What Is the Technical or Lexical Definition of Philosophy

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Russell`s main motivation for the vicious circle principle was logical and semantic paradoxes. Terms such as „truth“, „sentence“ and „class“ produce paradoxical conclusions under certain adverse conditions. Thus, the statement „Cheney is a liar,“ where „liar“ is understood as in (16), leads to paradoxical conclusions when Cheney has claimed that he is a liar, and all other claims he claims are in fact false. Russell took the vicious circle principle to imply that when „Cheney is a liar“ expresses a sentence, it cannot be in the realm of the quantifier in the definitions of (16). More generally, Russell was of the view that the quantification of all sentences and classes violated the vicious circle principle and was therefore illegitimate. Moreover, he argued that expressions such as „true“ and „false“ do not express a single concept—a unique „propositional function“ in Russell`s terminology—but a hierarchy of propositional functions of different orders. The lesson Russell drew from paradoxes is therefore that the realm of meaning is more limited than it normally seems, that the traditional presentation of concepts and definitions had to be made more restrictive to exclude concepts such as (16) and (17). Keeping in mind the distinction between expansion and intension, it is possible to approach the definition of a general term (on one of the five types of definitions we discussed last time) in two ways: Now let`s equip (L) with the semantics of model theory. That is, we associate (L) with a class of interpretations, and we provide the terms „valid in (L) in the (M) interpretation“ (alias: „true in (L) in (M)“) and „semantically equivalent in (L) with respect to (M)“. The terms „valid in (L^{+}) in (M)“ and „semantically equivalent in (L^{+}) with respect to (M)“ result when the semantics of (L) are supplemented by those of the definition (mathcal{D}).

The criteria for prudence and eliminatibility can now be specified as follows: where (phi) is the conjunction of the members of (T^*). (If (T^*) is infinite, then for each sentence (psi) in (T^*) a determination of the above form is necessary.) [11] The definition is traditionally legitimate, provided it meets the criteria of prudence and eliminability. If it meets these criteria, it is called (T^*) allowed (for a definition of X). The traditional presentation therefore accommodates the idea that theories can necessarily introduce new terms, but it makes a strong demand: theories must be allowed. [12] However, if there is a violation of eliminability in this case, it is superficial and can easily be corrected in two ways. The first way — the way that best suits our usual practices— is to understand the enriched languages that result from adding definitions to exclude sentences like (18) and (19). For if we establish a definition like (16), we do not intend to speak of first cousins once they have been removed from the numbers; On the contrary, we want to exclude any speech as inappropriate. Similarly, by determining (17), we want to exclude the discourse of division by 0 as legitimate. The first is therefore to recognize that a conditional definition such as (16) and (17) entails limitations on the enriched language and, therefore, meets the criterion of eliminability once the enriched language is properly delimited. This idea can be formally implemented by formulating conditional definitions in languages with sorting quantization. If (T^*) is allowed, then (T^*) is an implicit semantic definition of (X).

The word philosophy is also used to refer to a particular doctrine based on such inquiry, as in my article on Plato`s philosophy. The definitions corresponding to points (7) to (9) are heterogeneous; The definition is sensual, but the term defined is not. One source of the specific conditions on (7) and (9) is their heterogeneity. Specific conditions are necessary to ensure that definitions, although not in the logical category of the defined term, convey the correct logical behavior to it. The conditions thus ensure that the logic of the extended language is the same as that of the base language. This is why the specific conditions on normal forms can vary with the logic of the basic language. Note that, regardless of this logic, no specific conditions are required for regular homogeneous definitions. A connotative definition attempts to identify the intent of a term by providing a synonymous linguistic term or an operational method for determining the applicability of the term. Of course, it is not always easy to find an alternative word or phrase that has exactly the same meaning, or to specify a concrete test of applicability.