Diction is the application of different words
Students of university must be ready for stimulating talk
than lecture. Brace yourself
‘There are
several levels to comprehending truth and falsehood, and individuals differ
vastly with respect to acceptance and rejection of them. The general rule, with
regards to the truth, is that the heart should be inclined towards Allah, His
commandments and the realities, while the rule with regards to falsehood, is
that the heart should be averse to things that are prohibited and related to
other than Allah, and the interior should be kept away from dirty and impure
carnal attachments.
A pious person
comprehends that falsehood weans a person away from realities and it shall
cease to exist, and it is only truth, which is deep-rooted and continues to
exist. Thus, one must adhere to the people of truth and stay away from the
people of falsehood.’
Creativity
is the different application of the same word
· Diction enables writer to define the
difference between two things through application of two different words. Creativity
enables writer to define the difference between two things through different
application of same word.
By Prof
Dr Sohail Ansari
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Validity
From
Wikipedia, the free encyclopedia
In logic, an argument is valid if and only if it takes a form that makes
it impossible for the premises to be true and the conclusion nevertheless to be
false.[1] It is not required that a valid argument
have premises that are actually true,[2] but to have premises that, if they were
true, would guarantee the truth of the argument's conclusion. A formula is valid if and only if it is true under every interpretation, and an argument form (or
schema) is valid if and only if every argument of that logical form is valid.
Arguments[edit]
An argument is valid if and only if the truth of
its premises entails the truth of its conclusion and each
step, sub-argument, or logical operation in the argument is valid. Under such
conditions it would be self-contradictory to affirm the premises and deny the
conclusion. The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding
conditional is a contradiction.
The conclusion is a logical consequence of its premises.
An argument that is not valid is said to be "invalid".
An example of a valid argument is given by the following
well-known syllogism:
All men are mortal.
Socrates is a man.
Therefore, Socrates is
mortal.
What makes this a valid argument is not that it has true
premises and a true conclusion, but the logical necessity of the conclusion,
given the two premises. The argument would be just as valid were the premises
and conclusion false. The following argument is of the same logical form but with false premises and a false
conclusion, and it is equally valid:
All cups are green.
Socrates is a cup.
Therefore, Socrates is
green.
No matter how the universe might be constructed, it could never
be the case that these arguments should turn out to have simultaneously true
premises but a false conclusion. The above arguments may be contrasted with the
following invalid one:
All men are immortal.
Socrates is a man.
Therefore, Socrates is
mortal.
In this case, the conclusion contradicts the deductive logic of
the preceding premises, rather than deriving from it. Therefore, the argument
is logically 'invalid', even though the conclusion could be considered 'true'
in general terms. The premise 'All men are immortal' would likewise be deemed
false outside of the framework of classical logic. However, within that system
'true' and 'false' essentially function more like mathematical states such as
binary 1s and 0s than the philosophical concepts normally associated with those
terms.
A standard view is that whether an argument is valid is a matter
of the argument's logical form.
Many techniques are employed by logicians to represent an argument's logical
form. A simple example, applied to two of the above illustrations, is the
following: Let the letters 'P', 'Q', and 'S' stand, respectively, for the set
of men, the set of mortals, and Socrates. Using these symbols, the first
argument may be abbreviated as:
All P are Q.
S is a P.
Therefore, S is a Q.
Similarly, the third argument becomes:
All P are not Q.
S is a P.
Therefore, S is a Q.
An argument is termed formally valid if it has structural
self-consistency, i.e. if when the operands between premises are all true the
derived conclusion is always also true. In the third example, the initial
premises cannot logically result in the conclusion and is therefore categorized
as an invalid argument.
Main
article: Well-formed formula
A formula of a formal language is a valid formula if and only if it
is true under every possible interpretation of the language. In propositional
logic, they are tautologies.
Statements[edit]
A statement can be called valid, i.e. logical truth, if it is
true in all interpretations.
Soundness[edit]
Validity of deduction is not affected by the truth of the
premise or the truth of the conclusion. The following deduction is perfectly
valid:
All animals live on Mars.
All humans are animals.
Therefore, all humans live
on Mars.
The problem with the argument is that it is not sound.
In order for a deductive argument to be sound, the deduction must be valid and all the premises true.
Satisfiability[edit]
Main article: Satisfiability
Model theory analyzes
formulae with respect to particular classes of interpretation in suitable
mathematical structures. On this reading, formula is valid if all such
interpretations make it true. An inference is valid if all interpretations that
validate the premises validate the conclusion. This is known as semantic validity.[3]
Preservation[edit]
In truth-preserving validity, the interpretation under
which all variables are assigned a truth value of 'true' produces a truth value of
'true'.
In a false-preserving validity, the interpretation under
which all variables are assigned a truth value of 'false' produces a truth
value of 'false'.[4]
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