Is this argument (about theories, evidence and observations) valid?

Hallucinogen

(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.

unenlightened

Let T = "God did it."

Everything that happens is evidence for God.

Hmm.

Lionino

Is this supposed to be defending this obviously wrong statement from the previous thread?

(2) If some observation corresponds to some Bible-specific proposition, then it is evidence that Christianity is true. — Hallucinogen

Edit:
It is.

Hallucinogen

↪Lionino

Why would that be false?

Hallucinogen

↪unenlightened

Well if "God did it" explains O relative to other members of T, it would seem "God did it" is evidenced relative to the others.

tim wood

↪Hallucinogen

You have a whole lot of work to do on - at least - defining your terms and how they relate to each other. Until that's done there won't be much sense here. Example: in Genesis is the story of a flood. There is evidence of a flood. Therefore Christianity true??? Or more simply, in Genesis is a story of the creation of man. There is evidence that men exist. Therefore Christianity is true???

Lionino

Why would that be false? — Hallucinogen

So the answer is yes. :yawn:

↪tim wood

He won't give in.

Hallucinogen

You have a whole lot of work to do on - at least - defining your terms and how they relate to each other. — tim wood

It seems to me like you bring up this red-herring as a way of avoiding the OP of this thread.

tim wood

↪Hallucinogen

Only if the comment of yours I replied to is a red herring - but that would be your call.

jgill

(1eg) If a theory explains an observation, then the theory is evidenced. — Hallucinogen

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:

unenlightened

Well if "God did it" explains O relative to other members of T, it would seem "God did it" is evidenced relative to the others. — Hallucinogen

And that doesn't trouble you at all?

I have another theory: — "unenlightened did it".

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: — jgill

Nay, it is unenlightened, playing with his chalk.

Hallucinogen

I have another theory: — "unenlightened did it". — unenlightened

Changing the semantics doesn't change the validity of the argument.

AmadeusD

validity of the argument. — Hallucinogen

Validity doesn't have much of a relationship with truth.

unenlightened

Changing the semantics doesn't change the validity of the argument. — Hallucinogen

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:

If a theory explains an observation, then the theory is evidenced. — Hallucinogen

Hallucinogen

But since unenlightened is not God, there is a contradiction. — unenlightened

You didn't say unenlightened isn't God, before. As far as I could see, you only changed one word to another.

If everything is evidence that God did it, then everything is evidence that unenlightened did it. — 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.

Hallucinogen

Validity doesn't have much of a relationship with truth. — AmadeusD

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.

AmadeusD

Validity is the relationship a true premise has with a true conclusion — Hallucinogen

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).

Hallucinogen

That's soundness — AmadeusD

No, soundness is the truth of the premises, not the relationship it has to the conclusion.

Validity is mere formal agreement between premises and conclusion. — 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.

If your premises are empirically wrong, the argument is unsound — AmadeusD

Correct, so your first sentence was false. Soundness isn't a relationship between premise and conclusion.

AmadeusD

↪Hallucinogen

to be brief: no. What I said was correct. Soundness is a relationship between true premises and a valid conclusion. A true premise with a false conclusion is not sound as this applies to the whole argument, not the premise. It is relational.
Onward…

unenlightened

You didn't say unenlightened isn't God, before. — Hallucinogen

Do not attempt to argue with Me, worm. Cower in fear of My wrath.

Hallucinogen

Soundness is a relationship between true premises and a valid conclusion. — AmadeusD

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.

A true premise with a false conclusion is not sound — AmadeusD

Because it isn't valid.

Hallucinogen

Do not attempt to argue with Me, worm. Cower in fear of My wrath. — unenlightened

But since unenlightened is not God — unenlightened

unenlightened

↪Hallucinogen

Have it which way you want, dude. Look at the evidence, form a theory.

Hallucinogen

↪unenlightened

Consistency with reality is a form of evidence, so if one theory is more consistent than others, that serves as evidence for that theory.

tim wood

↪Hallucinogen

Your language has no bones in it; thus like a sponge you can squeeze it into any queer shape you like. But stop squeezing and it will lose that shape. So as a toy maybe fun to play with but as structure, lacking any structural integrity, useless - and there are things that are more fun to play with.

AmadeusD

Because it isn't valid. — Hallucinogen

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.

Hallucinogen

False.
Your premises can be entirely false — AmadeusD

Why are you bringing up false premises?
What you're responding to is my response to this comment:

A true premise with a false conclusion is not sound — AmadeusD

I'm going on the basis of this:

Soundness: An argument is sound if it meets these two criteria: (1) It is valid. (2) Its premises are true. — colorado.edu

What I am saying is that sound arguments are a subset of valid arguments.

The addition of the premises being true creates soundness. — 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

Validity doesn't have much of a relationship with truth. — AmadeusD

ought to have been was that validity is a requirement for soundness.

AmadeusD

↪Hallucinogen

It seems you're claiming that you cannot have a valid argument without true premises. That's is untrue. If i've got that wrong, apologies.

where one has false premises validly leading to a "supported" conclusion. — Hallucinogen

I have explained this one. To reiterate:

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). — 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.

Lionino

If a discussion revolves around a piece of information that is easily understandable and available online, both sides lost the debate before it even started.

Hallucinogen

It seems you're claiming that you cannot have a valid argument without true premises. — AmadeusD

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:

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. — Hallucinogen

What I am saying is that sound arguments are a subset of valid arguments. — Hallucinogen

This is why I said this :

A true premise with a false conclusion is not sound — AmadeusD

Because it isn't valid. — 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:

Your premises can be entirely false — AmadeusD

And I got lost because your answer was no longer talking about a true premise.

If your premises are empirically wrong, the argument is unsound, but can be considered valid — 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.

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. — 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.

AmadeusD

↪Hallucinogen

Right right, yes you've adequately cleared up the confusion there.

If your premises are true, you can only have a valid argument be sound, that's right.

If a discussion revolves around a piece of information that is easily understandable and available online, both sides lost the debate before it even started. — Lionino

Tell that to the Lounge.

Is this argument (about theories, evidence and observations) valid?

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