The Problem of Existential Import Presents a Counter-Factual Problem for Logical Solutions

I believe that beem0r has taken this topic far to seriously... But in the spirit of good debate, I will answer his four objections. 1. On Existential Import. Existential import is indeed a problem when you make a the claim "Some P is Q" if there are no P. He admits that it is a logical implication of the statement, and thus, the problem of existential import is thus: The logical implication of "some P is Q" is that the statement cannot be true if no P exist. 2. On Counter-Factuals. A counter-factual, when given in a logical argument may save the validity of the argument, but not the soundness, as a counter-factual is by its very nature a false premise. A counter-factual is a problem because it purports a conclusion to be true based on a premise that is false. The form is not merely "If X, then Y" but rather, "If X, then it WOULD be the case Y." While not far apart, the two are indeed distinct. Consider: 1. If Nazi Germany had won WWII, the Allies would have lost. 2. If Nazi Germany had won WWII, Hitler would not have committed suicide. The two are distinct in that the first conclusion is a function of the premise. It's basically the following argument: (N v A) - this is an exclusive or... (N) ---------- :. ~A The second has a conclusion that cannot be drawn from the premise in the same way that the first can, and thus, only the second of the two statements is actually a counter-factual statement. These statements do indeed present a problem for arriving at a sound logical conclusion. 3. On Logical Solutions. I mean logical solutions to be a sound conclusion from premises. In other words, that what follows a THEREFORE is drawn from true premises. A "logical solution" would be consistent, valid, and sound. 4. On Existential Import & Counter-Factuals. If one's premise in an argument is of the form "Some P is Q" and it also happens to be the case that no P exist, then this would create a counter-factual premise if the argument is to continue. Consider: Some unicorns are gray unicorns. All gray unicorns have mud on them. (Suppose too, that only gray unicorns have mud on them... keep it simple). Therefore, some unicorns have mud on them. Since no unicorns exist, the first premise is false, the logical implication being (by contradiction) that no unicorns are gray unicorns. If this is the case, then the statement that all gray unicorns have mud on them makes no sense because there ARE no gray unicorns. On top of that, the conclusion is false, because there are no gray unicorns that can have mud on them. Thus, to consider the argument, it introduces a counter-factual: If there were unicorns, some would be gray unicorns. All gray unicorns have mud on them. Therefore, if there are unicorns, some unicorns have mud on them. The first premise in this argument is clearly a counter-factual. **************************************** I did indeed address the point my opponent makes in his closing statements concerning the validity and soundness of arguments. It is true that logic does not insist on true premises, but it does insist on them to be sound arguments. Like I said - While the argument is valid, it is not sound because it has a false premise... **************************************** 5. On the company Logical Solutions. Any company that produces computer code would be concerned with existential import in their code. If a computer tries to analyze "Some P is Q" but cannot find an instance of P, the program will return an error message, even if the P is intended to be hypothetical. So in order to run hypothetical situations, the computer must create an instance of P in order to evaluate the logical claim. Thus, by creating the instance of P, the programmers are avoiding the situation that "If it were the case that P existed, it would be the case that some P is Q" which is indeed a counter-factual. Thus, Logical Solutions IS indeed concerned with existential import and counter-factuals. *********************************** Like I said... a fun debate on a serious topic. I'm actually chuckling to myself at my own last paragraph....