 Given that the proof of Frege’s Theorem makes no appeal to Basic Law V, some philosophers have argued Frege’s best strategy for producing an epistemologically-justified foundation for arithmetic is to replace the primitive term \(\epsilon F\) with the primitive term \(\#F\), replace Basic Law V with Hume’s Principle, and argue that Hume’s Principle is an analytic principle of  logic.[17]  However, we have just seen one reason why such a strategy does not suffice. The claim that Hume’s Principle is an analytic principle of logic is subject to the same problem just posed for Basic Law V. A reason must be given as to why the claim: