Information Technology Reference
In-Depth Information
In the case of arithmetic, we already know what numbers are and what symbols we
should use to represent them. We have all been trained to do this symbolic processing
starting at a very early age, without a second thought.
But what about ideas? What symbols should stand for them?
1.3.2 Propositions vs. sentences
A
proposition
, as the word is used in the philosophical literature, is an idea that can
be expressed by a declarative sentence of English (or other language). So one can
think of the sentence as a symbolic representation of the proposition. Consider these
examples:
My keys are in my coat pocket.
Dinosaurs were warm-blooded.
The stock market composite index will rise to twice its current value within
the next three years.
Hate literature should not be tolerated, even if that impinges on free speech.
These are all English sentences. The first one uses seven words of English, for exam-
ple. But apart from being English sentences, they each express an
idea
, an idea that
can be expressed in other languages with other sentences. So we have the
sentence
,on
the one hand (like the first one with seven words), and the
proposition
it expresses, on
the other (like the idea that my keys are located somewhere).
What can be said about the propositions themselves? They are abstract entities, like
numbers, but they have some special properties:
Propositions are considered to
hold
or to
not hold
. A sentence is
true
if the
proposition it expresses holds, and
false
if that proposition does not hold.
This does not mean that there will be no controversy about whether the propo-
sition holds. It just means that it makes sense to ask
if
it holds (or if the
corresponding sentence is true). A number is a very different sort of abstract
object; we do not ask if a number holds in this sense.
Propositions are considered to be related to people in certain ways: people may
or may not believe them, fear them, regret them, wish for them, worry about
them, and so on. These various relationships between people and propositions
are what philosophers call
propositional attitudes
.
Propositions are related to each other in certain ways: a proposition might imply,
or provide evidence for, or contradict another proposition.
