Cubey
The Formality
What is a posteriori reasoning then you ask? A posteriori is the opposite of a priori. Whereas a priori reasoning relies solely on rationality and deduction to reach a conclusion, a posteriori reasoning uses experience to conclude its argument.
For example, mathematics is [so far] a posteriori. We are taught by experience because numbers are not an innate idea to humans. When we are taught mathematics as kids, we’re shown objects: an apple for instance. The teacher says this is one Apple. Child shows confusion so the teacher shows her an additional Apple. Now these are two. And so on. Once the child has grasped the concept mathematic can move forward but this doesn’t change the fact that it was learned by experience and not sheer logic. Model and proof theory however are aiming to put mathematics on a purely logical basis and it will certainly be done, so I await that eagerly
But I digress. A posteriori is learned through experience. It’s also a generalization-to-specific argument. So for example, EVERYONE agrees 1 + 1 = 2. Therefore it is proof of a universal truth.
So that’s it for the a priori and a posteriori reasoning. I could make one last post regarding the four kinds of arguments that can be formulated using the synthetic, analytic, a priori and a posteriori reasonings. If people want ofc
For example, mathematics is [so far] a posteriori. We are taught by experience because numbers are not an innate idea to humans. When we are taught mathematics as kids, we’re shown objects: an apple for instance. The teacher says this is one Apple. Child shows confusion so the teacher shows her an additional Apple. Now these are two. And so on. Once the child has grasped the concept mathematic can move forward but this doesn’t change the fact that it was learned by experience and not sheer logic. Model and proof theory however are aiming to put mathematics on a purely logical basis and it will certainly be done, so I await that eagerly
But I digress. A posteriori is learned through experience. It’s also a generalization-to-specific argument. So for example, EVERYONE agrees 1 + 1 = 2. Therefore it is proof of a universal truth.
So that’s it for the a priori and a posteriori reasoning. I could make one last post regarding the four kinds of arguments that can be formulated using the synthetic, analytic, a priori and a posteriori reasonings. If people want ofc