It is not a category mistake. One can talk about men and women belonging to the category “human”. The point is that Seraiah’s argument is invalid. You can substitute anything:
Or, even better:
A more in depth explanation of categories can be found here. If you search for category mistake, you can read up on their explanation, though the wiki explanation is sufficient.
GotLucky is correct, Seraiah’s argument is still invalid, it violates the law of identity.
\It is not a category mistake. One can talk about men and women belonging to the category “human”.
It is a catagory mistake in the sense of conceptual levels. They aren’t equal, just that one is included into one another.
Friedmanite,
I was thinking some more about this, and I think Seraiah’s statements show that he does intend to use iff even if “=” is not standard for “iff”.
It seems that Seraiah is under the impression that “is” means synonymous. As in, a bachelor is synonymous with an unmarried man. But this would not be the standard use of “is”, as we could also say a bachelor is a man. I think what he is trying to say is:
Also, so that Seraiah can see why what he said is not how to express it logically:
We are not saying that Socrates is synonymous with man. We are saying that Socrates belongs to the category “man”.
I still maintain that it is not a category mistake. Men and women both belong to the category human. Men and women are not the same. That is the point. The argument is invalid because it can lead to conclusions such as “men are women”. A valid argument can never do that.
If you create an argument using the form Seraiah provided, and you had true premises and a true conclusion, it would only be by coincidence.
I know that and also can follow why you said that. Carefully read what one of your own sources did say.
Double posted.
You still haven’t adequately addressed the issues I pointed out in my last post. Attempting to undermind logic is a very big task, requiring extensive thought on epistemology, which I am fairly certain you haven’t studied enough. The argument you presented in your last post still didn’t explain why Occam’s Razor is essential to logic, or rather it wasn’t a valid explanation.
It is essential to probability. Or rather, probability is essential to it. It is just the condensed form of saying that the more assumptions one makes, the more likely one is to be wrong. I have never studied logic, but I’m certain you would be above ad hominems. Anyway, I’m fairly certain there’s a very simple refutation to all of this.
I also note that while many people have used the old “your argument is circular because it uses logic itself” argument, I preemptively responded to that in the opening post and nobody has refuted or even acknowledged those arguments. I claim victory.
Torsten,
Upon reading your original response to me, I’m wondering if I might have misunderstood what you were getting at. Were you saying that the argument was invalid because it leads to category mistakes? Or were you saying that the argument was valid and I was the one making the mistake?
I assumed you meant the former, but after rereading maybe I misread you.
It is blatantly obvious what I meant by “is” in the context, even if it was not 100% true to the term. I have since then ammended, and clarified, the statements so I fail to see what you’re still discussing.
My “original argument” wasn’t any less valid, as I have simply clarified what I meant the entire time. (Which again, was blatantly obvious to anyone less than a grammar Nazi.)
I was just looking at the statement (man=human, woman=human, hence man=woman). I didn’t mean that this is a vertical category mistake, but rather a horizontal one. Actually there is already a hidden mistake in the premises I think a man doesn’t equal a human, but man is part of the humans as umbrella term for a group of subdivisions(man, woman).
None of this disproves logic of course.
Seraiah,
Your original argument wasn’t blatantly obvious. It had nothing to do with grammar; it was completely false according to the rules of logic. Posters have pointed numerous examples why it isn’t true. If you still don’t understand why, go back reread what you posted. I’m under the impression that you still don’t understand where your mistake is.
Again, this is exactly what you wrote:
Take this example:
A is B
C is B
Therefore
A is C
This is completely 100% false.
Don’t confuse things here.
Mathematically,
if a = b and b = c, then a = c.
That’s called transitivity. It’s valid because the equal sign is an equivalence relation.
You cannot confuse this in propositional logic. The equal sign makes no sense.
This is precisely what I said earlier. Suppose A, B, and C are statements, or in logic terms, atomic sentences
=> means only if
<= means if
<=> means if and only if
((A => B) and (B => C)) => (A => C) is always true in all possible combinations of truth values of A, B, and C. We call such propositions tautologies. Tautologies are true precisely due to the meanings of the truth functional connectives. In the preceding example, the connectives are => and “and”. Note that there is a difference between tautological truth and logical truth. Logical truths depend on the meanings of the atomic sentences themselves, and hence may not be tautologies.
Right, man is not synonymous with human. I was criticizing Seraiah’s original argument which he did not state correctly.
No, it was not blatantly obvious what you meant. You are in a thread on logic, and you used logical terms incorrectly. Forgive me for thinking that you knew how to use logical terms correctly.
I was giving you the benefit of the doubt in that post, that while your original argument was invalid, it was not the argument you meant to state. I suppose I shouldn’t extend that anymore.
Really Sherlock?
You wrote 5 posts after I wrote my argument before you went into grammar nazi mode.
You understood what I meant up until your 6th post, because it was obvious.
@ Luminar
The problem is you haven’t made a argument explaining how Occam’s Razor is needed for probability. There are people who reject Occam’s Razor and still have no problem with probability. As I pointed out in my first post in this thread, you also need to make a argument that Foundationalism is the only valid epistemological position for circularity to be a serious problem with logic or Occam’s Razor, the reason being that some epistemological positions (such as Coherentism) don’t see circularity as deadly to validity. I recommend you read a book on critical thinking, it will help you better understand what is necessary when creating a argument, reading up on epistemology is also a good idea. ( “Asking the Right Questions: A Guide to Critical Thinking” )
One last thing, I didn’t commit the ad hominem fallacy in my last post. It was mentioned that you hadn’t studied epistemology, that was all, for it to be a ad hominem I would have needed to claim that since you haven’t studied epistemology you are wrong. I never said that.
Seraiah,
The problem with your original argument is not grammar or ambiguity. It’s just flat out false - end of story. You can admit that you made a mistake, or continue to insist that “it was obvious”, and make yourself look even more foolish.