Slight edits for an entry on academia.edu for April 7, 2023
The continuation of text review:
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
--
The Truth of the Proposition
Philosopher Langer writes that in the book, so far, nothing had been mentioned in regard to the truth of a proposition. (188). An implied proposition is true if all the premises are true. (188). The implied proposition could also be defined as the conclusion. If the premises are false, she opines that the proposition may or may not be true. (188). There can be false premises and a true conclusion for a valid argument, but there cannot be true premise (s) and false conclusion with validity. Validity is a set of premises supporting a conclusion. Technically in logic the premises do not have to be true, simply valid. Elements (1997: 33).
Therefore a valid deductive argument can have
False premises and a true conclusion (FT)
False premises and a false conclusion (FF)
True premises and a true conclusion (TT)
However
True premises and a false conclusion (TF) is invalid.
Valid arguments with all true premises are called sound arguments. A sound argument also has a true conclusion.
Langer explains
Brutus killed Caesar ⊃ Caesar is dead. (188). (⊃ is means the same as).
Since the implied premise is true the proposition is also true (consequent). (188). If Brutus killed Caesar ˜ ⊃ Caesar is dead (my equation using not the same), this would not change the implication that Caesar was dead. (188). Brutus did not kill Caesar; Caesar died in another way.
---
Logic versus Truth
February 13, 2018
Importantly, philosopher Langer explains that there is no guarantee that there is truth in a logical system. (189). Logic does not necessarily promote a fact, rather 'it stands for the conceptual possibility of a system'. (189). Logic documents with the deduction of premises. It stands for 'the consistency of all propositions'. (189). It is standing for logical validity. (189), not factual certainty or truth. (189).
This is standard from philosophy, logic, texts. Certainly not something Langer or I manufactured as original.
In many cases when a person states that a premise or argument is logical, the person means that it is true. But a premise or argument can be logical and false. Therefore, it would be more accurate in many cases to claim that a premise or argument is true and or reasonable.
L ˜ = T
Logic does not equal truth
L ˜ ⊃ T
Logic is not the sane as truth
BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)
The continuation of text review:
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
--
The Truth of the Proposition
Philosopher Langer writes that in the book, so far, nothing had been mentioned in regard to the truth of a proposition. (188). An implied proposition is true if all the premises are true. (188). The implied proposition could also be defined as the conclusion. If the premises are false, she opines that the proposition may or may not be true. (188). There can be false premises and a true conclusion for a valid argument, but there cannot be true premise (s) and false conclusion with validity. Validity is a set of premises supporting a conclusion. Technically in logic the premises do not have to be true, simply valid. Elements (1997: 33).
Therefore a valid deductive argument can have
False premises and a true conclusion (FT)
False premises and a false conclusion (FF)
True premises and a true conclusion (TT)
However
True premises and a false conclusion (TF) is invalid.
Valid arguments with all true premises are called sound arguments. A sound argument also has a true conclusion.
Langer explains
Brutus killed Caesar ⊃ Caesar is dead. (188). (⊃ is means the same as).
Since the implied premise is true the proposition is also true (consequent). (188). If Brutus killed Caesar ˜ ⊃ Caesar is dead (my equation using not the same), this would not change the implication that Caesar was dead. (188). Brutus did not kill Caesar; Caesar died in another way.
---
Logic versus Truth
February 13, 2018
Importantly, philosopher Langer explains that there is no guarantee that there is truth in a logical system. (189). Logic does not necessarily promote a fact, rather 'it stands for the conceptual possibility of a system'. (189). Logic documents with the deduction of premises. It stands for 'the consistency of all propositions'. (189). It is standing for logical validity. (189), not factual certainty or truth. (189).
This is standard from philosophy, logic, texts. Certainly not something Langer or I manufactured as original.
In many cases when a person states that a premise or argument is logical, the person means that it is true. But a premise or argument can be logical and false. Therefore, it would be more accurate in many cases to claim that a premise or argument is true and or reasonable.
L ˜ = T
Logic does not equal truth
L ˜ ⊃ T
Logic is not the sane as truth
BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press.
CONWAY DAVID A. AND RONALD MUNSON (1997) The Elements of Reasoning, Wadsworth Publishing Company, New York.
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
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.
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