Definition:Premise

Definition

A premise is an assumption that is used as a basis from which to start to construct an argument.

When the validity or otherwise of a proof is called into question, one may request the arguer to "check your premises".

Also known as

Some sources use the word hypothesis or supposition, but these tends nowadays to have a slightly different meaning from premise.

Some sources use the older (some say archaic) spelling premiss, whose plural is premisses.

Also defined as

Some authors use the term premise to mean the antecedent of a conditional statement.

Also see

• Definition:Conclusion
• Rule of Assumption

• Results about premises can be found here.

Historical Note

In the early days of (mathematical) logic, there was a significant distinction between premises on the one hand, and assumptions on the other hand.

Premises ought to be essential for the validity of the argument, while assumptions were expected to be discharged at some point in the argument.

Over the years, through abstraction and change of perspective on (symbolic) logic, this distinction is becoming less important; however, it still retains considerable conceptual value.

For example, the Rule of Assumption of natural deduction is a symbolic representation of both these concepts, but allows to distinguish between them to make it easier to convey the overall structure of a proof to the reader.

Technical Note

When invoking a premise in a tableau proof, use the Premise template:

{{Premise|line|statement}}

or:

{{Premise|line|statement|comment}}

where:

line is the number of the line on the tableau proof where the premise is to be invoked

statement is the statement of logic that is to be displayed in the Formula column, without the $ ... $ delimiters

comment is the (optional) comment that is to be displayed in the Notes column.

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.9$: The Use of Implication
• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): Chapter $\text I$ Introductory: $3$. Logical Form
• 1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{I}$: 'NOT' and 'IF': $\S 3$
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $1$ Introduction: Logic and Language: $1.2$: The Nature of Argument
• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.5$: Theorems and Proofs
• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): argument: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): deduction
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): premise
• 2000: Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems ... (previous) ... (next): $\S 1.2$: Natural Deduction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): argument: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): deduction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): premise
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 3.2$: Definition $3.2$