Summary Reasoning & Arguing, part of Logic
Week 2 (Logic)
LPL introduction p.1-16
The special role of logic in rational inquiry
- All fields presuppose an underlying acceptance of basic principles of logic
➔ All rational inquiry depends on logic, on the ability of people to reason correctly
most of the time, and, when they fail to reason correctly, on the ability of others
to point out the gaps in their reasoning
- What is it that makes one claim “follow logically” from some given information, while
some other claim does not?
- Some people have claimed that the laws of logic are simply a matter of convention
➢ But there is an overwhelming intuition that the laws of logic are somehow more
fundamental, less subject to repeal, than the laws of land or physics
- It’s crucial to understand just what the laws of logic are, and why they are laws of
logic
➢ These are the questions that one takes up when studying logic itself
- Convention is crucial in giving meaning to a language, but once the meaning is
established the laws of logic follow inevitably
- 2 main aims:
1. Learn a new language: the language of first-order logic
2. Learn about the notion of logical consequence, and about how one goes about
establishing whether some claim is or is not a logical consequence of other
accepted claims
Why learn an artificial language?
- The language of first-order logic is very important
➢ A not-spoken language, used every day in several academic fields
➢ In some ways it is the universal language, the lingua franca, of the symbolic
sciences
➢ Goes by various names: the lower predicate calculus, the functional calculus, the
language of first-order logic, FOL
- FOL:
➢ Goes back to Aristotle, but the language as we know it has emerges over the past
100 years
➢ Gottlob Frege, Guiseppe Peano, Charles Sanders Peirce; late 19th cent.: these 3
logicians independently came up with the most important elements of the
language, known as the quantifiers
◼ Since then, there’s been a process of standardization and simplification,
resulting in the language in its present form
➢ There are several dialect
➢ FOL is used in different ways in different fields
◼ Mathematical discourse
Week 2 (Logic)
LPL introduction p.1-16
The special role of logic in rational inquiry
- All fields presuppose an underlying acceptance of basic principles of logic
➔ All rational inquiry depends on logic, on the ability of people to reason correctly
most of the time, and, when they fail to reason correctly, on the ability of others
to point out the gaps in their reasoning
- What is it that makes one claim “follow logically” from some given information, while
some other claim does not?
- Some people have claimed that the laws of logic are simply a matter of convention
➢ But there is an overwhelming intuition that the laws of logic are somehow more
fundamental, less subject to repeal, than the laws of land or physics
- It’s crucial to understand just what the laws of logic are, and why they are laws of
logic
➢ These are the questions that one takes up when studying logic itself
- Convention is crucial in giving meaning to a language, but once the meaning is
established the laws of logic follow inevitably
- 2 main aims:
1. Learn a new language: the language of first-order logic
2. Learn about the notion of logical consequence, and about how one goes about
establishing whether some claim is or is not a logical consequence of other
accepted claims
Why learn an artificial language?
- The language of first-order logic is very important
➢ A not-spoken language, used every day in several academic fields
➢ In some ways it is the universal language, the lingua franca, of the symbolic
sciences
➢ Goes by various names: the lower predicate calculus, the functional calculus, the
language of first-order logic, FOL
- FOL:
➢ Goes back to Aristotle, but the language as we know it has emerges over the past
100 years
➢ Gottlob Frege, Guiseppe Peano, Charles Sanders Peirce; late 19th cent.: these 3
logicians independently came up with the most important elements of the
language, known as the quantifiers
◼ Since then, there’s been a process of standardization and simplification,
resulting in the language in its present form
➢ There are several dialect
➢ FOL is used in different ways in different fields
◼ Mathematical discourse
