Hi. Take the following syllogism : John believes that green people should be killed. Mushmush is a green person, a neighbour of John. ====================== Thus, John believes that Mushmush should be killed. Formally, the argument seems valid. However, in reality it doesn't work. A persona can believe that all people with quality X should be killed, but not think it about a specific person he knows. So is there a logical contradiction here? What happens? Thank you, Sam

Hello. What exactly is completeness in logic? What makes some system of logic complete? And what is incompleteness?

Is logic ever wrong?

I have a question about the identity of a certain kind of fallacy, namely: A = C B = C therefore A = C Confusingly, I have read that the above syllogism is valid; and yet consider this argument I've heard recently: Obama = Good speaker Hitler = Good speaker therefore Obama = Hitler Clearly the latter is a fallacy. So, I have two questions, really: 1) What is the name of this fallacy? 2) How can it be a fallacy if the first syllogism (A = C, B = C, therefore A = C), whose form it follows, is considered to be valid . . . or am I wrong about it being valid?

Why is that if P entails not-Q and Q (a contradiction) do we conclude not-P? I understand that this a reductio ad absurdum and that because of the law of bivalence P either has to be true or false so if it entails a contradiction it is proved not true therefore false. But that last step is what I can't seem to justify...why does it become Not-P if it entails a contradiction? If I had to guess it's because contradictions don't exist in real life so if P were true and it entailed something that could never exist then it must be the case that P is not true (and this is true because of modus tollens: not-Q entails not-P). But we are dealing with symbols in the case of formal logic so how does this apply? Is formal logic an analogy of real life? I hope the question is clear after this rant!

What are the defenses to the attacks on the law of non-contradiction. In other words, what is the traditional philosophical orthodoxy's response to developments in paraconsistent logics (Graham Priest's "Doubt Truth to be a Liar" or "In Contradiction", etc.)?

I have heard that Gödel Proved that Arithmetic cannot be reduced to logic or formal logic. Although I have read explanations which basically state that arithmetic is not complete and thus not definitional like in formal logic, I cannot get my head around how 1+1=2 is NOT reducible to formal logic. This seems like an obvious analytic statement in which "one and one" is the same as saying "two". Can anyone shed light on this?

Is modal logic first-order logic or second-order logic or higher-order logic? What makes a logical system fall into any of those categories? Is it based on expressive power?

I have always been more talented at exposing flaws in reasoning or hypocrisy in actions than in constructing anything to replace what I criticize. Naturally many people are bothered when they're criticized and aggravated beyond that when not presented with an alternative. What is the status of this ability? Should someone hold his silence if he has nothing better to offer, or is just being critical worthy by itself?

This question has been given to my year 7 son and he has permission from his teacher to seek help from the web! Any assistance gratefully received. "A wicked year 7 pupil, the self-styled "Logician", was up before the year head on a serious charge of misleading the rest of the year into avoiding homework through clever argument. The head of year promised expulsion from the school, but added the following strange condition that, if on the day of expulsion the Logician signed a statement making one true declaration about his punishment, the expulsion would be reduced to confinement in the Head's study for 10 days. If on the other hand the statement is false, then the sentence will be carried out immediately. The day of expulsion arrives and the Logician, beaming, signs a declaration which is handed to the head of year who reads it in bewilderment. Tearing the document to shreds in his anger he orders that the Logician suffers no punishment whatsoever." What could the Logician have said which resulted in...