Ok, this is an all new level of dubiousness. Here is what you are proposing: if Provoker is a hamster and Provoker is still Provoker when he becomes a human, then "is a hamster" was never a necessary property of being Provoker. (1) This is a fruitless analogy as a hamster cannot become a human the way a blacksmith can become a carpenter. In the former case, hamster and human are conditions of existence, while in the latter case, blacksmith and capenter are attributes that are applied to a particular condition of existence (2) You are treating "is a hamster" and "is a human" as if they are attributes of something, rather than essential conditions of existence that allow for attributes to apply to them. In other words, there is a person who occupies a place in spacetime who is called Provoker and posts at typologycentral. Provoker is not the condition of existence, (I can change my forum name and still be the same person who posts on the forum), Provoker is merely a name to refer to the existence of this human entity in spacetime that posts on typologycentral. It follows, therefore, that being human is a necessary condition of the existence of the Provoker we are referring to in the conclusion. This is not to be conflated with a hamster named Provoker that may very well existence, but whose existence depends on a different set of conditions than Provoker the forum poster. And this would have to be the case since it is a precondition of existence that something is itself: if it was not itself it would be something else and that something else is itself, and if something is not itself or something else it isn't. Given this basic law of logic, it should be impossible for Provoker the human forum poster and Provoker the hamster that may exist to be the same entity in spacetime. Your premise refers to one, while the truth of the conclusion depends on reference to the other. It follows, then, that nothing you have said demonstrates that your example is one in which false premises entail a true conclusion as it still makes the basic categorical error I outlined in my former post. Namely, it takes Provoker in the conclusion to apply to a different category than the Provoker in the premise. And this would have to be the case since the truthfulness of the conclusion requires that Provoker is necessarily a human and what is human cannot be hamster (as Provoker is defined in the premise). It is, therefore, an equivocation fallacy and not a case where false premises entail a true conclusion. That you have failed to recognize this and continue to introduce more names is beyond me. I do not care about names, what concerns me is the fallacy and basic categorical error you have thoughtlessly made and continue to parade.
Good work, provoker. You have exposed an egregious epistemic error that reason has made. You have pointed out that an entity's identity would be changed if it was to become a different creature, reason overlooked this as he claimed that it is possible to say that provoker could be regarded as the same creature whether he be a person or a hamster, exactly like John could be the same creature whether he be a blacksmith or a carpenter.
However, I do not think that you even need to go that far to refute the contemptible non-sense that he has espoused. It can be refuted on purely logical grounds, as after all, his argument was about logic and not epistemology. He merely attempted to introduce an epistemic argument to conceal his sinister infractions against basic logic. (After all, he tried to cite an example of a deductively valid argument with true premises that entailed a false conclusion. He failed because his argument was either invalid or contained a fallacy of equivocation.)
Below, we may appreciate a very succinct and a trenchant demonstration of the verity of the thesis that reason's argument is either deductively invalid (contains a formal logical fallacy) or is guilty of an equivocation (contains an informal logical fallacy). My argument shows that even if reason did not make an error that you have argued he did, his argument would still be refutable on purely logical grounds.
-------------------------------------------------------------------
In recapitulation, reason's epistemic error consists in this; if provoker can be defined as either a hamster or a human, the two could be used interchangeably, as after all provoker's not change enough for us to regard him as a completely different creature.
Suppose he said that provoker could be either a student of law or a student of sociology. In this case, the name of provoker as a student of sociology can be used interchangeably with the name of provoker as a student of law. In this case, if you, provoker were to change your major from law to sociology, we could still regard you as the same person.
Suppose we are trying to prove a conclusion that is quite similar to that of reason (in this case we are not guilty of the epistemic howler that he has committed earlier), the conclusion is that provoker (the student of law) is a member of typologycentral.
The following are our premises;
1. Provoker is a student of sociology (False premise)
2. All students of sociology are members of typologycentral (False premise)
Conclusion: Provoker (the student of law) is a member of typologycentral. (True conclusion).
This argument is invalid because the truth of the two premises does not guarantee that the conclusion is true. The premises imply that any student of sociology is a member of typologycentral. Even if that is true, the conclusion that provoker the student of law is a member of typologycentral is not vindicated because the premises can only entail the conclusion that only students of sociology may be members of typologycentral.
Suppose we make a deductively valid argument, but in this case it would be guilty of the informal fallacy of equivocation and therefore the conclusion would be false.
1. Provoker is a student of sociology (False premise)
2. All students of sociology are members of typologycentral (False premise)
Conclusion: Provoker (the student of sociology) is a member of typologycentral. (False conclusion).
The bottom line is that if reason's argument is valid, it entails a false conclusion and entails a true conclusion only if it is deductively invalid.
--------------------------------------------------------------------
One may retort that we should not be defining our terms that way! After all, Provoker can be the same person regardless of whether he is a sociology student or a law student! That is true, but then the problem is not with the syllogism but with the way the terms are defined here, the universe of discourse in this argument offers two different definitions of provoker (one is a student of law and the other is the student of sociology). If an argument is to be left unedited, it should be evidence of an espistemic error as provoker can be the same entity despite the change of his academic course of action.
True this may be, however, Logic and epistemology are different disciplines. Logic is purely concerned with relation of propositions, not with the definitions of terms, epistemology is concerned with the definitions of terms, logic merely deals with the terms as they have been defined by epistemology.
