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I'm looking for an expression to say that an idea has no firm foundation, that is, the premises aren't quite right enough. Also, it would be good to know the contrary as well, an expression to express an idea that is one hundred per cent right.

I would use the expression in a sentence like this:

Socrates didn't expound ideas that don't have a firm foundation. Socrates's ideas always have a firm foundation.

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    The single word groundless might do. The contrary could be irrefutable. Dec 9 '20 at 11:38
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    By the way, 'expose' is a false friend here. We don't use it like that in English. The relevant cognate is 'expound', but that is quite rare.
    – legatrix
    Dec 9 '20 at 11:53
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'Firm foundation' is already pretty good. There are lots of related expressions. If I was writing your sentences I might say the following (note that they do not all have the same, or even very similar, meanings):

  • Socrates gave only arguments which were thoroughly grounded
  • Socrates only presented arguments grounded in solid principles
  • Socrates always gave clear, well-grounded arguments
  • Socrates always began from explicit premises and built arguments which followed from those premises
  • Socrates always produced logically flawless arguments, starting from clear premises

And the contrary:

  • Socrates' arguments lacked firm logical grounding
  • Socrates' arguments proceeded inconsistently from their premises
  • Socrates' premises were faulty, and so his arguments were invalid

Again, these are just ideas. The sentences are not intended to be interchangeable.

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