Is this argument (about theories, evidence and observations) valid?
(1) If T explains an O, then T is a member of E.
(2) S is a member of O.
(3) If (C member of T) explains S, then C is a member of E.
(4) (C member of T) explains S, therefore C is a member of E.
See expanded example below.
Note that "a member of E" is a set of T such that they contain a mapping to a member of O.
Note also that in the expanded version it is emphasized that for a member of T to be evidenced to a greater degree than other members of T, this would involve it corresponding to members of O that others don't.
(1eg) If a theory explains an observation, then the theory is evidenced.
(2eg) People observe a common process of imagination (for e.g.).
(3eg) If C-Theory of imagination explains the common process of imagination that other theories don't, then C-Theory is evidenced.
(4eg) C-Theory of imagination explains the common process of imagination that other theories don't, therefore C-Theory is evidenced.
Would greatly appreciate any formal logic contributions or hints as to restructure the argument.
(2) S is a member of O.
(3) If (C member of T) explains S, then C is a member of E.
(4) (C member of T) explains S, therefore C is a member of E.
See expanded example below.
Note that "a member of E" is a set of T such that they contain a mapping to a member of O.
Note also that in the expanded version it is emphasized that for a member of T to be evidenced to a greater degree than other members of T, this would involve it corresponding to members of O that others don't.
(1eg) If a theory explains an observation, then the theory is evidenced.
(2eg) People observe a common process of imagination (for e.g.).
(3eg) If C-Theory of imagination explains the common process of imagination that other theories don't, then C-Theory is evidenced.
(4eg) C-Theory of imagination explains the common process of imagination that other theories don't, therefore C-Theory is evidenced.
Would greatly appreciate any formal logic contributions or hints as to restructure the argument.
Comments (33)
Everything that happens is evidence for God.
Hmm.
Quoting Hallucinogen
Edit:
It is.
So the answer is yes. :yawn:
He won't give in.
It seems to me like you bring up this red-herring as a way of avoiding the OP of this thread.
What is that flying across the sky leaving behind it a trail? It must be Icarus on his way. Yes, my theory is evidenced! :roll:
And that doesn't trouble you at all?
I have another theory: "unenlightened did it".
Quoting jgill
Nay, it is unenlightened, playing with his chalk.
Changing the semantics doesn't change the validity of the argument.
Validity doesn't have much of a relationship with truth.
Just so. If everything is evidence that God did it, then everything is evidence that unenlightened did it. But since unenlightened is not God, there is a contradiction.
Therefore, it is false that:Quoting Hallucinogen
You didn't say unenlightened isn't God, before. As far as I could see, you only changed one word to another.
Quoting unenlightened
This is now no longer the case, because now you've added the information that unenlightened isn't God.
Hence, if "God did it" explains O relative to other members of T that it is a member of E, that doesn't entail that changing "God did it" to "unenlightened" implies that "unenlightened" is a member of E, because they don't have the same intension or extension.
Validity is the relationship a true premise has with a true conclusion, just like invalidity is the relationship a false premise has with true premises.
That's soundness. Validity is mere formal agreement between premises and conclusion. If your premises are empirically wrong, the argument is unsound, but can be considered valid(in the case that the premises, however false, would support the conclusion as written/formulated).
No, soundness is the truth of the premises, not the relationship it has to the conclusion.
Quoting AmadeusD
No, an argument can be invalid with a false conclusion that still doesn't follow from a false premise.
Validity consists of the rules of logic being applied consistently to each line of the argument.
Quoting AmadeusD
Correct, so your first sentence was false. Soundness isn't a relationship between premise and conclusion.
Onward
Do not attempt to argue with Me, worm. Cower in fear of My wrath.
I agree, but before we were talking about soundness and validity in terms of how they differ. You began by saying that validity doesn't have much to do with truth, but now you're pointing out what they have to do with each other in terms of soundness. For an argument to be sound, it has to be valid already. A requirement for soundness is the truth of the premises, whereas validity is to do with how the rules of logic are applied.
Quoting AmadeusD
Because it isn't valid.
Quoting unenlightened
False.
Your premises can be entirely false - as long as, in the world in which they are true, the conclusion is supported, the argument is valid but unsound. The addition of the premises being true creates soundness. Validity is purely formal.
Why are you bringing up false premises?
What you're responding to is my response to this comment:
Quoting AmadeusD
I'm going on the basis of this:
Quoting colorado.edu
What I am saying is that sound arguments are a subset of valid arguments.
Quoting AmadeusD
I'm not disagreeing that true premises makes an argument sound. I don't see how you could have the type of argument you're using to illustrate your point, where one has false premises validly leading to a "supported" conclusion. Could you give an example?
What my first response to your statement
Quoting AmadeusD
ought to have been was that validity is a requirement for soundness.
Quoting Hallucinogen
I have explained this one. To reiterate:
Quoting AmadeusD
So, an example could be:
P1: Hitler was German
P2: Hitler carried out his acts in service of Germany
C: Hitler was a German dictator.
This is false. He was an Austrian dictator of Germany.
But the above is a valid argument. In the world where Hitler was German, it holds. However, P1 is untrue, therefore it is not a Sound argument.
Another example:
P1: It is raining today where i am
P2: I am outside, unshaded
C: I am wet with rain.
Logically consistent, and valid. However, it is not raining where i am. So this is unsound.
What I'm saying is the other way around: you cannot have a sound argument without true premises. You cannot have a sound argument without true premises and validity.
For example: Quoting Hallucinogen
Quoting Hallucinogen
This is why I said this :
Quoting Hallucinogen
Sound premise + valid argument = sound conclusion. I can't see how a true premise could lead to a false conclusion without an invalid argument.
But you said this is false because:
Quoting AmadeusD
And I got lost because your answer was no longer talking about a true premise.
Quoting AmadeusD
I agree with that. I didn't realize by "supported conclusion" in your other statement only meant following validly (from the false premise). I thought it meant a true conclusion.
Quoting AmadeusD
OK, but I misunderstood what you earlier said. I thought you were saying that a false premise with a valid argument could produce a true conclusion.
So in summary, my answer to why validity is related to truth is that it preserves the truth of a sound premise. In other words, validity is required for soundness, or a requirement for truth.
If your premises are true, you can only have a valid argument be sound, that's right.
Quoting Lionino
Tell that to the Lounge.
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That's wrong. That's not how "sound" is used in a logical argument. This is how it's correctly used:
True premise + Valid argument = Sound argument
The Lounge doesn't listen, and I think it is because it is unable to. Nevertheless, I blocked the Lounge from my browser, so no more peering into the cesspool.