Deductive Reasoning and Arguments
A deductive argument aims to make its conclusion follow necessarily from its premises. If the argument is valid and the premises are true, the conclusion cannot be false. Inductive arguments instead offer support without that guarantee.
THE IDEA
Deductive Reasoning and Arguments
Deductive arguments aim to establish a conclusion necessarily; inductive arguments offer support without guaranteeing it. In a deductive argument:
- The conclusion is intended to follow necessarily from the premises;
- If the reasoning is valid and all premises are true, the conclusion cannot be false;
- Testing validity means asking whether the premises could all be true while the conclusion is false.
These arguments are all deductive arguments utilizing deductive reasoning:
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There are only two ways for me to get to work – either Highway 1 or Main St.
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Highway 1 is closed due to construction.
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So, I have to take Main St. to work today.
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Politicians in the Crack Down Party are all conservative about spending.
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Congresswoman Smith is in the Crack Down Party.
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This shows us that Congresswoman Smith is conservative about spending.
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If my client committed the crime, then he would have been in Chicago.
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But he wasn’t in Chicago (check the gas receipts, GPS, and witness testimony).
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Therefore, my client did not commit the crime.
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If it’s raining we’ll stay inside, and if it’s snowing we’ll go outside to play.
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It’s either raining or snowing.
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Hence, we’ll either stay inside or go outside to play.
In these examples, accepting the premises commits us to the stated conclusion. We can “see” or “read” that implication from the argument’s structure. A set of premises may also entail other conclusions.
Two standard approaches are categorical logic, which studies relations among categories, and propositional logic, which studies how statements combine through forms such as if–then.
When to use it
Solving logic puzzles or riddles that require a series of deductions.
Constructing mathematical proofs where each step follows necessarily from the last.
Evaluating legal arguments to determine if a conclusion is logically forced by the evidence.
Writing computer programs with if-then statements to ensure correct conditional logic.
FROM THEORY TO EVERYDAY LIFE
In practice
Example 1: Route to Work
- There are only two ways for me to get to work – either Highway 1 or Main St.
- Highway 1 is closed due to construction.
- So, I have to take Main St. to work today.
Example 2: Political Party
- Politicians in the Crack Down Party are all conservative about spending.
- Congresswoman Smith is in the Crack Down Party.
- This shows us that Congresswoman Smith is conservative about spending.
Example 3: Client's Alibi
- If my client committed the crime, then he would have been in Chicago.
- But he wasn’t in Chicago (check the gas receipts, GPS, and witness testimony).
- Therefore, my client did not commit the crime.
Example 4: Weather Activity
- If it’s raining we’ll stay inside, and if it’s snowing we’ll go outside to play.
- It’s either raining or snowing.
- Hence, we’ll either stay inside or go outside to play.
A MOMENT TO REFLECT
Put it to work.
Can you identify a deductive argument in a recent news article? Does it meet the criteria of a necessary conclusion?
If all humans are mortal and Socrates is human, what conclusion can you deduce, and why is it deductive?
Given a set of premises, how would you test whether the argument is deductive or inductive?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Bad Arguments 100 of the Most Important Fallacies in Western Philosophy (Steven Barbone, Michael Bruce)