences get us from premises to conclusions in a very certain manner if done properly. But the premises and conclusions are not themselves grounded in logic. This is why it's important to understanding how to translate everyday language into logical language. This involves identifying and isolating each distinct statement in a piece of rhetoric and proceeding to substitute literals for them. It also requires the ability to identify the nature of the relationships between each of the statements in order to form schemata. Without performing these steps properly it is impossible to correctly test for logical implications.
Chapter one contains examples of how negation can be notated logically. And conjunction only requires reflection for its various every day forms to be understood (think of "and", "although", "but", etc.). Use of one of these forms over the other may provide extraneous interpretative tips about the speaker's disposition or beliefs, but cannot have any bearing on the truth or falsity of the claim itself.
Phrases like "if p then q", "p only if q", "q if p", "q provided that p", and "q in case p", all translate to the truth-functional "If then".
"P only if q" is different than the biconditional "p if and only if q".
"Unless" translates to "v", the logical symbol representing alternation.
A central principle to the absolutely imperative art of translating words into symbols is to assure that you do not assign more than one interpretation to the same expression. "Violation of this principle was known traditionally as the fallacy of equivocation" (p. 56).
Though translating vocabulary into logical terms may come with little effort to some, the broader task at hand may be more involved. When sentences begin to agglutinate and the semantics of words and phrases are contingent on others, translation of day to day rhetoric into schemata requires additional levels of critical thinking.
[Note: I will henceforth use "***" to mark sections that I intend to return to and annotate at a later time.]
***
There are three phases to paraphrasing statements logically:
1. The translation of words into symbols.
2. Rephrasing clauses to avoid the fallacy of equivocation.
3. Organizing paraphrased clauses correctly in order to form a whole compound.
It's usually best to look for the big picture of a statement first, then work your way inward.
***
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