One more time, just to clear up the confusion. Here is the argument:
Every hamster is a member of TypologyCentral
Provoker is a hamster
Therefore,
Provoker is a member of TypologyCentral
Now, if we include among a list of properties of Provoker, "is either a human or a hamster," then the conclusion can still be true even when the premise "Provoker is a hamster" is false. It's that simple: one little disjunction.
This should be quite obvious.
The conclusion is true only if the argument is deductively invalid. Invalid arguments with false premises and true conclusions are quite common and only a little interesting.
This is an example of such an argument.
The sky is red.
All trains run faster than the speed of light.
In conclusion we know that Barrack Obama is the president of the United States.
Lets try your argument.
1. There is a hamster called provoker. (True premise)
2. All hamsters are members of typology central. (False premise)
Provoker/Colin/author of this thread is a member of typology central. ( True conclusion). If you do not understand how this argument is invalid, may as well give up here or at the very least, since you are now a freshman in your undegraduate program enroll in an introduction to logic or a symbolic logic course. (They are usually titled as PHL 102, 103, sometimes 105 or 107 and so on...)
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Lets look at another way your argument can be constructed.
1. Provoker is a human and a hamster. (Premise 1)
2. All hamsters are members of typologycentral. (Premise 2)
True conclusion: There is a human named provoker who is a member of typologycentral.
Step 1 of proof: Provoker is a hamster (conjunction elimination).
2. If provoker is a hamster then he is a member of typologycentral. (Universal instantiation)
3. Provoker is a member of typologycentral. (2,3 modus ponens)
Note, here we have proved that there is a hamster called provoker who is a member of typologycentral. The case is such because this conclusion follows from step 2 of proof which states that provoker is a member if he is a hamster. Since he is a hamster, we know that he is a member.
Your conclusion is false because it states that there is a hamster who is a member of typologycentral. The true conclusion is that there is a human called provoker who is a member of typology central. Therefore this argument is not an instance of a deductively valid argument where there is a true conclusion entailed by false premises.
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Lets try another derivation.
Same argument.
1. Provoker is a human and a hamster. (Premise 1)
2. All hamsters are members of typologycentral. (Premise 2)
True Conclusion: A human named Provoker is a member of typologycentral
Step 1 of proof: Provoker is a human ( 1, conjunction elimination)
Step 2 of proof: If provoker is a hamster then he is a member of typology central. (2 Universal instantiation).
From here we cannot derive the conclusion that there is a human named provoker who is a member of typologycentral. In order to prove that provoker is a member of typologycentral, he needs to be a hamster as step 2 states that if he is a hamster he is a member of typology central.
Now, suppose I did this, Step 3: Provoker is a member of typologycentral. (Invalid inference! This is affirming the consequent which is a fallacy.)
Again, this underlines that you cannot prove that provoker is a member of typology central without maintaing that provoker is a hamster first. This proof must either remain incomplete, and if it is to be completed, it must be done by virtue of modus ponens where we start with the antecedent of provoker is a hamster (which we derive by conjunction elimination of premise 1). Thus by modus ponens we deduce that provoker is a member of typologycentral because he is a hamster.
The bottom line is that the conclusion that provoker who has a property of being a hamster is false, and by this argument, its impossible to prove that provoker is a member of typologycentral without maintaining that provoker is a hamster. Thus, the true conclusion that there is a human being named provoker who is a member of typologycentral is unattainable.
Provoker,
I understand SolitaryWalker's objection, but its just silly talk.
In short, the claim is that my conclusion, "Provoker is a member of TypologyCentral," is not actually true, is because the "Provoker" in that proposition refers to a hamster. However, this merely follows from including "is a hamster" as a necessary property of being "Provoker," but obviously I would never have meant to imply that when presenting the argument.
If John is a blacksmith and John is still John when he becomes a carpenter, then "is a blacksmith" was never a necessary property of being John. If the same is true of being Provoker and being a hamster, then these objections do not matter. In other words, the term "Provoker" just includes among its properties, "is either a human or a hamster."
Oh, I bet you do. Yet it is really hard to make sense of this mess when you haven't done a single proof in your entire life. Try again next year. When you do enroll in your logic class; don't just look over the nitty-gritty proofs assuming you know all of that stuff, take a pencil and paper out and write out your solution step by step.