Inlogic, thelogical form of astatement is a precisely specifiedsemantic version of that statement in aformal system. Informally, the logical form attempts toformalize a possiblyambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an idealformal language, the meaning of a logical form can be determined unambiguously fromsyntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than onestring that represents the same logical form in a given language.[1]
The logical form of anargument is called theargument form of the argument.
The importance of the concept of form to logic was already recognized in ancient times.Aristotle, in thePrior Analytics, was one of the first people to employ variable letters to represent valid inferences.[citation needed] Therefore,Jan Łukasiewicz claims that the introduction of variables was "one of Aristotle's greatest inventions."[citation needed]
According to the followers of Aristotle likeAmmonius, only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete termsman,mortal, and so forth are analogous to the substitution values of the schematic placeholdersA,B,C, which were called the "matter" (Greekhyle, Latinmateria) of the argument.
The term "logical form" itself was introduced byBertrand Russell in 1914, in the context of his program to formalize natural language and reasoning, which he calledphilosophical logic. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure."[2][3]
To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument.
All that has been done in theargument form is to putH forhuman andhumans,M formortal, andS forSocrates. What results is theform of the original argument. Moreover, each individual sentence of theargument form is thesentence form of its respective sentence in the original argument.[4]
Attention is given to argument and sentence form, becauseform is what makes an argumentvalid or cogent. All logical form arguments are eitherinductive ordeductive. Inductive logical forms include inductive generalization, statistical arguments, causal argument, and arguments from analogy. Common deductive argument forms arehypothetical syllogism,categorical syllogism, argument by definition, argument based on mathematics, argument from definition. The most reliable forms of logic aremodus ponens,modus tollens, and chain arguments because if the premises of the argument are true, then the conclusion necessarily follows.[5] Two invalid argument forms areaffirming the consequent anddenying the antecedent.
A logicalargument, seen as anordered set of sentences, has a logical form thatderives from the form of its constituent sentences; the logical form of an argument is sometimes called argument form.[6] Some authors only define logical form with respect to whole arguments, as the schemata or inferential structure of the argument.[7] Inargumentation theory orinformal logic, an argument form is sometimes seen as a broader notion than the logical form.[8]
It consists of stripping out all spurious grammatical features from the sentence (such as gender, and passive forms), and replacing all the expressions specific tothe subject matter of the argument byschematic variables. Thus, for example, the expression "all A's are B's" shows the logical form which is common to the sentences "all men are mortals", "all cats are carnivores", "all Greeks are philosophers", and so on.
The fundamental difference between modern formal logic and traditional, or Aristotelian logic, lies in their differing analysis of the logical form of the sentences they treat:
The more complex modern view comes with more power. On the modern view, the fundamental form of a simple sentence is given by a recursive schema, like natural language and involvinglogical connectives, which are joined by juxtaposition to other sentences, which in turn may have logical structure. Medieval logicians recognized theproblem of multiple generality, where Aristotelian logic is unable to satisfactorily render such sentences as "some guys have all the luck", because both quantities "all" and "some" may be relevant in an inference, but the fixed scheme that Aristotle used allows only one to govern the inference. Just as linguists recognize recursive structure in natural languages, it appears that logic needs recursive structure.
Insemantic parsing, statements in natural languages are converted into logical forms that represent their meanings.[9]
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