Here are the statements/question: Some Men are Doctors and, Some Doctors are Tall Does this mean some Men are Tall? My answer to this question was Yes, and my working was simplistically set based. Drawing it is Venn diagram style, I make a big box and write "Men" in it. Entirely within the box, I draw a circle, and write "Doctors" in it, and then within that circle i make a smaller circle with "Tall" in it. Within the bounds of the statement and bringing no knowledge about gender/career distribution of the human race into it, I believe I can state that all Doctors are Men As a software engineer, I create a link between the two statements using the word "Doctors" which I assert is discussing the same set in each statement in the same way that, in a computer program, using the same variable name in the same scope, refers to the same object in memory Other people have a different approach that essentially relies on the "Doctors" in each statement being a separate set.. They essentially draw two Venns, [Men (Doctors)] and [Doctors (Tall)], or one Venn that has extra elements not discussed, such as Women, and assert that the Doctors group crosses the boundary between Men/Women, of which all the "Tall" group could be entirely on the Women side: [Men (Doc|tors(Tall)) Women] Another guy gave me some predicate logic, upside down A and backwards E etc.. I remembered it vaguely from uni, but his predicates basically said: for all X there is an X such that Man(X) and Doctor(X) is true and, for all X there is an X such that Doctor(X) and Tall(X) is true Now, I can see how this leads to an answer of "No" to the "Are some men tall?" question, but I asserted that he had rewritten the original statements: Some Humans are Male Doctors Some Humans are Tall Doctors Does this mean that some Doctors are Tall? No Core to my argument is that the statements completely define the objects in the sets. If people are desperate to bring in outside knowledge: In Saudi Arabia, some Men are Drivers (can drive a car) In Saudi Arabia, some Drivers are Tall Does this mean, in Saudi Arabia, some Men are Tall? Yes - I can state concretely because in Saudi all drivers are men; I'll bring in the outside knowledge that women are not allowed to drive a car. Can someone help out here, with an explanation that makes sense to me? I can accept that I'm deliberately limiting my sets and this may lead to an induction problem, but hopefully I've stated why I'm being restrictive (i.e. the question discussed only Men, therefore nothing other than Men exists.. And Doctors are defined in terms of Men.. etc) from a computing point of view; the original program can only be written to deal with the variables known to exist at the time of its creation
This is unjustified. The statements "Some Men are Doctors" is not equivalent to "All Doctors are Men", which is what you state by drawing the circle fully inside the box. Consider the universe with Doctors set containing A and B, where A is also in the set Men and B is not. The statement "Some Men are Doctors" is true in this universe, but the statement "All Doctors are Men" is not. That the statements do not have the same truth value means that they are not semantically equivalent. Same problem as above. You can state it, but it wouldn't be valid (i.e. true regardless of the interpretation of "Doctor" and "Men"). Right. In predicate logic terms, the statements belong to the same "(first order) language." I wouldn't accept the first as reasonable. If the "Doctors" are supposed to refer to the same things, then obviously you cannot say anything about the truth of the third statement. Technical note: these are not predicates, but formulas. Predicate are technically relations over the atoms in some universe of discourse. I don't agree. You're inventing the new predicates "MaleDoctor" and "TallDoctor" (and "Humans"), but these terms do not occur in your friends' formulas. If I write \(\exists x \;Man(x) \wedge Doctor(x)\), then this is not the same formula as \( \exists x \; Human(x) \wedge MaleDoctor(x)\), if for no other reason, then because they simply aren't written in the same first order language. Ah, but this is entirely the wrong thing to do! You're interpreting the meaning of the predicates "Man" and "Doctor", but these are just strings (to use a familiar computer science term). Who exactly is a man, and who exactly is a doctor has no impact on whether or not you can make a valid line of reasoning to answer the question. But that's obviously not the purpose of this exercise. I myself am (reasonably) tall. Is the answer to the question therefore "yes"? That would be absurd. But programs can dynamically create variables (i.e. pointers to the heap, or by pushing registers to the stack) during runtime, such as in recursive calls. And interpreters can run programs that haven't even been written at the time of their creation, and which they therefore have no knowlegde of. Arguing aside, I think you're simply missing the object of the exercise. Whether some men (out here in the real world) actually are tall (yes), is entirely irrelevant. What you're probably being asked to due is to find a valid line of reasoning for or against the statement "Some Men are Tall" given the premises that "Some Men are Doctors" and "Some Doctors are Tall". Remove the words which gives you associations, and it should be more clear: "Some P are Q" "Some Q are R" --------------- "Some P are R"? This is completely the same statements, save for variable renaming (which has no impact on semantics.) Thinking of P, Q and R as set, the Venn diagram method can easily be used to find a concrete counterexample, a model, where P and Q overlap, Q and R overlap, but P and R do not. Meaning that it is not valid to conclude "Some P are R" from the premises "Some P are Q" and "Some Q are R".
No, simply prove it's not true give an example where it's not true. No men are tall And the statement still stands true. Thus it can't prove the statement: Does this mean some Men are Tall? The burden of proof is 100%, if it doesn't equal 100%...it's not accurate. Law 101. I think a thread like this is evidence that a separate math section would be beneficial
Some midgets are doctors Some doctors are tall Are midgets tall? This rewording should help you find your error. (hint: not all doctors are men)
Injustufied? Irregardless, why don't you loose the more stupider attitude alot! Please Register or Log in to view the hidden image!
