Qualities of Propositions

[Vik]

I'm claiming that the following concepts (among other attributes) are applicable to propositions:

1) truth

2) warrant

3) possibility

4) certainty

5) provability

For reference:

"Truth" appears in Galt's speech; ITOE pg63, 65, 136, 150; PWNI pg14

"Arbitrary" appears in ITOE pg110

"Possible" appears in LP's lectures and LP's analytic-synthetic essay

"Certainty" appears in LP's lectures and PWNI pg14

"Proof" and "prove" appear in Galt's speech; "prove" appears in ITOE pg73

3 questions:

Q1: Are these concepts in fact applicable to propositions?

Q2: If so, are there any others that Objectivists have commented on?

Q3: Is there a better way to think about propositions?

Edited April 1, 2010 by Vik

[khaight]

I'm not sure what you're trying to find out here. A list of adjectives that can be legitimately applied to propositions? What purpose would that serve? Why do you want one?

[Cmac19]

also i think an operationalized definition of propositions for the purpose of applying these concepts would be very helpful.

[Vik]

I'm not sure what you're trying to find out here. A list of adjectives that can be legitimately applied to propositions? What purpose would that serve? Why do you want one?

They're part of a longer list and a more complicated method for spot-checking my conclusions and evaluating the conclusions of others. But my method isn't rigorous. I think that improving my understanding of them will help me in that at regard.

The Objectivist literature has a lot on concepts but very little on propositions. I am even aware of certain "conceptual fallacies" that Rand points out in the works of others, as appears in The Marginalia. I should post something about that too actually.

[Vik]

also i think an operationalized definition of propositions for the purpose of applying these concepts would be very helpful.

What do you mean by "operationalized"?

By "proposition", I mean a statement that alleges or denies the existence of a conceived state of affairs.

"...the function of a proposition is similar to that of an equation: it applies conceptual abstractions to a specific problem"

ITOE pg75

Edited April 1, 2010 by Vik

[DavidOdden]

Truth, warrant, possibility, certainty and provability are not attributes, they are reifications of the attributes true, warranted, possible, certain and provable. Those are all properties of propositions. Same with arbitrary. The concept "proposition" is sufficiently high order that I think one can safely say that that is what cna be true, certain etc. and then any further refinement reduces to identifying a species of proposition.

There are vast numbers of attributes of propositions.

It is best to start by grasping the meanings of the basic terms, for example "statement", "proposition", "sentence", also "idea", "concept" to determine what they have in common and especially where they differ.

[Vik]

Truth, warrant, possibility, certainty and provability are not attributes, they are reifications of the attributes true, warranted, possible, certain and provable. Those are all properties of propositions. Same with arbitrary. The concept "proposition" is sufficiently high order that I think one can safely say that that is what can be true, certain etc. and then any further refinement reduces to identifying a species of proposition.

There are vast numbers of attributes of propositions.

It is best to start by grasping the meanings of the basic terms, for example "statement", "proposition", "sentence", also "idea", "concept" to determine what they have in common and especially where they differ.

"length" is an attribute, but we don't say "lengthed" or "lengthable".

"weight" is an attribute, so is "weighted", but not "weightable"

Hm... what's different about the concepts I mentioned...

Is it because they have to do with relationships between consciousness and existence while "length" and "weight" designate relationships that do not depend on consciousness?

Edited April 1, 2010 by Vik

[Vik]

...

It is best to start by grasping the meanings of the basic terms, for example "statement", "proposition", "sentence", also "idea", "concept" to determine what they have in common and especially where they differ.

I can see the need for distinguishing most of those, but I'm not sure about "idea". What's the relevance here?

Moving onto the others.

A "proposition" is a statement that asserts or denies a predication of a subject.

A "statement" is any meaningful declaration--including opinions not intended to be either true or false.

A "sentence" is any series of words that can be interpreted by a language-capable brain to express something. They can be declarations, questions, commands, exclamations for conveying emotions, etc.

"True", "warranted" (vs "arbitrary"), "possible", and "provable" apply to propositions, but they aren't applicable to just any statement.

"Warranted" and "possible" designate assessments about the evidence for a conclusion. There is no such thing as a warranted but impossible proposition. Nor is there such a thing as a provable but unwarranted proposition.

Suppose a light, wooden board hangs off the edge of a table. If an object of sufficient weight goes across the board a sufficient distance, the board will flip. Suppose a mouse is scurrying across the board. We don't know the weight of the mouse. It's possible that the board will flip, but it's arbitrary to say that it will. The lack of evidence means "arbitrary". But such an event is within the nature of what we know of boards and masses. It is possible.

