Is proof really reliable? Exploring the concept of axioms in mathematics.

In summary, the confidence in a line of argument is based on the axioms of logic, which determine if an argument is a proper proof. These axioms may be empirically verifiable in certain logical systems, such as the classical laws of identity, non-contradiction, and excluded middle. However, in mathematics, axioms are not considered to be true or false, but rather they simply exist and are used to create useful models.
  • #1
FulhamFan3
134
0
What makes us so confident that a line of argument works at all? Why do you trust statements so much?
 
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  • #2
Give an example.
 
  • #3
Do you mean mathematical proof? It is the axioms of logic that tell us when an argument is a correct proof, and they are just axioms.
 
  • #4
It depends on the logical system in which you prove a statement. Certain systems seem to be based on axioms that are empirically verifiable at least to some extent. The classical laws of identity, non-contradiction, and excluded middle all have some basis in the way we observe nature to operate. Beyond this observation, though, there isn't any formal way I can think of to prove their validity.
 
  • #5
Axioms in mathematics are not really true, or false, they just are. Eg the parallel postulate isn't true, or false. What we do is work in models which satisfy the axioms. In the case of the parallel postulate there a models which satisfy it, and those that do not, and they are all useful in many ways.
 

1. Can you explain what "proof works" means in science?

Proof works refers to the process of using scientific evidence and reasoning to support a hypothesis or claim. It involves collecting data, conducting experiments, and analyzing results to reach a conclusion that can be replicated and validated by others.

2. How do scientists prove that their evidence is valid?

Scientists use various methods to ensure the validity of their evidence, such as conducting controlled experiments, peer-reviewing their work, and replicating their results. They also follow the scientific method, which involves making observations, forming a hypothesis, testing it, and drawing conclusions based on the evidence.

3. Is it possible to prove something with 100% certainty in science?

No, it is not possible to prove something with absolute certainty in science. The nature of scientific inquiry involves constant questioning and refinement of knowledge, so there is always room for new evidence to emerge and change our understanding of a topic.

4. Can proof be subjective in science?

Proof in science is not subjective, as it is based on empirical evidence and logical reasoning. However, the interpretation of evidence and the conclusions drawn from it may differ among scientists, leading to different explanations or theories.

5. How does the concept of proof differ in different scientific fields?

The concept of proof may vary in different scientific fields due to the nature of their research and the type of evidence they gather. For example, in social sciences, proof may rely more on qualitative data and observations, while in natural sciences, it may involve quantitative data and experimental results.

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