An assertion in logic is a statement that claims a specific premise is true. In simpler terms, it's a declaration that something is the case.
Understanding Logical Assertion
The core concept of an assertion revolves around the idea of making a claim about the truth of a statement. It's not about demonstrating that a claim is true (that's the role of a proof), but rather about stating that it's true.
Key Characteristics of Logical Assertions
- Claim of Truth: At its heart, an assertion declares a premise to be true.
- Basis for Reasoning: Assertions often serve as the foundation for logical arguments. They are the starting points from which further conclusions are drawn.
- Not Necessarily Proven: Importantly, making an assertion doesn't automatically make it true or proven. It's simply a statement.
- Can Be a Premise: The reference states, "a statement that asserts that a certain premise is true." This highlights that assertions frequently act as premises in logical arguments.
Assertion vs. Proof
It is crucial to differentiate between an assertion and a proof:
| Feature | Assertion | Proof |
|---|---|---|
| Definition | A statement that claims something is true | A demonstration that something is true based on logical steps |
| Purpose | To declare a truth | To validate a truth |
| Required | A statement of belief | Evidence and logical reasoning |
| Truth Value | Can be true or false | Should demonstrate truth |
Example
Let’s consider an example:
- Assertion: "All dogs are mammals."
- Proof: To prove this assertion, one would need to define dogs and mammals, and then demonstrate that the characteristics of dogs fulfill the requirements for being classified as mammals. This proof relies on prior established knowledge and definitions.
The Fallacy of Proof by Assertion
The provided reference also mentions "proof by assertion," which is an informal fallacy. This occurs when a statement is repeatedly restated instead of being supported by actual evidence.
How Proof by Assertion is Fallacious
- Repetition Not Evidence: Simply repeating something does not make it true.
- Misleading: The repetitive nature might make it seem convincing, especially if repeated with confidence, despite lacking actual support.
- Lack of Logical Basis: This method lacks any logical structure or factual backing.
Example of Proof by Assertion
- "Our product is the best because we say it is."
- "This is a fact because it is always stated."
These examples do not provide any actual evidence of the claim; they are only repeatedly asserting it.
In Summary
An assertion in logic is a statement claiming a premise is true. It is a starting point in logical reasoning, but does not make the claimed premise true, it still needs proper validation and proof. One should be wary of proof by assertion fallacies where an idea is repeatedly stated instead of proven.
