I was trying to understand the truth functional definition of an implication "if A then B"/"if A, B". I was reading Stanford encyclopedia of philosophy article on indicative conditional and in the 3rd paragraph it seems they try to definition what an implication is. They discuss it in that paragraph but then they have the following statement (which I don't understand):
"If it's a square, it has four sides", said of an unseen geometric figure, is true, whether the figure is a square, a rectangle or a triangle.
what I don't understand is why the previous statement would be true (or actually take any boolean/logical value at all) if we don't actually have any figure to consider. For me it seems we are trying to define the boolean function f(A,B) = " if A, B" but in the context of the quote they give they essentially make A(x) a function of the shape and then ask me to consider what the truth value of g(x) = f(A(x),B(x)) would be. It seems really silly because we have not actually given the input x to A (or B in fact because "it" refers to the geometrical shape in question). Thus, for me regardless of what definition of implications I am trying to derive, I would leave that specific example as neither True or False, because we have not given the arguments to the function to be evaluated at all!
Am I right? Or am I missing something very simple? What is the purpose of that sentence in that article. It seems to be more confusing (and distracting) than helpful in convey whatever point they are trying to convey. How does it help them justify the definition of implication? Whats the use of that example in that paragraph?
After reading a response I got on reddit to this it made me consider a part of a sentence in that paragraph that might be relevant to understand the whole better:
its is uncontroversial that "if A, B" is sometimes true when A and B are respectively (true,true), or (false,True), or (false,false).
It seems to me that that it is very controversial depending on what you want "if A then B" to mean (i.e. we are coming up with its truth funtional definition). In the section of the article we are deciding what an implication should mean. A quick view in the dictionary says:
- the conclusion that can be drawn from something, although it is not explicitly stated.
- a likely consequence of something.
So it would make sense to bring up examples that are relevant to that definition (otherwise why use "if A, B" to define something if its not going to mean sort of what it usually means). So it seems to me that its suppose to bring an uncontroversial example of why implications can be True when (true,true), or (false,True), or (false,false). If that is the case, can someone explain me how this example exemplifies this? At this point of the text we have not defined what an implication means and the example should be self evident, so I'd love to know why its self evident.