Copyright (C) 2018, 2019 Dennis Joe Darland
I am going to explain how I would treat some topics raised by Samuel Lebens in his book, Bertrand Russell and the Nature of Propositions: A History and Defence of the Multiple Relation Theory of Judgement.
First Chapter 1 Section 1. What Role Are Propositions Supposed to Play?
1. The information content of a sentence relative to a context of utterance.
Suppose Russell believes Jupiter is a Planet.
“Planet” P i”Is_a_Planet”
“Jupiter” P i”Jupiter”
i”Is_a_Planet” R iPlanet
i”Jupiter” R iJupiter
believes_relation(Russell, iPlanet, iJupiter)
The belief would be true if, in addition.
iPlanet S Planet
iJupiter S Jupiter
and
Planet(Jupiter)
[Here the P, R, and S relations have suppressed arguments for Russell, and the time of the utterance. – which need to be the same for P, R, and S]
P is a relation between words and ideas of words.
R is a relation between ideas of words and ideas of objects.
S is a relation between ideas of objects and objects.
Thus if the relations stated for the sentence to be true hold, Jupiter is a Planet.
That is the content of the sentence.
2. That which synonymous sentences have in common.
That the sentences are true or false is irrelevant.
Generally if for all words “W1” in one sentence, and “W2” in another sentence
“W1″ P i”W1” and “W2″ P i”W2″
i”W1″ R iW1 and i”W2” R iW2
and iW1 = iW2
Note: it could be true for Russell, but not Quine. (Remember the suppressed arguments)
3. The object of understanding and other propositional attitudes.
There isn’t a single object, but rather just a relation of ideas. (e.g. believes_relation)
4. The primary bearers of truth or falsity.
Truth is the believes relation along with the S relations. Plus relation holding between objects. (e.g. Planet(Jupiter)
Falsehood is failure failure of any of those.
Truth of sentences is derivative.
5. Primary bearers of modally qualified truth-values.
This would be same as 4. (I included a modal operator)
6. The representational content of experience.
I think this is wrong – we do not experience propositions – this is an abbreviated expression of an inference.
7. The ontological foundation of possible worlds.
I think whatever is possible here is given by the modal logic.
8. The content of the common ground in a conversation.
I think this wrong – but not completely. There is not necessarily a common ground of propositions that all accept. There would be some common ground in the use of words. Our idea are learned through a social coordination of words and objects.
9. The semantic value of non-factive that-clauses.
Not clear on what he means.
10. The semantic value of certain demonstratives and anaphora.
Would just be references to the propositional attitude relations holding.
11. The domain for certain quantifiers.
Quine and Russell believe some monadic relations in common.
(E P)(E J)(E iP1)(E iJ1)(E iP2)(E iJ2)
Russell believes-relation (iP1,iJ1)
Quine believes-relation (iP2,iJ2)
for Russell iP1 S P and iJ1 S P
for Quine iP2 S P and iJ2 S J
(you can think of P as e.g. Planet and J as e.g. Jupiter)
Quine and Russell might speak different languages.
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First Chapter 1 Section 2. What Problems Must a Theory of Propositions Avoid?
1. The Problem of Unity.
Beliefs- relations (& other propositional attitudes) are relations between ideas.
For them to be true (in the case of belief) the objects must exist & the proper relation to hold between the objects. The ideas can exist without the objects existing, or the objects could exist without the relation holding. The propositional attitudes are relations within one mind (whatever that is).
I think there is no more a problem of a Bradlean regress than with any relation.
2. The Representation Concern.
The S relation answers this. Note that S can be meaningful even if an object corresponding to the idea does not exist.
3. The Problem of Quantity.
There will be an enormous quantity of propositions, and if will be impossible to precisely individualize them. We just do not know enough.
4. The Problem of Aboutness.
The S relation answers this.
5. The Problem of Dependence.
I struggled with this a very long hard time. I finally decided on the obvious. Propositions do depend upon sentient agents. Without sentient agents there would be no propositions. There would still be facts however. And, as sentient agents, we can consider worlds in which there are no sentient agents. Since we are here, the propositions can exist.