I will formalize it. I don’t know what your second statement means; to me induction and deduction are completely different. 2+2=4 is a deductive statement, provably true within the context of a certain formal system. “Mars is red” is an inductive statement, it can’t be derived from some larger theory; we believe it because of empirical evidence.
“Mars is red” is an inductive statement, it can’t be derived from some larger theory; we believe it because of empirical evidence.
That’s not an example of a non-trivial induction, since you’re talking about a set with only one element. A truly inductive statement says something about a larger set of things where we don’t have the relevant empirical data about each single one of them. And once you start formalizing a procedure for non-trivial induction, the boundary between induction and deduction becomes very blurry indeed.
Maybe an example will clarify the issue. Compare general relativity to a world atlas. Both are computational tools that enable predictions, so both are, by my definition, scientific theories. Now GR is very complex deductively (it relies on complex mathematics), but very simple parametrically (it uses only a couple of constants). The world atlas is the opposite—simple deductively but complex parametrically (requires a lot of bits to specify).
I trust you’ve read the discussions and articles regarding the status of purported “a priori” knowledge, then? If not, I have reason to suspect your ideas will not appear informed and will thus not yield inslight.
I will formalize it. I don’t know what your second statement means; to me induction and deduction are completely different. 2+2=4 is a deductive statement, provably true within the context of a certain formal system. “Mars is red” is an inductive statement, it can’t be derived from some larger theory; we believe it because of empirical evidence.
That’s not an example of a non-trivial induction, since you’re talking about a set with only one element. A truly inductive statement says something about a larger set of things where we don’t have the relevant empirical data about each single one of them. And once you start formalizing a procedure for non-trivial induction, the boundary between induction and deduction becomes very blurry indeed.
Maybe an example will clarify the issue. Compare general relativity to a world atlas. Both are computational tools that enable predictions, so both are, by my definition, scientific theories. Now GR is very complex deductively (it relies on complex mathematics), but very simple parametrically (it uses only a couple of constants). The world atlas is the opposite—simple deductively but complex parametrically (requires a lot of bits to specify).
I trust you’ve read the discussions and articles regarding the status of purported “a priori” knowledge, then? If not, I have reason to suspect your ideas will not appear informed and will thus not yield inslight.