Unit 1: Introduction to Logic
Logic: Nature and Scope
What is Logic?
The word "Logic" comes from the Greek word "logos," which can mean "reason," "discourse," "word," or "study."
Logic is the systematic study of the principles of correct reasoning.
It is not the study of *how* people actually think (that's psychology). Instead, it is the study of *how* people *ought* to think if they want to reason correctly. Its main goal is to distinguish good arguments (correct reasoning) from bad arguments (incorrect reasoning).
Nature of Logic
- A Science: Logic is a science because it is a systematic and organized body of knowledge.
- An Art: Logic is also an art because it teaches us the *skill* or *technique* of reasoning correctly.
- Normative: Logic is a normative science, not a positive one. A positive science (like biology) describes *what is*. A normative science (like logic or ethics) prescribes *what ought to be*. Logic sets the "norms" or "rules" for correct reasoning.
- Formal: Logic is concerned with the form (or structure) of an argument, not its content (or subject matter). This is a crucial point that will be explained in "Truth and Validity."
Scope of Logic
The scope of logic is vast. It is the "scaffolding" of all other fields of study, from mathematics and science to law and philosophy. The syllabus for this paper focuses on Traditional or Aristotelian Logic, which is a type of Deductive Logic.
The main types of logic are:
- Deductive Logic: The study of arguments where the conclusion is claimed to follow from the premises with absolute necessity. If the premises are true, the conclusion *must* be true. (This is the focus of this course).
- Inductive Logic: The study of arguments where the conclusion is claimed to follow from the premises with probability. The premises support the conclusion but do not guarantee it. (e.g., scientific reasoning).
Truth and Validity
This is the most important distinction in all of deductive logic. It separates the *content* of an argument from its *structure*.
Truth (and Falsity)
- Truth and Falsity are properties of propositions (statements).
- A proposition is a declarative sentence that is either true or false (e.g., "The sky is blue," "All cats are mammals").
- Truth is the correspondence of a proposition to reality (a "fact").
Validity (and Invalidity)
- Validity and Invalidity are properties of deductive arguments.
- An argument is not "true" or "false." A proposition is not "valid" or "invalid."
- An argument is valid if its conclusion follows necessarily from its premises. This means: IF the premises are true, the conclusion MUST be true.
- An argument is invalid if its conclusion does not follow necessarily from its premises. This means: It is *possible* for the premises to be true and the conclusion to be false.
Exam Tip: Memorize this table. This is a guaranteed exam question.
|
Truth / Falsity |
Validity / Invalidity |
| Applies to: |
Propositions (Statements) |
Arguments (The whole structure) |
| Concerns: |
Content (Its relation to facts) |
Form (Its logical structure) |
| Example: |
"All men are mortal" (is True) |
"All A are B. All C are A. So, All C are B." (is Valid) |
Examples of Truth and Validity
You can have valid arguments with false premises and invalid arguments with true premises.
- Valid Argument, True Premises, True Conclusion (This is a "Sound" Argument)
- All men are mortal. (True)
- Socrates is a man. (True)
- Therefore, Socrates is mortal. (True)
- Valid Argument, False Premises, False Conclusion
- All cats are green. (False)
- Socrates is a cat. (False)
- Therefore, Socrates is green. (False)
(The *form* is valid. IF cats were green and IF Socrates were a cat, he *would* be green).
- Valid Argument, False Premises, True Conclusion
- All mammals have wings. (False)
- All whales are mammals. (True)
- Therefore, all whales have wings. (False)
(Wait, that's a false conclusion. Let's try again.)
- All fish are mammals. (False)
- All whales are fish. (False)
- Therefore, all whales are mammals. (True)
(The form is valid: All A are B, All C are A, So All C are B. The conclusion *happens* to be true, but not *because* of the premises.)
- Invalid Argument, True Premises, True Conclusion
- All dogs are mammals. (True)
- All cats are mammals. (True)
- Therefore, all cats are dogs. (False)
(Wait, that's a false conclusion. Let's try again.)
- If it rains, the ground is wet. (True)
- The ground is wet. (True)
- Therefore, it rained. (False - it could have been a sprinkler).
(This argument is invalid, even if the premises and conclusion are all true. The conclusion does not *necessarily* follow.)
A Sound Argument is a valid argument that also has all true premises. This is the "gold standard" of deductive reasoning.
Argument and Argument-Form
What is an Argument?
In logic, an argument is not a quarrel.
An Argument is a structured set of propositions, one of which (the conclusion) is claimed to follow from the others (the premises).
- Premises: The propositions that provide the evidence or reasons. (Indicators: "because," "since," "for," "as")
- Conclusion: The proposition that is claimed to be supported by the premises. (Indicators: "therefore," "thus," "so," "hence")
Example Argument (Content):
- (Premise 1) All humans are mortal.
- (Premise 2) All Greeks are humans.
- (Conclusion) Therefore, all Greeks are mortal.
What is an Argument-Form?
The Argument-Form is the logical "skeleton" or "structure" of the argument, with the specific content removed. We get the form by replacing the content-words (like "humans," "mortal") with variables (like S, P, M).
Example Argument-Form (Structure):
- (Premise 1) All M are P.
- (Premise 2) All S are M.
- (Conclusion) Therefore, all S are P.
This argument-form is valid. Any argument that has this exact form will be valid, no matter what content you put in for S, P, and M.
Example of an Invalid Form:
- (Premise 1) All P are M.
- (Premise 2) All S are M.
- (Conclusion) Therefore, all S are P.
(This is a fallacy. Example: "All dogs (P) are mammals (M). All cats (S) are mammals (M). Therefore, all cats (S) are dogs (P)." This is clearly false, which proves the *form* is invalid.)
Key Takeaway: Logic is the study of argument-forms. We test for validity, not truth. A logician's job is to see if the "machine" of the argument is built correctly (valid form), not if the "materials" put into it are good (true premises).