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| I finally lead with a photo of this textbook. |
Brought to you by the letter 'R'
'R' quite convenient...
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy).
The review 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
# = Higher in pitch
Previously
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).
This book review of sorts, since 2016, has now advanced to Chapter X: Abstraction and Interpretation. Philosopher Langer explains that logic is the study of forms and these forms are derived within systems from common human experiences, reality and life. (240). This is done by abstraction. (240).
She further explains that the science of logic is a continued progression from the concrete to the abstract. (240). That would be concrete ideas and things to abstract symbolic logic.
'From contents with certain forms to those forms without contents, from instances to kinds, from examples to concepts.' (240).
Langer explains that the first step is to the replacement of individual elements by formalized elements of variable meaning. (240). These are formalized elements, as in symbols within symbolic logic. The meaning of these elements is 'presently fixed.' (240). Not to be interpreted by their original terms. (240). Langer states that the symbolic logic has them interpreted in 'an entirely new way.' (240).
From Langer's explanation, what the symbolic logic provides is through quantifiers, are the old elements (which set meanings in contexts, my add), by new terms, which are general terms. (240). Symbolic logic provides a degree of formation from specific elements to quantified variables that are general terms. (240).
August 9, 2020
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).
Practical philosophy
I have noted within the review series that it is significant academic work to make Langer's complex, technical, textbook, practical. In reality, propositions, premises and conclusions will be far more presented in written language as opposed to symbolic logic. Regardless of the format presentations should be logical and reasoned for accuracy.
Perhaps the comparison of reflexive and non-reflexive terms demonstrates the requirement for the sake of reason, of considering possibilities, as in counter propositions that are in disagreement with propositions held to. This requirement was a definitive and definite aspect of my British MPhil/PhD works, even more so that my previous Canadian work.
Considering contrasting statements and arguments does not necessarily lead to a change of view, but it may lead to a superior, wider, deeper understanding of subjects under review.
Moderate left meets moderate right
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| Zoom last night. The moderate left meets the moderate right. British Columbia. Florida, Norway... |
People will be ticked
The losing Toronto Maple Leafs, at this point tonight, might join the Edmonton Oilers, Winnipeg Jets, Pittsburgh Penguins and four other teams with a reasonable possibility of winning the first pick overall in the next entry draft. The winner will be announced Monday. The pick is expected to be Alexis Lafrenière, a possible all-star. If the Leafs lose tonight, the result will offend many Leaf/Oiler fans and non-fans, alike.
