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Revision as of 20:00, 15 January 2009
, 20:00, 15 January 2009→1.3.10.3. Propositions and Sentences: integrate changes from later version
The ''projective imagination'' of <math>\underline\mathbb{B}^k</math> is the imagination <math>(\pi_1, \ldots, \pi_k).</math>
The ''projective imagination'' of <math>\underline\mathbb{B}^k</math> is the imagination <math>(\pi_1, \ldots, \pi_k).</math>
A ''sentence about things in the universe'', for short, a "sentence", is a sign that denotes a proposition. In other words, a sentence is any sign that denotes an indicator function, any sign whose object is a function of the form <math>f : X \to \underline\mathbb{B}.</math>
A ''sentence about things in the universe'', for short, a ''sentence'', is a sign that denotes a proposition. In other words, a sentence is any sign that denotes an indicator function, any sign whose object is a function of the form <math>f : X \to \underline\mathbb{B}.</math>
To emphasize the empirical contingency of this definition, one can say that a sentence is any sign that is interpreted as naming a proposition, any sign that is taken to denote an indicator function, or any sign whose object happens to be a function of the form <math>f : X \to \underline\mathbb{B}.</math>
To emphasize the empirical contingency of this definition, one can say that a sentence is any sign that is interpreted as naming a proposition, any sign that is taken to denote an indicator function, or any sign whose object happens to be a function of the form <math>f : X \to \underline\mathbb{B}.</math>
