having innate knowledge of the "laws of thought", Russell renames this sort of knowledge a priori. And while Russell agrees with the empiricists that "Nothing can be known to exist except by the help of experience,", he also agrees with the rationalists that some knowledge is a priori, specifically "the propositions of logic and pure mathematics, as well as the fundamental propositions of ethics". This question of how such a priori knowledge can exist directs Russell to an investigation into the philosophy of Immanuel Kant, which after careful consideration he rejects as follows: "... there is one main objection which seems fatal to any attempt to deal with the problem of a priori knowledge by his method. The thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic. ... Thus Kant's solution unduly limits the scope of a priori propositions, in addition to failing in the attempt at explaining their certainty". His objections to Kant then leads Russell to accept the 'theory of ideas' of Plato, "in my opinion ... one of the most successful attempts hitherto made."; he asserts that " ... we must examine our knowledge of universals ... where we shall find that [this consideration] solves the problem of a priori knowledge.". Principia Mathematica (Part I: 1910 first edition, 1927 2nd edition) Unfortunately, Russell's "Problems" does not offer an example of a "minimum set" of principles that would apply to human reasoning, both inductive and deductive. But PM does at least provide an example set (but not the minimum; see Post below) that is sufficient for deductive reasoning by means of the propositional calculus (as opposed to reasoning by means of the more-complicated predicate calculus)—a total of 8 principles at the start of "Part I: Mathematical Logic". Each of the formulas :❋1.2 to :❋1.6 is a tautology (true no matter what the truth-value of p, q, r ... is). What is missing in PM’s treatment is a formal rule of substitution; in his 1921 PhD thesis Emil Post fixes this deficiency (see Post below). In what follows the formulas are written in a more modern format than that used in PM; the names are given in PM). ❋1.1 Anything implied by a true elementary proposition is true. ❋1.2 Principle of Tautology: (p ⋁ p) ⊃ p ❋1.3 Principle of [logical] Addition: q ⊃ (p ⋁ q) ❋1.4 Principle of