# Can Predicate Properties Be Neither True nor False?

• MHB
• lemonthree
In summary, the conversation discusses the concept of a predicate and its truth set. It is concluded that a predicate can have an empty truth set and that it cannot contain infinite variables. However, there is some ambiguity in the questions asked and the definition of a predicate.
lemonthree

I'm not very sure whether a predicate can be neither true or false, and I haven't seen any example so far.

The second choice is false because it is the truth set that is the set of all values which make the predicate true.
A predicate has finite variables, so the third choice is false too.

I believe the truth set of a predicate can be empty, so the last choice is true.

I agree with your choices, but I find the questions not precise enough. According to Wikipedia, a predicate on a set $X$ is a function from $X$ to $\{\text{true}, \text{false}\}$. With this definition it is not clear what "always" means in question 1 and what it means for a predicate to contain variables in question 3.

## 1. Can predicate properties be neither true nor false?

Yes, it is possible for predicate properties to be neither true nor false. This concept is known as "indeterminacy" or "undecidability" in logic and mathematics.

## 2. How can predicate properties be neither true nor false?

This can occur when there is insufficient information or evidence to determine the truth or falsity of a statement. It can also happen when a statement is self-referential or paradoxical.

## 3. Is it important to consider indeterminacy in scientific research?

Yes, acknowledging and addressing indeterminacy is crucial in scientific research because it helps us understand the limits of our knowledge and the uncertainties in our findings. It also encourages critical thinking and promotes further investigation.

## 4. Are there any real-world examples of indeterminacy in science?

Yes, there are many examples of indeterminacy in science, such as the famous Schrödinger's cat thought experiment in quantum mechanics, the concept of free will in psychology, and the nature of time in physics.

## 5. Can indeterminacy ever be resolved?

It depends on the specific case. In some cases, further research and evidence may lead to a resolution of indeterminacy. In other cases, indeterminacy may be inherent in the nature of the question or statement, and therefore cannot be resolved definitively.

Replies
19
Views
3K
Replies
21
Views
10K
Replies
11
Views
4K
Replies
2
Views
2K
Replies
10
Views
5K
Replies
2
Views
4K
Replies
2
Views
2K
Replies
16
Views
2K
Replies
16
Views
5K
Replies
4
Views
3K