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I can't believe I am asking this at this stage - I am deep into Chapter 3 of Testmasters and I should have this down pat by now, but I think I am having a brain freeze moment....

If you have a compound conditional statement - a sufficient with 2 necessary statements, and one necessary is missing, is the sufficient still true?

Example:
A scientific theory is a good theory if it satisfies 2 requirements - It must describe a large class of observations in a simple model with only a few elements, and it must make definite predictions about the results of future observations.

So..
Good Theory (GT)
Observations in Simple Model with only a few elements (SM)
Definite Predictions ... (P)

GT -> SM and P
(~P or ~SM -> GT)
Right? So far, so good.

Then Aristotle is missing one of those - he only has the SM. He didn't make predictions.

So, is Aristotle's theory still a GT? I have no idea why I am stuck on this. It isn't even what the question asks, and I actually got the question right...but I noticed that I forgot something about compound statements while diagramming this.

thanks!

The contrapositive of the statement GT-->SM + P would be ~SM or ~P--> ~GT. The neccesary conditions are negated and the AND becomes OR so ~SM or ~P is now the sufficient condition. So if Aristotle's is missing just one, that's sufficient to say it must not be a good theory.

Not sure if that answers your question.

Yes it does BV.
Thank you - the answer is right there with the and/or, but I kind of needed a nudge.
thanks!

I think you also made a mistake in what you say after "Example":

You mean that a scientific theory is good ONLY IF it satisfies two requirements...

Just wanted to warn you -- you need to be very careful about distinguishing between "IF" and "ONLY IF".

Good luck!

fvigaud wrote:I can't believe I am asking this at this stage - I am deep into Chapter 3 of Testmasters and I should have this down pat by now, but I think I am having a brain freeze moment....

If you have a compound conditional statement - a sufficient with 2 necessary statements, and one necessary is missing, is the sufficient still true?

Example:
A scientific theory is a good theory if it satisfies 2 requirements - It must describe a large class of observations in a simple model with only a few elements, and it must make definite predictions about the results of future observations.

So..
Good Theory (GT)
Observations in Simple Model with only a few elements (SM)
Definite Predictions ... (P)

GT -> SM and P
(~P or ~SM -> GT)
Right? So far, so good.

Then Aristotle is missing one of those - he only has the SM. He didn't make predictions.

So, is Aristotle's theory still a GT? I have no idea why I am stuck on this. It isn't even what the question asks, and I actually got the question right...but I noticed that I forgot something about compound statements while diagramming this.

thanks!