Logical truth

(1) If death is bad only if life is good, and death is bad, then life is good. (2) If no desire is voluntary and some beliefs are desires, then some beliefs are not voluntary. (3) If Drasha is a cat and all cats are mysterious, then Drasha is mysterious. As it turns out, it is very hard to think of universally accepted ideas about what the generic properties of logical truths are or should be. A widespread, perhaps universally accepted idea is that part of what should distinguish logical truths from other kinds of truths is that logical truths should have a yet to be fully understood modal force. It is typical to hold that, in some sense or senses of “could”, a logical truth could not be false or, alternatively, that in some sense or senses of “must”, a logical truth must be true. But there is little if any agreement about how the relevant modality should be understood.

Another widespread idea is that part of what should distinguish logical truths is that they should be in some sense yet to be fully understood “formal”. That a logical truth is formal implies at the very least that all the sentences which are appropriate replacement instances of its logical form are logical truths too. In this context, the logical form of a sentence S

is supposed to be a certain schema determined uniquely by 

S , a schema of which S

is a replacement instance, and of which sentences with the same form as 

S

are replacement instances too. A form has at the very least the property that the expressions in it which are not schematic letters (the “logical expressions”) are widely applicable across different areas of discourse. Among people who accept the idea of formality there would be wide agreement that the forms of (1), (2) and (3) would be something like 

( 1 ′ ) , ( 2 ′ )

and 

( 3 ′ )

respectively:

( 1 ′ ) If a

is 

P

only if 

b

is 

Q , and a

is 

P , then b

is 

Q . ( 2 ′ ) If no Q

is 

R

and some 

P s are Q s, then some P s are not R . ( 3 ′ ) If a

is a 

P

and all 

P s are Q , then a

is 

Q . ( 1 ′ ) , ( 2 ′ )

and 

( 3 ′ )

do seem to give rise to sentences that intuitively must be true for all appropriate replacements of the letters “

a ”, “ b ”, “ P ”, “ Q ”, and “ R ”. And expressions such as “if”, “and”, “some”, “all”, etc., which are paradigmatic logical expressions, do seem to be widely applicable across different areas of discourse. But the idea that logical truths are or should be formal is certainly not universally accepted. And even among those who accept it, there is little if any agreement about what generic criteria determine the form of an arbitrary sentence.