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To me, deductive logic is essential not just for distinguishing between foundational and coherent knowledge, but to any sort of reasoning. For instance if you want to really figure out (reason) whether a certain proposition (or a piece of knowledge) coheres with your previous beliefs, you have to do some sort of deductive, abductive, inductive reasoning or a combination of two or more. For instance, let's say we want to evaluate the truthfulness (truth value or whatever else) of a proposition :

"High scorers on the SAT are intelligent"

  1. The SAT measures intelligence
  2. (Derived from #1) The SAT is devised such that it measures what it intends to measure
  3. (Derived from #1) A high score on the SAT indicate a high level of intelligence

#2 and #3, while not explicitly in the form of

  1. "Socrates is a man"
  2. "All men are mortal"
  3. "Socrates is mortal"

they still rely on #1 to have any truth value, and are hence part of deductive logic. So one must practice deductive logic in order to accept or reject a particular statement.

(Addition) I looked up "deductive reasoning" just to be sure, and the above (Derived from #1)s are examples of modus ponens; i.e. classic deductive reasoning. Then what is the purpose of distinguishing coherentism from foundationalism if they are so intertwined in actual use?

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  • Coherentism explicitly endorses the use of deductive logic, coherence essentially means deductive consistency, or perhaps some informal version of it. The difference with foundationalism is not the absence of deductions but rather the absence of a privileged set of "fundamental beliefs" that are treated as axioms. Some beliefs may be more "entrenched" than others, but none are, in principle, immune to revision, see SEP, Coherentism Versus Foundationalism.
    – Conifold
    Commented Aug 27, 2020 at 20:22

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