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Non sequitur fallacy – where the conclusion does not logically follow the premise. [8] Masked-man fallacy (illicit substitution of identicals) – the substitution of identical designators in a true statement can lead to a false one. [9]
The identity substitution, which maps every variable to itself, is the neutral element of substitution composition. A substitution σ is called idempotent if σσ = σ, and hence tσσ = tσ for every term t. When x i ≠t i for all i, the substitution { x 1 ↦ t 1, …, x k ↦ t k} is idempotent if and only if none of the variables x i ...
A conservative replacement (also called a conservative mutation or a conservative substitution or a homologous replacement) is an amino acid replacement in a protein that changes a given amino acid to a different amino acid with similar biochemical properties (e.g. charge, hydrophobicity and size).
Amino acid replacement is a change from one amino acid to a different amino acid in a protein due to point mutation in the corresponding DNA sequence. It is caused by nonsynonymous missense mutation which changes the codon sequence to code other amino acid instead of the original.
A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion). For example:
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.
An admissible rule is one whose conclusion holds whenever the premises hold. All derivable rules are admissible. To appreciate the difference, consider the following set of rules for defining the natural numbers (the judgment n n a t {\displaystyle n\,\,{\mathsf {nat}}} asserts the fact that n {\displaystyle n} is a natural number):