Photo courtesy of Winquist Photography . <| sep |> Ok , I think I see the issue here . You are reading implies and related words as meaning something a bit different from what they are typically taken to mean in logic . In natural English , you are right that it sounds very odd to say something like Bob ' s house is red implies that 5 7 12 or If Bob ' s house is red , then 5 7 12 . That is because in natural language , we often expect some type of causal , explanatory , or truthmaking connection when we use implies or if . then statements . But in traditional logic , we are using those terms in different ways just like when , in traditional logic we use an inclusive or when in natural language , we very often use an exclusive or . EDIT There are lots of interesting philosophical issues with conditionals , and how we should represent them in logic see conditionals