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| Lampeter, Wales |
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
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White house versus black house
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).
Encyclopaedia Brittanica
Cited
Quantification, in logic, the attachment of signs of quantity to the predicate or subject of a proposition.
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Langer continues by explaining that it has been established in her text (and my reviews) that K =int as houses. (241). K (a, b, c, d...etc) is various types of houses. (241). At the same time, in her text (and my reviews) nt =interpretation as north of. (241).
It could be written that:
wh= White house
bh= Black house
wh ˜ ⊃ bh
The white house is not the same as the black house.
(wh) ˜ ⊃ (bh)
The white house is not the same as the black house.
(wh) . nt (bh)
The white house is therefore north of the black house.
(bh) ˜ nt (wh)
The black house is not north of the white house.
(bh) ˜ ⊨ (wh)
The black house does not entail the white house.
Practical philosophy
Ten Chapters and over four years into this textbook review:
Positive: Philosophically, the book assists the reader to better understand the technical differences between logic and truth, the logical and the true.
I now have a greater familiarity with the terms and symbols. I can decently read the equations in Langer's textbook, correctly. Potentially reading symbolic logic, more than the limited amount I read for my MPhil/Ph.D. work, in philosophical journals and books was a reason I bought the Langer textbook for review.
Negative: It is quite clear that most commonly for typical readers, academics, and most philosophers, written prose and standard language is generally a more clear, reasonable and proficient method for presenting concepts, premises and conclusions than is symbolic logic.
Langer states that the symbolic logic has them interpreted in 'an entirely new way.' (240).
Many times in everyday writing and in academia, explaining the concrete reasonably and in truth is more beneficial for most readers than creating an abstraction with its own internal rules that requires significant new learning from the reader. I reason that symbolic logic does have its merits at some technical points.
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| Laurel Bern photoshop via online websites. There is nothing politically intended by me as it just fits this section of the Langer text. |
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