Are all iff s definitions?

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In summary: For example, in modal logic, it can represent strict implication, which is stronger than equivalence. However, in most contexts, "iff" is used to indicate logical equivalence. Therefore, most statements of the form "p if and only if q" can be considered either definitions or equivalences. In summary, the conversation discusses the concept of "if and only if" and its relation to definitions and equivalences. It is explained that "iff" is typically interpreted as a logical equivalence, but can also represent strict implication in certain contexts. It is also mentioned that definitions and logical equivalences are closely related, with definitions being less precise. Therefore, most statements of the form "p if and only if q" can be considered either definitions
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lolgarithms
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are all "iff"s definitions?

are all statements of the form "p if and only if q" definitions or equivalences? can there be any iff statements that are not statements of equivalence?
 
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lolgarithms said:
are all statements of the form "p if and only if q" definitions or equivalences? can there be any iff statements that are not statements of equivalence?

In logic there's material implication and strict implication which might be related to the notion of equivalence as follows:

In material implication we have P implies Q iff (P^Q)or(~P^Q)or(~P^~Q).

In strict implication we have P implies Q iff (P^~Q) is not possible. This is a modal logic which deals with the concepts of possibility and necessity.

My understanding is that 'equivalence' is more appropriate to saying that at least one formula can be substituted for another in some formal language which in this example would suggest material implication.

In strict implication, there is only one formula with no equivalent formulas for P=>Q Therefore I would think that this would be a case where 'iff 'that does not represent 'equivalence'. Strict implication is stronger than equivalence.

As for what a definition is, I think the basic truth tables of formal logic(s) are essentially axioms which conform to our intuition regarding some application.
 
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lolgarithms said:
are all statements of the form "p if and only if q" definitions or equivalences?
"If and only if" is normally interpreted as a kind of logical equivalence. An equivalence states that two things are the same in some way. The precise way in which they are the same depends on the context and your definitions. What is your definition of iff? What do you think is the difference between a definition and a logical equivalence? Definitions aren't usually defined as precisely as logical equivalences are, but that two terms have "the same meaning" usually means that they are at least logically equivalent.
can there be any iff statements that are not statements of equivalence?
Sure, if you interpret iff to mean something other than equivalence.
 

1. What is the meaning of "iff" in scientific definitions?

"Iff" stands for "if and only if" and is often used in mathematical and scientific definitions to indicate that a condition is both necessary and sufficient for a statement to be true.

2. How is "iff" different from "if" in scientific definitions?

"If" is used to indicate a conditional statement, meaning that the statement following the "if" may or may not be true. "Iff" is more precise and indicates that the statement following it is a necessary and sufficient condition for the preceding statement to be true.

3. Can "iff" be used in non-scientific contexts?

Yes, "iff" can be used in any context where precise and logical statements are necessary. It is commonly used in mathematics, logic, and computer programming as well as in scientific definitions.

4. How do scientists come up with "iff" definitions?

Scientists use "iff" definitions to precisely define concepts and establish logical relationships between them. These definitions are often based on extensive research and experimentation to determine the necessary and sufficient conditions for a concept to be true.

5. Are "iff" definitions universally accepted in the scientific community?

Yes, "iff" definitions are widely accepted in the scientific community as they provide a clear and precise way of defining concepts and establishing logical relationships between them. However, there may be some disagreement or debate about the specific conditions chosen for a particular definition.

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