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

Hallucinogen August 02, 2024 at 21:27 6325 views 33 comments
(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.

Comments (33)

unenlightened August 03, 2024 at 17:47 #922644
Let T = "God did it."

Everything that happens is evidence for God.

Hmm.
Lionino August 03, 2024 at 18:00 #922646
Is this supposed to be defending this obviously wrong statement from the previous thread?

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


Edit:
It is.
Hallucinogen August 03, 2024 at 18:33 #922664
Reply to Lionino Why would that be false?
Hallucinogen August 03, 2024 at 18:35 #922665
Reply to 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.
Deleted User August 03, 2024 at 18:54 #922669
This user has been deleted and all their posts removed.
Lionino August 03, 2024 at 19:04 #922674
Quoting Hallucinogen
Why would that be false?


So the answer is yes. :yawn:

Reply to tim wood He won't give in.
Hallucinogen August 03, 2024 at 19:13 #922677
Quoting tim wood
You have a whole lot of work to do on - at least - defining your terms and how they relate to each other.


It seems to me like you bring up this red-herring as a way of avoiding the OP of this thread.
Deleted User August 03, 2024 at 19:19 #922678
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jgill August 03, 2024 at 22:12 #922698
Quoting Hallucinogen
(1eg) If a theory explains an observation, then the theory is evidenced.


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 August 04, 2024 at 07:12 #922775
Quoting Hallucinogen
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.


And that doesn't trouble you at all?

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

Quoting jgill
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:


Nay, it is unenlightened, playing with his chalk.
Hallucinogen August 04, 2024 at 23:14 #922912
Quoting unenlightened
I have another theory: — "unenlightened did it".


Changing the semantics doesn't change the validity of the argument.
AmadeusD August 04, 2024 at 23:48 #922921
Quoting Hallucinogen
validity of the argument.


Validity doesn't have much of a relationship with truth.
unenlightened August 05, 2024 at 05:48 #922997
Quoting Hallucinogen
Changing the semantics doesn't change the validity of the argument.


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



Hallucinogen August 06, 2024 at 04:30 #923224
Quoting unenlightened
But since unenlightened is not God, there is a contradiction.


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

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


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 August 06, 2024 at 04:31 #923225
Quoting AmadeusD
Validity doesn't have much of a relationship with truth.


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 August 06, 2024 at 04:38 #923227
Quoting Hallucinogen
Validity is the relationship a true premise has with a true conclusion


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 August 06, 2024 at 04:51 #923228
Quoting AmadeusD
That's soundness


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

Quoting AmadeusD
Validity is mere formal agreement between premises and conclusion.


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
If your premises are empirically wrong, the argument is unsound


Correct, so your first sentence was false. Soundness isn't a relationship between premise and conclusion.
AmadeusD August 06, 2024 at 05:33 #923233
Reply to 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 August 06, 2024 at 09:36 #923251
Quoting Hallucinogen
You didn't say unenlightened isn't God, before.


Do not attempt to argue with Me, worm. Cower in fear of My wrath.
Hallucinogen August 06, 2024 at 16:46 #923327
Quoting AmadeusD
Soundness is a relationship between true premises and a valid conclusion.


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
A true premise with a false conclusion is not sound


Because it isn't valid.
Hallucinogen August 06, 2024 at 16:47 #923329
Quoting unenlightened
Do not attempt to argue with Me, worm. Cower in fear of My wrath.


Quoting unenlightened
But since unenlightened is not God


unenlightened August 06, 2024 at 16:51 #923330
Reply to Hallucinogen Have it which way you want, dude. Look at the evidence, form a theory.
Hallucinogen August 06, 2024 at 17:32 #923337
Reply to 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.
Deleted User August 06, 2024 at 18:53 #923348
This user has been deleted and all their posts removed.
AmadeusD August 06, 2024 at 22:14 #923389
Quoting Hallucinogen
Because it isn't valid.


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 August 07, 2024 at 16:01 #923575
Quoting AmadeusD
False.
Your premises can be entirely false


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

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


I'm going on the basis of this:
Quoting colorado.edu
Soundness: An argument is sound if it meets these two criteria: (1) It is valid. (2) Its premises are true.


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

Quoting AmadeusD
The addition of the premises being true creates soundness.


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


ought to have been was that validity is a requirement for soundness.
AmadeusD August 07, 2024 at 20:58 #923616
Reply to 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.

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


I have explained this one. To reiterate:

Quoting AmadeusD
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).


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 August 07, 2024 at 23:07 #923647
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 August 08, 2024 at 01:29 #923673
Quoting AmadeusD
It seems you're claiming that you cannot have a valid argument without true premises.


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


This is why I said this :
Quoting Hallucinogen
A true premise with a false conclusion is not sound — AmadeusD

Because it isn't valid.


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
Your premises can be entirely false


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

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


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
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.


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 August 08, 2024 at 01:32 #923674
Reply to 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.

Quoting 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.


Tell that to the Lounge.
night912 August 08, 2024 at 15:33 #923784
Sound premise + valid argument = sound conclusion.

- Reply to Hallucinogen

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
Lionino August 08, 2024 at 22:30 #923851
Quoting AmadeusD
Tell that to the Lounge.


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.
AmadeusD August 08, 2024 at 23:57 #923878
Reply to Lionino LMAO that may be a good move