# Is Math a Science? Philosophers' Refutation Criterion

• jk22
In summary, the conversation discusses the criteria for determining what is considered a science. While some philosophers believe that an assertion can be considered scientific if it can be disproven through experimentation, this definition does not apply to math as it does not involve experimentation.
jk22
For some philosophers an assertion is scientific if an experiment could refute it (all crows are black if we find an albinos one then it is wrong)

But the axioms in maths are not refutable so can it be considered a science with this criterion ?

By strict definition? Science is defined as "the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment." By that definition, no, math is not a science, as no experiments are performed in math.

jk22 said:
For some philosophers an assertion is scientific if an experiment could refute it (all crows are black if we find an albinos one then it is wrong)

But the axioms in maths are not refutable so can it be considered a science with this criterion ?

Sorry, we no longer allow philosophical discussions on the PF. They are too difficult for us to Moderate effectively. Thread is closed.

## 1. Is math considered a science?

There is a lot of debate around whether math is considered a science. Some argue that it is a branch of science, while others argue that it is its own distinct field. Ultimately, it depends on your definition of science, but most would agree that math is closely related to science and plays a significant role in many scientific fields.

## 2. What is the Philosophers' Refutation Criterion?

The Philosophers' Refutation Criterion is a philosophical principle that states any theory or proposition must be capable of being proven false in order to be considered a valid scientific theory. In other words, a scientific theory must be falsifiable in order to be considered scientific.

## 3. How does the Philosophers' Refutation Criterion apply to math?

In terms of math, the Philosophers' Refutation Criterion is often used to distinguish between mathematical theories and scientific theories. While scientific theories must be falsifiable, mathematical theories are considered to be self-evident and do not need to be proven false. Therefore, some argue that math is not a science according to this criterion.

## 4. What are some arguments against math being considered a science?

Some arguments against math being considered a science include the fact that it does not rely on empirical evidence and that its theories are not falsifiable. Additionally, many argue that math is a tool used by scientists to study the natural world, rather than a science in and of itself.

## 5. What are some arguments for math being considered a science?

On the other hand, some argue that math should be considered a science because it follows the scientific method and is used to make predictions and test hypotheses. It also has its own set of theories and principles that can be explored and studied, similar to other scientific fields.

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