"Provable" designates a judgment about the conditions for drawing a conclusion, given the nature of that conclusion and the channels of information available. If we know the mass of the mouse and the length of the board, including the overhang, we can calculate whether the board WILL flip. THAT proposition is provable.

The following morning, we find the board on the floor. The mouse is nowhere to be found.

It is possible that the mouse flipped the board.

It is warranted that the mouse flipped the board.

But unless we have evidence that the mouse reached a location that WOULD flip the board, it is not provable that the mouse flipped the board.

So warranted propositions aren't necessarily provable.

[DavidOdden]

“Idea” is very broad and includes things that are not fully-formed assertions. “Proposition” is much narrower. The relevance is to understand the logical relationship between concepts.

As for the others, I’m hoping to avoid endless tail-chasing. So if a proposition is a kind of statement, I first need to know what a statement is. If a statement is a kind of “meaningful declaration” then I need to know first what a “declaration” is. Is a “statement” a species of “sentence”? My opinion is that the distinction between “statement” and “proposition” is not necessary, in fact under your definition, they refer to exactly the same things. The difference that you seem to be suggesting is that with a statement you can declare something without that something being a fact or the opposite of a fact, but with a proposition I suppose you must be requiring there to be a declaration of fact / non-fact. If that is what you mean, I think that is wrong: the concept “declare” entails “declare to be the case”. If a person makes the statement “My coffee cup wrote a symphony”, he’s declaring it to be the case that an inanimate object did something that only man can do, so he has made a false statement. Once you declare something (as opposed to command something or ask something), that something either does describe a fact in which case it is true, or it does not describe a fact in which case it is false.

One crucial distinction between “sentence” and “proposition” is that propositions declare and sentences declare and other things. Declaring includes “declaring to be false” hence “assert or deny” is already entailed by defining a proposition as a declaration. However, there is something significantly missing between sentence and proposition, namely referential binding. The sentence “My brother did that last week” maps to zillions of separate propositions, depending on what referent you bind to “me”, “brother”, “that”, and “last week”. This is why sentences themselves cannot be said to be the bearers of truth. In a context, you may be able to associate the words to specific referents and determine the proposition being asserted, or maybe not, in which case there are multiple propositions that might be intended (from the listener’s “decoding” perspective; but probably not from the speaker’s perspective).

So the problem is that if a proposition is a kind of sentence, it doesn’t necessarily have the requisite property of proposition of having a truth value (because terms may have multiple referents). But we clearly want propositions to have truth values.

Another problem with taking propositions to be actual linguistic forms (i.e. sentences) is that it makes it impossible to talk usefully about synonymy, the fact that many sentences can express a single proposition and describe the same fact of reality. An example is “The cat scratched the sofa”, “The cat scratched the davenport” and “The cat scratched the couch”. These three sentences express the same proposition, and it is a mere linguistic detail that that proposition can map to three (or more) different sentences.

[Vik]

“Idea” is very broad and includes things that are not fully-formed assertions. “Proposition” is much narrower. The relevance is to understand the logical relationship between concepts.

As for the others, I’m hoping to avoid endless tail-chasing. So if a proposition is a kind of statement, I first need to know what a statement is. If a statement is a kind of “meaningful declaration” then I need to know first what a “declaration” is. Is a “statement” a species of “sentence”? My opinion is that the distinction between “statement” and “proposition” is not necessary, in fact under your definition, they refer to exactly the same things. The difference that you seem to be suggesting is that with a statement you can declare something without that something being a fact or the opposite of a fact, but with a proposition I suppose you must be requiring there to be a declaration of fact / non-fact. If that is what you mean, I think that is wrong: the concept “declare” entails “declare to be the case”. If a person makes the statement “My coffee cup wrote a symphony”, he’s declaring it to be the case that an inanimate object did something that only man can do, so he has made a false statement. Once you declare something (as opposed to command something or ask something), that something either does describe a fact in which case it is true, or it does not describe a fact in which case it is false.

One crucial distinction between “sentence” and “proposition” is that propositions declare and sentences declare and other things. Declaring includes “declaring to be false” hence “assert or deny” is already entailed by defining a proposition as a declaration. However, there is something significantly missing between sentence and proposition, namely referential binding. The sentence “My brother did that last week” maps to zillions of separate propositions, depending on what referent you bind to “me”, “brother”, “that”, and “last week”. This is why sentences themselves cannot be said to be the bearers of truth. In a context, you may be able to associate the words to specific referents and determine the proposition being asserted, or maybe not, in which case there are multiple propositions that might be intended (from the listener’s “decoding” perspective; but probably not from the speaker’s perspective).

