Can someone explain Gottlob Frege's basic law V to me?
it is “for concepts F and G, the extension of F equals the extension of G if and only if for all objects a, Fa if and only if Ga”.
Its for a paper on the philosophy of mathematics I'm writing.
how do ou turn a friction into %
You take the numerator and divide it by the denominator....
numerator= on top
demoninator = on bottom
Who will participate in extension and why
Certainly! Gottlob Frege's basic law V is a fundamental principle in his philosophy of mathematics. It expresses an equivalence between two concepts F and G based on their extensions. The extension of a concept refers to the collection of objects that the concept includes or applies to.
The law states that the extension of concept F is equal to the extension of concept G if and only if, for every object a, a is in the extension of F if and only if a is in the extension of G.
To explain this further, let's break it down into steps:
Step 1: Understand the concept of extension
An extension refers to the collection of objects that a concept includes or applies to. For example, the concept "even numbers" has an extension that includes the numbers 2, 4, 6, etc. The concept "prime numbers" has an extension that includes 2, 3, 5, 7, etc.
Step 2: Compare the extensions of concepts F and G
Consider two concepts, F and G. To apply Frege's law V, you need to compare their extensions.
Step 3: Check if the extensions are equal
The law states that the extensions of F and G are equal if and only if, for every object a, a is in the extension of F if and only if a is in the extension of G.
To verify this, take any object a and check if it belongs to the extension of F and G in the same way. If, for all objects a, whenever Fa is true, Ga is also true (and vice versa), then the extensions of F and G are equal.
Step 4: Interpretation and Application
Understanding this law is essential in Frege's philosophy of mathematics. It provides a criterion for establishing the equivalence of concepts based on their extensions. This notion of extension allows Frege to develop a system of logic and mathematics that is grounded in objectivity and independent of subjective opinions or interpretations.
When writing your paper on the philosophy of mathematics, it would be helpful to explain the significance of Frege's basic law V in his overall philosophical framework. You can discuss how it connects with his views on logic, truth, and the nature of mathematical concepts.