Be like Bill of the human being class
Photo: Buenos-Aires-homes-1-of-1 gateway to south america 2019 LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy).This book review of sorts, since 2016, continues
Key symbols
≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
. = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives)
x = variable
. = Conjunction meaning And
0 = Null class
cls = Class
int = Interpretation
∧ = Logical conjunction
From the previous related entry
Properties of Relations is section 2 in Chapter X: Abstraction and Interpretation.
Philosopher, Langer explains that with a general or abstract proposition, it is stated 'there is at least one relation, R having certain properties; and the form of the proposition to be expressive of those properties. Relations which have all their logical properties in common are of the same type, and are possible values of the same variable R.' (246).
Langer explains that the most fundamental characteristic of a relation is its degree. (246). Forming dyads, triads, tetrrads, etc.. (246). Sets of 2, 3, 4, etc..my add. A symbol of R2 (246) is also in the form of a R b. (246). The symbolic logic symbols of 'a' and 'b' here are considered identical. (246). These are known as reflexive. (246).
Taking one of the examples:
(a) . ˜ (a nt a) (247).
(A) therefore not (house 'a' is north of house 'a')
In other words, house 'a' is not north of itself.
A non-reflexive symbol possibly, but not necessarily, combines a term with itself. (257).
Langer example:
(∃a) . a likes a (247).
(A exists) therefore 'a' likes 'a'
(∃a) . ˜ (a likes a) (247)
(A exists) therefore 'a' does not like 'a'
Langer implies that a creature may or may not like itself. (247).
March 18 2021
Cited
'A transitive relation is such that if it relates two terms to a mean (average my add), it relates the extremes to each other. The significance of this trait lies in the fact that it allows us to pass, by the agency of a mean term, to more and more terms of which is thus related to every one of the foregoing elements. This creates a chain of related terms; in ordering a whole universe of elements, such a relation which transfers itself from couple to couple when new terms are added one at a time, is of inestimable value (too great to accurately calculate in value, my add). This is the type of relation by virtue of which we reason from two premises, united by a mean or "middle terms," to a conclusion''. (248).
I will not use Langer's now non-politically correct and offensive to many in 2021, language, that was used commonly in the 1950's and 1960's. But the following is based on Langer on page 248.
All Canadians are human beings
All human beings are mortals
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Therefore all Canadians are mortals
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Note that academic arguments do not have to be syllogistic to be logically valid and reasonable.
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Therefore < = Is included
< Canadians, human beings, mortals (based on Langer 248).
They are taken as three classes as transitive, but if there was no relation between the classes it would be intransitive. (248). Back on page 115, Langer writes that a class has members that have certain character. (115).
Related equations
Canadians=c
Human beings=h
Mortals=m
(∃c) < (∃h) ∴ (∃m)
Canadians exist, is included in human beings exist, therefore mortals exist
(∃c) ⊨ (∃h) = (∃!m)
Canadians exist, entails human beings exist, equals mortals exist
Practical philosophy
The use of a class (term) and related classes (terms) as transitive can assist in the development of valid, logical, reasonable, premises and conclusions (arguments).
BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.
PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