So the problem is that if a proposition is a kind of sentence, it doesn’t necessarily have the requisite property of proposition of having a truth value (because terms may have multiple referents). But we clearly want propositions to have truth values.

Another problem with taking propositions to be actual linguistic forms (i.e. sentences) is that it makes it impossible to talk usefully about synonymy, the fact that many sentences can express a single proposition and describe the same fact of reality. An example is “The cat scratched the sofa”, “The cat scratched the davenport” and “The cat scratched the couch”. These three sentences express the same proposition, and it is a mere linguistic detail that that proposition can map to three (or more) different sentences.

The idea of "likeness"

The idea of "field lines".

The idea of light as EM propagation.

Would you say an "idea" is what you have before you form a proper concept or proposition?

As for the genus of propositions:

I'm not taking propositions to be linguistic forms. After all, concept aren't merely symbols associated with arbitrary collections.

I meant something else by "declaration" but I can't think of a suitable example.

I'll drop "statement" and get at the genus of propositions indirectly.

Concepts integrate units. Every concept implies a set of units. Some of those units are different from the others. They are distinguished by certain measurements that were omitted during the process of concept-formation.

A particular cat can be viewed as a unit in the set of cats.

A particular sofa can be viewed as a unit in the set of sofas.

A particular action of scratching can be viewed as a unit as well.

These units can be "mentally juxtaposed" in several ways. However, the nature of the existents and actions conceptualized determine the validity of such juxtapositions. Actions are done by entities. It isn't in the nature of sofas to run up to a cat and scratch it. That sort of thing.

Also, we aren't talking about scratching as such. We're talking about a specific scratching happening relative to the present. We are specifying the time of the scratching.

"The cat scratched the sofa" asserts that the conceived event actually took place.

It alleges that a particular entity performed a certain type of action on another, different kind of entity.

We conceived of an entity-action-object relationship, and we asserted that it actually took place.

"The sofa was scratched by the cat" focuses on the cause of a state of the sofa.

We conceived of an object-acted-on-by-entity relationship, and we asserted that it actually took place.

So a proposition involves asserting or denying that a relationship among certain units holds for their respective identities.

(Again, I don't have a word to designate the genus of propositions, but I know very well that it isn't a linguistic form)

[DavidOdden]

Would you say an "idea" is what you have before you form a proper concept or proposition?

Yes, since concepts and propositions are species of ideas, ones made cognitively specific.

I'm not taking propositions to be linguistic forms. After all, concept aren't merely symbols associated with arbitrary collections.

I agree: what I am still working through in my mind is the exact cognitive ontology of a proposition (i.e. “what is semantics really about”). On the one hand, it’s convenient to use some kind of formal calculus for presenting propositions, but on the other hand the integration of conceptual content (where there is something more to propositions like “cats meow” than simply writing words in capital letters) is basically ignored in such an approach, where equating propositions and natural language sentences seems more satisfactory.

[Vik]

what I am still working through in my mind is the exact cognitive ontology of a proposition (i.e. “what is semantics really about”). On the one hand, it’s convenient to use some kind of formal calculus for presenting propositions, but on the other hand the integration of conceptual content (where there is something more to propositions like “cats meow” than simply writing words in capital letters) is basically ignored in such an approach, where equating propositions and natural language sentences seems more satisfactory.

We know that a subject specifies an existent or set of units under consideration.

We also know that a predicate has to be compatible with the nature of the units specified in the subject. Consider:

"Cats meow" asserts that a certain type of action is part of the nature of certain units capable of action.

"Cats make arguments" is a false proposition because it specifies an action that is not within the nature of the units specified by the subject.

"Cats with sufficiently large wings fly" is arbitrary because it's unwarranted. But it qualifies as a proposition because the genus of flying is action and animals are certainly capable of action.

"Whiskers flood vigorously" satisfies the rules of grammar but the genii of the concepts are incompatible.

As for language seeming more satisfactory, I think the satisfaction we get stems from the fact that language enables us to think more clearly and more quickly. Specification of units means clarity of subject and speed of accessing conceptual content. It is very difficult to capture the features of a thing when the thing itself hasn't been clearly differentiated.