Lets try to define the terms of our discourse in logic in accordance to the epistemic model that we have devised above (one that is devoid of reason's ignominous howler). In this case, the distinction between provoker as a law student and a sociology will be insignificant and we may use the terms interchangeably.
1. Provoker is either a law a student or a sociology student. (He can be either one and legitimately claim the identity of provoker) ----True premise
2. Provoker is a sociology student.---False premise
3.All sociology students are members of typologycentral.--False premise
Conclusion---Provoker (the law student) is a member of typologycentral. (True conclusion)
This argument is deductively invalid as the premises cited above do not guarantee the verity of the conclusion. Again, that is the case because the membership of the forum of provoker the law student is not entailed by anything in the premises. The premises only entail that provoker the sociology student could be a member of typologycentral. Premise one says that he could be a sociology student, but it does neither that premise nor any other supposition of the argument evinces that he is. The or statement means that he is at least one of the two or both, but alone, the 'or' statement does not specify which of the two he is or that he is both.
This version of the argument could also be rendered valid, but only at the price of committing the equivocation fallacy and subsequently the entailment of a false conclusion.
1. Provoker is either a law a student or a sociology student. (He can be either one and legitimately claim the identity of provoker) ----True premise
2. Provoker is a sociology student.---False premise
3.All sociology students are members of typologycentral.--False premise
Conclusion---Provoker (sociology student) is a member of typologycentral. (False conclusion)
The true conclusion is that provoker the law student is a member, not provoker the sociology student is. If one is to assume that the true conclusion that provoker the law student is a member of the forum is entailed by this argument, one is to committ the equivocation fallacy. Whenever you define terms in any way that is different from how you have defined them in your universe of discourse, you do so without a logical justification and are therefore guilty of the equivocation error in reasoning.
------------------------------------------------------------
Alas, not all is lost. Reason's argument could have been salvaged! Perhaps we did not define his conclusion adequately! Lets give this another try.
1. Provoker is either a sociology student or a law student.
Premise 2. Provoker is a sociology student. (False premise)
Premise 3. All sociology students are members of the forum.
Conclusion: Provoker who is either a law student or a sociology student is a member of the forum.
This argument is perfectly valid.
Below is the symbolization of the argument that proves the deductive validity of the reasoning chain in question.
Mx-x is a member of the forum.
Lx-x is a law student
Sx-x is a sociology student
a-provoker
1. Sa V La (Provoker is either a sociology student or a law student. The implications of this is that he could be either one or both without changing his identity)---True premise
2. Sa (Provoker is a sociology student)---False premise
3. (x) (Sx-Mx) All sociology students are members of the forum. ---False premise
4. Sa-Ma (3, universal elimination. If provoker is a sociology student, he is a member of the forum.)
5. Sa ( 2 Reiteration, provoker is a sociology student)
6. Ma (provoker is a member of the forum, 4,5 modus ponens, provoker is a member of the forum because he is a sociology student)
7. Sa V La (Remember, once I prove X, I can say X or anything else true. (X---X V or anything else)
(Statement 7 reads that provoker is either a law student or a sociology student)
8. (Sa V La ) * Ma (6, 7 conjunction) Since I have proved that both items 6 and 7 are true, I am free to say 6 and 7 is true. (Statement reads that provoker is either a sociology student or a law student and is a member of the forum).
In this case we have an unremarkable conclusion of a provoker being a member of the forum regardless of whether he is a sociology student or a law student.
This is a true conclusion that was derived by deductively valid means from a set of premises where at least one of the premises was false. If reason was not guilty of the error you cited in the previous post, he could have corrected his flagrant error by reconstructing his original argument in a way that it is valid and devoid of the informal fallacy of equivocation. As it stands, it is completely hopeless. In fact, if we still have any doubt about this, why don't we plug it into the syllogism so we may be amused at the preposterous results it yields.
1. Provoker is either a hamster or a person. (True premise)
Premise 2. Provoker is a hamster. (False premise)
Premise 3. All hamsters are members of the forum.
Conclusion: Provoker who is either a hamster or human is a member of the forum.
Hx-x is a hamster
Dx-x is a human
Mx-x is a member of the forum
a-provoker
1. Hx V Dx (Provoker is either a hamster or a human)
2. (x) (Hx----Mx) (All hamsters are members of the forum)
3. Ha (provoker is a hamster)
4. Ha-Ma (If provoker is a hamster then he is a member, universal elimination)
5. Ma (3,4 modus ponens. Provoker is a member of the forum because he is a hamster.)
6. Ha V Da ( 3 Vedge introduction)
7. (Ha V Da) * Ma (provoker is either a hamster or a human and is a member of the forum.)
The conclusion is merely saying that either the human named provoker is a member of the forum or a hamster is. It is true, but useless and overly general. It does not cut to the main point that the human named provoker is a member of the forum. Although this syllogistic structure redesigns reason's argument to be both deductively valid and devoid of informal fallacies, most notably equivocation, its epistemically worthless exactly for the reason that you have cited--the category mistake. Knowing that provoker could be either a human or a hamster does not at all help us prove that a human named provoker is a forum member, as here we are dealing with radically different identities, one of an animal and the other of a human. On the other hand, if we used the argument that I have cited where we used two properties of provoker's possible identity (namely, law student or a sociology student). It is conceivable that when we have these propositions, we are talking about the same person (who could either be a law student or a sociology student), yet it is inconceivable that we are talking of the same entity who could either be a human who posts here or a hamster called provoker that runs in the wild.