FREE BOOKS

Author's List




PREV.   NEXT  
|<   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46  
47   48   49   50   51   52   53   54   55   56   57   58   59   60   >>  
st. 4.28 There correspond to these combinations the same number of possibilities of truth--and falsity--for n elementary propositions. 4.3 Truth-possibilities of elementary propositions mean Possibilities of existence and non-existence of states of affairs. 4.31 We can represent truth-possibilities by schemata of the following kind ('T' means 'true', 'F' means 'false'; the rows of 'T's' and 'F's' under the row of elementary propositions symbolize their truth-possibilities in a way that can easily be understood): 4.4 A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions. 4.41 Truth-possibilities of elementary propositions are the conditions of the truth and falsity of propositions. 4.411 It immediately strikes one as probable that the introduction of elementary propositions provides the basis for understanding all other kinds of proposition. Indeed the understanding of general propositions palpably depends on the understanding of elementary propositions. 4.42 For n elementary propositions there are ways in which a proposition can agree and disagree with their truth possibilities. 4.43 We can express agreement with truth-possibilities by correlating the mark 'T' (true) with them in the schema. The absence of this mark means disagreement. 4.431 The expression of agreement and disagreement with the truth possibilities of elementary propositions expresses the truth-conditions of a proposition. A proposition is the expression of its truth-conditions. (Thus Frege was quite right to use them as a starting point when he explained the signs of his conceptual notation. But the explanation of the concept of truth that Frege gives is mistaken: if 'the true' and 'the false' were really objects, and were the arguments in Pp etc., then Frege's method of determining the sense of 'Pp' would leave it absolutely undetermined.) 4.44 The sign that results from correlating the mark 'I' with truth-possibilities is a propositional sign. 4.441 It is clear that a complex of the signs 'F' and 'T' has no object (or complex of objects) corresponding to it, just as there is none corresponding to the horizontal and vertical lines or to the brackets.--There are no 'logical objects'. Of course the same applies to all signs that express what the schemata of 'T's' and 'F's' express. 4.442 For example, the following is a propositional sign: (Frege's
PREV.   NEXT  
|<   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46  
47   48   49   50   51   52   53   54   55   56   57   58   59   60   >>  



Top keywords:

propositions

 

possibilities

 
elementary
 

proposition

 

conditions

 

disagreement

 

expression

 

agreement

 

understanding

 

objects


express

 
correlating
 
propositional
 

existence

 
complex
 
falsity
 

schemata

 

applies

 

concept

 

explanation


mistaken

 

notation

 

explained

 

object

 

conceptual

 

arguments

 

undetermined

 

absolutely

 

vertical

 
results

horizontal

 

logical

 
method
 

brackets

 

starting

 
determining
 

palpably

 
symbolize
 

easily

 
immediately

understood

 

represent

 

combinations

 
correspond
 

number

 

states

 
affairs
 

Possibilities

 

strikes

 
absence