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BASIC CONCEPTS OF LOGIC
1. What is Logic?
Logic = science of reasoning, but not an empirical science like physics or psychology.
Logic does not study how the brain thinks — that is psychology/neuroscience.
Instead, logic tells us whether reasoning is correct or incorrect.
2. Inferences and Arguments
Inference
To infer = to draw a conclusion from premises (facts, information, data).
Examples:
Seeing smoke → inferring fire
20 people initially, now only 19 → someone is missing
Infer ≠ Imply
We infer conclusions.
Evidence implies something.
Argument
An argument = collection of statements, where:
One statement = conclusion
Remaining = premises
A statement = declarative sentence capable of being true or false.
Questions, commands, exclamations are not statements.
Examples of statements:
It is raining.
2 + 2 = 4.
Example not a statement:
Are you hungry?
Arguments are recognized using keywords:
, 2
Conclusion markers: therefore, hence, so, consequently
Premise markers: since, because, for
Premises are intended to support/justify the conclusion.
3. Deductive vs. Inductive Logic
Two types of reasoning:
Inductive Logic
Premises make conclusion probable, not guaranteed.
Example: Smoke → likely fire, but not guaranteed.
Used in science, statistics, probability.
Inductive arguments are fallible.
Deductive Logic
If premises are true, conclusion is 100% necessarily true.
Example:
20 people originally + 19 now = someone missing.
Deductive validity guarantees correctness.
Every deductively correct argument is also inductively strong,
but not every inductively strong argument is deductively correct.
4. Statements vs. Propositions
Statements = sentences (linguistic expressions).
Propositions = meanings or states of affairs expressed by statements.
Example:
"Snow is white"
"Der Schnee ist weiss"
"La neige est blanche"
→ Different statements, same proposition.
Same statement can express different propositions depending on context:
“I am hungry” means different things depending on the speaker.
Logic focuses on statements, because propositions are abstract and harder to analyze.
BASIC CONCEPTS OF LOGIC
1. What is Logic?
Logic = science of reasoning, but not an empirical science like physics or psychology.
Logic does not study how the brain thinks — that is psychology/neuroscience.
Instead, logic tells us whether reasoning is correct or incorrect.
2. Inferences and Arguments
Inference
To infer = to draw a conclusion from premises (facts, information, data).
Examples:
Seeing smoke → inferring fire
20 people initially, now only 19 → someone is missing
Infer ≠ Imply
We infer conclusions.
Evidence implies something.
Argument
An argument = collection of statements, where:
One statement = conclusion
Remaining = premises
A statement = declarative sentence capable of being true or false.
Questions, commands, exclamations are not statements.
Examples of statements:
It is raining.
2 + 2 = 4.
Example not a statement:
Are you hungry?
Arguments are recognized using keywords:
, 2
Conclusion markers: therefore, hence, so, consequently
Premise markers: since, because, for
Premises are intended to support/justify the conclusion.
3. Deductive vs. Inductive Logic
Two types of reasoning:
Inductive Logic
Premises make conclusion probable, not guaranteed.
Example: Smoke → likely fire, but not guaranteed.
Used in science, statistics, probability.
Inductive arguments are fallible.
Deductive Logic
If premises are true, conclusion is 100% necessarily true.
Example:
20 people originally + 19 now = someone missing.
Deductive validity guarantees correctness.
Every deductively correct argument is also inductively strong,
but not every inductively strong argument is deductively correct.
4. Statements vs. Propositions
Statements = sentences (linguistic expressions).
Propositions = meanings or states of affairs expressed by statements.
Example:
"Snow is white"
"Der Schnee ist weiss"
"La neige est blanche"
→ Different statements, same proposition.
Same statement can express different propositions depending on context:
“I am hungry” means different things depending on the speaker.
Logic focuses on statements, because propositions are abstract and harder to analyze.
