FIRST DAY OF A LOGIC COURSE
(from comments I made on a paper) (Purpose is to illustrate the difference between how P describes logic and how the present academy explains it.)
[A] few suggestions, that give the students context where that context limits the majority of student errors not only in class but throughout life.
1) The sciences consist of the formal sciences we call the Logics, the Physical Sciences, and Social Sciences(psychology, and sociology).
- Formal Sciencies (Logics) > Physical Sciences > Human Sciences
2) Most of us are familiar of the logic of positions we call mathematics and its application to measurements; and the logic of operations, we call algorithms, programming, procedures, or the logic of sequential actions in time, and in addition, we use the general term ‘logic’ of the logic of sets applied more broadly language; So within the formal sciences that we call the logics, we use a least the logic of one property in measurement, the logic of more properties in sequences of operations, and the logic of speech using words that are unlimited, in a spectrum of increasing complexity.
- One Dimension: math (Positional Logic) > N-Limited Dimensions (Operational Logic) > N-Unlimited Dimensions (Set Logic).
3) These methodologies in formal science are possible because of the human logical facility. The human logical facility consists of neurological tests of the spectrum of relations that are constant, inconstant, contingent, potential, contradictory, and non-sensical relations that are perceivable by the spectrum of physical sensation, intuitionistic auto-association we call perception, and the sequence of thought we call dreaming, daydreaming thinking, reasoning, rationalism (“logic”), calculation (transformation of inputs into outputs), and computation.
- Human Faculties ( Physical, Intuitionistic, and Rational) > Human Logical Facility > The Sciences > Formal Sciences > Tests of {constant, inconstant, contingent, potential, contradictory, and non-sensical} relations > Using {hinking, reasoning, rationalism (“logic”), calculation (transformation of inputs into outputs), and computation.}
4) While the human brain operates in massively parallel competition for coherence between past present and future, describing our internal thoughts requires serial communication by signs or speech. When we serially communicate using signs or speech, we depend on rules we call ‘grammars’.
Humans evolved not only the logical facility by massive parallel competition, we evolved a grammar facility to organize and communicate all or part of the experience that results. This grammar vacility and what we call rules of grammar, consists of rules of continuous recursive disambiguation. We use serial language, grammatical rules of continuous recursive disambiguation, to suggest meaning to others, by causing them to continuously recursively predict what we experience (mean). The audience uses those same rules of grammar to predict what the speaker intends to convey. The audience then conveys understanding, and either asks for, or is given, further disambiguation, until both parties satisfy the need (demand) for disambiguity.
In the discipline of logic we refer to this more general term prediction as inference. And the discipline of logic as rules of inference. In this sense, with this understanding, the discipline of logic is either an extension of grammar or grammar is an extension of logic – and until the 20th century truthful speech, grammar, logic, and rhetoric (meaning argument) were taught as a continuum. (And, aside from the intentional removal of adversarialism from the curriculum in order to allow girls to compete, there is very likely a political reason you were not taught grammar, logic, and rhetoric.)
- Human Logic Facility (parallel comparison) > Human Grammar Facility (sequential disambiguation) > Grammar(organization) > Logic(tests of consistency) > Rhetoric (argument).
5) Inferences (predictions) are steps in reasoning, beginning with premises and ending with conclusions. We divide inference into the sequence: deduction, induction, and abduction. Deduction is inference that predict logical conclusions from premises known or assumed to be true. Induction is the inference (prediction) from particular premises to a universal conclusion. Abduction is the inference (prediction) to the best explanation. But that spectrum of deduction, induction, and abduction describes only the sufficiency of information we have to work with, as three points on a continuum.
- Premises > Constant Relations > Inferences (Prediction) > Conclusion
6) In this course, we are largely interested in language and we the logic of sets, with the laws of valid (not false) inference (prediction), under the general label we conventionally refer to as “logic”, using that human faculty of reason we call “rationalism”(limiting our reasoning to rules of logic).
- Logical Facility > Grammar(disambiguation) > Sets of Properties > Rules of Inference (Prediction) => “Logic”
7) We apply the logic of sets to language to test the truth, falsehood, or undecidability of propositions. When we say a statement or set of statements is false, they are inconsistent or contradictory. When we say a statement or set of statements is true, we mean the set of properties is internally consistent.
- Degree of Decidability: Undecidable > Truth Candidate > False.
When we say a statement is or set of statements is contingent, it is dependent on information external to the statement. And when we say that a statement is undecidable, the properties are insufficient to determine consistency – which means ambiguous.
- Relations: Consistent > Contingent > Inconsistent > Contradictory
8) When we say a statement or set of statements is true we mean it satisfies both the demand for disambiguity, and the demand for infallibility in the context – meaning it’s coherent with and consistent and sufficient for infallibility within the broader context.
- True: Context > Demand for Infallibility > Coherent, Consistent, and Sufficient
9) The spectrum of truth claims ranges from tautological – meaningless, to ideal – meaning the testimony we would give if we were omniscient; to testifiable – meaning that one has done due diligence against ignorance, error, bias, and deceit; to honest – meaning the promise that one does not deceive, obscure, load, frame, or fictionalize.
- True: Tautlogical > Ideal > Real (Testifiable) > Honesty
10) And people frequently make truth claims using a spectrum of paradigms using analogies to experience from the most general to the most specific:
- Theological (allegorical, supernatural)
- Fictional-Mythical (Allegorical natural-supernormal)
- Psychological (and Moral)
- Rational (Kantian)
- Historical (analogical)
- Descriptive (ordinary language).
- Empirical (observable)
- Ratio-empirical ( scientific )
- Operational (testifiable, testimony)
11) Despite the efforts of hundreds if not thousands of great thinkers, the result of the 19th and 20th-century research is that set logic applied to human speech is largely a falsificationary rather than justificationary system of thought. In other words, we tend to prove very little of consequence, but we falsify the infinity of falsehoods by ignorance, error, bias, and deceit. And this is the principle function of study of the logics: to improve our ability to identify ignorance, error, bias, and deceit, and to seek sufficiently unambiguous, sufficiently infallible, sufficiently testifiable knowledge despite the many human failings.
Empistemology: Auto Association( Possibility: Idea ) > Justification (Explanation: Hypothesis) > Falsification (Survival: Theory) > Truth Candidate
12) So this is the context of logic that we will cover in this course, and the primary benefit to you, in your life, will be the advantage of freedom from falsehoods by ignorance, error, bias and deceit.
In my understanding, logic, as it is taught in university as the logic of sets and inference, is as archaic as scriptural interpretation, textual interpretation, and legal interpretation that it evolved from. And that between mathematics and set logic we are better off studying operational logic since it is operational logic that eliminates the limits of set logic.