If I want to answer negatively this question,
Is science any thing other than logic applied to the manifested existences?
Should I say I think not or I think no?
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Is science any thing other than logic applied to the manifested existences?
Should I say I think not or I think no?
I think not is the correct choice of the two you propose.
I think no is ungrammatical. You might be able to write I think--no where the double hyphens represent an em-dash which itself represents a speaker pausing to think and change what he was going to say.
You might be able to use something like this:
"Is science any thing other than logic applied to the manifested existences?
"I think no, it is exactly as described."
But that's part of a larger construction.
No might be a simpler answer if you disagree.
I don't think so might be a little more gentle and could be followed by ...because... and then you list reasons why you disagree.
I think not is tending towards a formulaic phrase and tends to be used as a strong negation, possibly because in current English we don't often use such old fashioned constructions with the negating adverb at the end of the sentence. The most notable exception is possibly when following did as in I did not. Otherwise you sound like you're trying to imitate English from a few hundred years ago and that pattern sounds odd today.