No and no.
The shard of windshield glass found ten meters from the crash site may be some part of the northbound vehicle.
The engine block with the VIN number on it is some part of the northbound vehicle.
Therefore, the shard of windshield glass may be the engine block.
You gave an example where the two parts are
necessarily different. You could indeed contrive an infinity of such examples.
Yes, but it only takes one. Your beautiful theory is slain by an ugly fact.
Yet, that's not what the original argument says. There's nothing in the original argument implying that x and y are necessarily different. I hope you agree with that.
So?
Every counterexample to
every claimed inference rule adds some detail to the original argument. Surely you aren't going to claim that disproof by counterexample is an illogical procedure.
So, in effect, you've rewritten the argument to add one premise, as follows:
x may be some part of B;
y is some part of B;
x is different from y;
Therefore, x may be y.
Which obviously is not valid.
Huh? Where the heck did you see me say a shard of glass is different from an engine block? My counterexample followed your proposed rule form perfectly. You're the one who filled in "x is different from y", with your own background knowledge. Your own background knowledge is sufficient to show your argument is invalid.
Look at it this way. If some argument "P1. P2. Therefore C." is valid, then how the heck do you imagine adding a third premise could ever turn it invalid? If a conclusion follows from premises, it still follows from any expanded list of premises. It's not as though an argument is even required to use every one of its premises. (Recall in the example in your other thread that the conclusion followed from premises 2 through 5, and never used premise 1.) You can't have a "P1. P2. P3. Therefore C." that's an invalid argument when "P1. P2. Therefore C." is a valid argument -- validly drawn conclusions do not magically go away just because you add premises. But, as you say, when you add the third premise the argument is obviously not valid. Therefore, the argument with only two premises is obviously not valid.
As you framed it, the additional premise is left implicit, relying on the semantic of the English lexical terms you use, "shard of windshield" and "engine block". I take it you understand that.
It's not an implicit additional premise; it's simply a detail of the counterexample. I take it you don't understand that distinction, and that's your problem, not mine; but even if it were an additional premise that wouldn't help your case, for the reason I just explained.
However, the validity of syllogisms is assessed on form only. So, you have to disregard implicit semantic connections and assess validity on form only. That's a well-known bias.
And since it is assessed on form only, that means for the rule to be valid
it must have no counterexamples. There must be
nothing you can plug into the variables that makes the premises true and the conclusion false. That's why counterexamples kill syllogism claims. When one is claiming a rule is valid based on assessment of its form only, "Your example has such-and-such a property" is not a substantive defense. "You gave an example where the two parts are
necessarily different." is not a substantive defense. Your proposed syllogism is dead on arrival. If your rule gives right answers when the two parts are not necessarily different, but wrong answers when they are necessarily different,
its conclusion depends on semantic connections, not just on form only! Why are you having a problem with this?
The situation is different with soundness, because the truth of the premises has to be assessed on the basis of what the premises mean and of empirical reality.
But we're only interested in validity, here.
Well, if I were only showing unsoundness and not invalidity, then that would mean that since the conclusion in my example is clearly false, the premises must be false. I.e., your rule would prove that either the glass shard didn't come from the northbound car or the engine block didn't. How clever of your rule to draw an empirical conclusion from a priori reasoning.
So, your "counterexample" is smart but flawed.
Can you reply to that?
EB
No flaw in the counterexample, just a flaw in your proposed syllogism.