Show that 1+1+1=3
1+1+1 = (1 + (1+1)) = (1+3) =3
The mistake in the inner bracket calculation is that I considered 1+1 to be equal 3, and that of the outer bracket is that is that I considered 1 plus 3 to be equal 3 again.
Would the above constitute as a Gettier paradox, or simply, a misapplication of deductive reasoning?
What is the Gettier Paradox?
I think it's best understood by the following excerpt from wikipedia
In a 1966 scenario known as "The sheep in the field", Roderick Chisholm asks us to imagine that someone, X, is standing outside a field looking at something that looks like a sheep (although in fact, it is a dog disguised as a sheep). X believes there is a sheep in the field, and in fact, X is right because there is a sheep behind the hill in the middle of the field. Hence, X has a justified true belief that there is a sheep in the field.
In analogy to here, the inner most bracket computation and outermost bracket is like thinking they dog in the sheep's clothing is a sheep, and then, the ultimate fact that I get three is like there actually being sheep in the field.
The point is, if I were to use inductive or abductive reasoning, then even application of correct reasoning doesn't neccesiate correct result.
Also, suppose I did a deduction with no mistakes, then I'd imagine that Gettier would never occur. Hence, for title question, only the case of double negative in the deduction need to be considered.