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Symbolic Logic and Reasoning
Conclusion
A conclusion is the statement an argument tries to establish from its premises.
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Conclusion
Definition
A conclusion is the statement an argument tries to establish.
It is the result of reasoning from premises.
Example:
Premise 1: If P, then Q
Premise 2: P
Conclusion: Q
The conclusion is:
Q
Conclusion = statement reached from premises.
Conclusion vs Premise
A premise is a starting point.
A conclusion is what follows from the starting points.
Example:
Premise: All humans are mortal.
Premise: Socrates is human.
Conclusion: Socrates is mortal.
The conclusion is not assumed at the beginning.
It is what the argument is trying to support.
Premises support; conclusion is supported.
Conclusion vs Output
In computation, output is the result of applying rules to input.
In reasoning, conclusion is the result of applying inference rules to premises.
Comparison:
Computation:
input -> rules -> output
Reasoning:
premises -> inference rules -> conclusion
The structures are related.
Both are rule-governed transformations.
A conclusion is the reasoning-side result.
A Conclusion Can Be True Or False
A conclusion is a proposition.
That means it can be true or false.
Example:
Conclusion: 2 + 3 = 5
This is true.
Example:
Conclusion: 2 + 3 = 9
This is false.
But whether a conclusion is true is separate from whether the argument structure is valid.
Truth of a conclusion and validity of an argument are different questions.
Unsupported Conclusion
A statement can be placed after premises without actually following from them.
Example:
Premise: It is raining.
Conclusion: The moon is made of cheese.
The conclusion is a statement.
But it is not supported by the premise.
A conclusion must be connected to the premises by inference.
Final Summary
- A conclusion is the statement an argument tries to establish.
- Premises are starting points; conclusion is the result.
- A conclusion is like the output of reasoning.
- A conclusion can be true or false.
- A conclusion may be unsupported if it does not follow from the premises.
- Arguments are evaluated by how premises support conclusions.
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Continue the series.
Valid Argument