Rules of Thinking, The: A Personal Code To Think Yourself Smarter, Wiser And Happier

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Dasgupta, Surendranath (1991), A History of Indian Philosophy, Motilal Banarsidass, p.110, ISBN 81-208-0415-5 Arthur Schopenhauer, The World as Will and Representation, Volume 2, Dover Publications, Mineola, New York, 1966, ISBN 0-486-21762-0 That is to say, if we wish to prove that something of which we have no direct experience exists, we must have among our premises the existence of one or more things of which we have direct experience"; Russell 1912, 1967:75 Figure 3.10 visually depicts the MECE and NONG requirement filled (A) and not filled (B and C). MECE and NONG mean the same thing, so you can use whichever one makes more sense to you. No overlaps and mutually exclusive mean that the distinctions you make in a system are not overlapping. They are in fact distinct. No gaps and collectively exhaustive mean that the system of distinctions you have assembled to describe the problem is sufficient and complete and that everything that needs to be considered has been. MECE and NONG establish what is inside and outside the boundary of any system. What is important to understand is that while MECE and NONG help you to consider the system of distinctions that you are using, all of the items inside your system of distinctions is also a thing-other distinction. Distinctions are occurring at different scales with regard to the smallest ideas and things as well as the largest ideas and things. So you can see that in (A) there are distinctions occurring wherever there are red lines, which includes not only the distinctions between the parts inside the system, but also the distinction between what lies inside and outside of the system (not-S). To review, DSRP rules operate on information simultaneously and a single bit of information can be a distinction, system, relationship, and/or perspective. Imagine, for example, a systemic diagram representing some set of ideas or a network as in the thought bubble in Figure 3.5. First, notice that each bit of information in the network is distinct from other bits (cards). Note that when a relationship is distinguished, a card exists in the center of the line indicating not only that there is a relationship, but also explicating what it is. Some of the relationships (lines) have not yet become distinctions (i.e., they are currently undefined). Some of the cards are also whole systems because they contain parts, whereas other cards are not yet whole systems (perhaps because we haven't explored them yet). And some but not all of the cards are acting as perspectives, viewing or experiencing the system in different ways from each other. DISTINCTIONS RULE: Any Idea or Thing Can Be Distinguished from the Other Ideas or Things It Is with

Theaetetus, by Plato". The University of Adelaide Library. November 10, 2012. Archived from the original on 16 January 2014 . Retrieved 14 January 2014. The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated into an algebraic representation of his "laws of the mind", honed over the years into modern Boolean algebra.Russell sums up these principles with "This completes the list of primitive propositions required for the theory of deduction as applied to elementary propositions" (PM:97). 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; [34] 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). He does not call his inference principle modus ponens, but his formal, symbolic expression of it in PM (2nd edition 1927) is that of modus ponens; modern logic calls this a "rule" as opposed to a "law". [23] In the quotation that follows, the symbol "⊦" is the "assertion-sign" (cf PM:92); "⊦" means "it is true that", therefore "⊦p" where "p" is "the sun is rising" means "it is true that the sun is rising", alternately "The statement 'The sun is rising' is true". The "implication" symbol "⊃" is commonly read "if p then q", or "p implies q" (cf PM:7). Embedded in this notion of "implication" are two "primitive ideas", "the Contradictory Function" (symbolized by NOT, "~") and "the Logical Sum or Disjunction" (symbolized by OR, "⋁"); these appear as "primitive propositions" ❋1.7 and ❋1.71 in PM (PM:97). With these two "primitive propositions" Russell defines "p ⊃ q" to have the formal logical equivalence "NOT-p OR q" symbolized by "~p ⋁ q": By 1912 Russell in his "Problems" pays close attention to "induction" (inductive reasoning) as well as "deduction" (inference), both of which represent just two examples of "self-evident logical principles" that include the "Laws of Thought." [4] Distinctions Rule: Any idea or thing can be distinguished from the other ideas or things it is with;

Induction principle: Russell devotes a chapter to his "induction principle". He describes it as coming in two parts: firstly, as a repeated collection of evidence (with no failures of association known) and therefore increasing probability that whenever A happens B follows; secondly, in a fresh instance when indeed A happens, B will indeed follow: i.e. "a sufficient number of cases of association will make the probability of a fresh association nearly a certainty, and will make it approach certainty without limit." [15]George Spencer-Brown in his 1969 " Laws of Form" (LoF) begins by first taking as given that "we cannot make an indication without drawing a distinction". This, therefore, presupposes the law of excluded middle. He then goes on to define two axioms, which describe how distinctions (a "boundary") and indications (a "call") work: Lastly is a notion of "identity" symbolized by "=". This allows for two axioms: (axiom 1): equals added to equals results in equals, (axiom 2): equals subtracted from equals results in equals. Logical OR: Boole defines the "collecting of parts into a whole or separate a whole into its parts" (Boole 1854:32). Here the connective "and" is used disjunctively, as is "or"; he presents a commutative law (3) and a distributive law (4) for the notion of "collecting". The notion of separating a part from the whole he symbolizes with the "-" operation; he defines a commutative (5) and distributive law (6) for this notion:

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". [32]Later, in 1844, Schopenhauer claimed that the four laws of thought could be reduced to two. In the ninth chapter of the second volume of The World as Will and Representation, he wrote: As part of his PhD thesis "Introduction to a general theory of elementary propositions" Emil Post proved "the system of elementary propositions of Principia [PM]" i.e. its "propositional calculus" [36] described by PM's first 8 "primitive propositions" to be consistent. The definition of "consistent" is this: that by means of the deductive "system" at hand (its stated axioms, laws, rules) it is impossible to derive (display) both a formula S and its contradictory ~S (i.e. its logical negation) (Nagel and Newman 1958:50). To demonstrate this formally, Post had to add a primitive proposition to the 8 primitive propositions of PM, a "rule" that specified the notion of "substitution" that was missing in the original PM of 1910. [37] When we take a CAS perspective on systems thinking, we ask ourselves: what are its simple underlying rules? The simple rules are based on distinctions (D), systems (S), relationships (R), and perspectives (P). That is, each bit of information can distinguish itself from other bits, each bit can contain other bits or be part of a larger bit, each bit can relate to other bits of information, and each bit of information can be looked at from the perspective of another bit of information and can also be a perspective on any other bit. DSRP Rules Occur Simultaneously Boole begins his chapter I "Nature and design of this Work" with a discussion of what characteristic distinguishes, generally, "laws of the mind" from "laws of nature":