III 342
Definition/Kripke: a definition is a "great fundamental principle". Definitions must be formulated in a language already understood - then there is little room for alternative interpretations of a metalanguage (even if the syntactic and semantic structure can be interpreted differently). >
Loewenheim, >
Meta language, >
Object language.
III 390
Implicit Definition/Kripke: an implicit definition is given by rule - otherwise no generalizations in finite systems can be derived from (infinite) instances.
III 392
Definition/Kripke: no inductive definition is possible if it does not start with a general characterization of the atomic (basic) case.
III 393
Direct definition: a direct definition is not recursive. Recursive definition: is indirect. In Tarski the definition of truth is given via a recursive definition of fulfillment. Question: could he also have defined truth directly? If so, would fulfillment be definable in terms of truth?
>
Satisfaction, >
Satifiability.
III 399
Implicit Definition: depends on axioms. These imply (for example) truth implicit in the sense that truth is the only interpretation of the predicate T(x) which makes all the axioms true. Explicit definition: does not depend on axioms, but on expressive power of the language (not theory). Sat1(x,y) is explicitly definable in terms of T(x) - it is an explicit definition by introducing a new variable (II 402).
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Kripke I 66ff
Definition/reference/standard meter/Kripke: Kripke does not use this definition to specify the meaning, but to define the reference.
There is a certain length which he would like to denote. He denotes it through an accidental property. Someone else may refer to the same reference by another accidental property. He can still definitely say: if heat had been in the game, the length would have changed.
Rigid: the meter is rigid. Not rigid: the length of S at time t is not rigid.
>
Standard meter, >
Rigidity/Kripke, >
Reference/Kripke.
I 136f
The "definition" does not say that the two terms are synonymous, but that we have determined the reference of the term "one meter" by establishing that it should be a rigid designation expression that actually has the length S. So not a necessary truth! We must distinguish between definitions that specify a reference, and definitions that specify a synonym.
>
Synonymy/Kripke.
Definition: is not necessary: e.g. tiger: large, carnivorous, four legged cat, etc. Suppose someone says: "This is the meaning of tiger in German".
ZiffVs: this is wrong. E.g. a tiger with three legs is not a contradiction in itself.
I 153
In the case of proper names the reference can be defined in various ways.
Determination of reference: is a priori (contingent) and not synonymous.
Meaning: is analytical (required). Definition: specifies reference and expresses a priori truth.
>
Meaning/Kripke.