[Vik]

The concept of "action" is compatible with the concept of "entity" in the sense that actions are performed by entities.

Propositions assert or deny that juxtapositions of "compatible" concepts have correspondence.

Their truth depends on both that correspondence AND whether the concepts were defined in terms of essentials

What do you think?

Edited April 4, 2010 by Vik

[Vik]

On the one hand, it’s convenient to use some kind of formal calculus for presenting propositions, but on the other hand the integration of conceptual content (where there is something more to propositions like “cats meow” than simply writing words in capital letters) is basically ignored in such an approach, where equating propositions and natural language sentences seems more satisfactory.

Are you referring to things like:

* examples of the concept

* reduction of a concept to its referents in reality

* chain (or tree) of abstractions down to the perceptual level

* list of measurements that have been omitted

[DavidOdden]

Are you referring to things like:

* examples of the concept

* reduction of a concept to its referents in reality

* chain (or tree) of abstractions down to the perceptual level

* list of measurements that have been omitted

No, I am referring to the practice of translating sentences into some kind of symbolic notation, so as to remove those aspects of the sentence that give you a 1-to-many relationship between sentences and propositions. That would include some visually-obvious notation that highlights the difference between the meaning of "the dog" in the sentences "The dog is a coward" (a specific dog and there is shared knowledge of the referent) versus "The dog is a mammal" (a universal statement). This leads to traditional formulations like "∀x(D(x)M(x))" for universal dog statements. The implication of this, though, is that in addition to the natural language(s) that we know and learn as children, there is an underlying metalinguistic "language" for symbolic logic that we also know but didn't have to learn, and that meanings are expressed in this underlying metalanguage. Of course that idea is indefensible. I just do not know what conceptual / symbolic form such propositional knowledge takes. It would surely be related to examples of concepts, the logic of reducing a concept to referents, a statement of measurements omitted, but it isn't the same as that.

[Plasmatic]

We conceived of an entity-action-object relationship, and we asserted that it actually took place.

Entity and object are synonyms.

[Vik]

Entity and object are synonyms.

In the context of "entity-action-object", the word "object" was used to distinguish things appearing in a predicate from things appearing in a subject, as the subject is what unifies predicates.

If you're talking about physical existents, the concept of "object" is a species of the concept "entity"

[Plasmatic]

In the context of "entity-action-object", the word "object" was used to distinguish things appearing in a predicate from things appearing in a subject, as the subject is what unifies predicates.

If you're talking about physical existents, the concept of "object" is a species of the concept "entity"

Yeah , after I posted I thought of that as what you may have intended by "object".

[Vik]

No, I am referring to the practice of translating sentences into some kind of symbolic notation, so as to remove those aspects of the sentence that give you a 1-to-many relationship between sentences and propositions. That would include some visually-obvious notation that highlights the difference between the meaning of "the dog" in the sentences "The dog is a coward" (a specific dog and there is shared knowledge of the referent) versus "The dog is a mammal" (a universal statement). This leads to traditional formulations like "∀x(D(x)M(x))" for universal dog statements. The implication of this, though, is that in addition to the natural language(s) that we know and learn as children, there is an underlying metalinguistic "language" for symbolic logic that we also know but didn't have to learn, and that meanings are expressed in this underlying metalanguage. Of course that idea is indefensible. I just do not know what conceptual / symbolic form such propositional knowledge takes. It would surely be related to examples of concepts, the logic of reducing a concept to referents, a statement of measurements omitted, but it isn't the same as that.

You mean how we use certain words to narrow the scope of a phrase so that we can classify the sentence, given a set of alternatives:

A specific thing exists.

There exist members of a class.

A specific unit has an attribute.

Members of a class have an attribute.

A specific thing is a member of a wider category.

A class is a subcategory of a wider category.

[claire]

Does anyone here have any idea what they are talking about or is everyone just enjoying a game of word salad?

[DavidOdden]

Does anyone here have any idea what they are talking about or is everyone just enjoying a game of word salad?

Yes, I know what I'm talking about. Do you have a clue?

[claire]

Of course. Was there something about what I said that was difficult for you to understand?

[DavidOdden]

Of course. Was there something about what I said that was difficult for you to understand?

No, you just didn't seem to have a clue about the topic, and all you had to contribute was a pointless (and ineffective) insult. If you have something to actually contribute, feel free.

[JayR]

Does anyone here have any idea what they are talking about or is everyone just enjoying a game of word salad?

Are you adressing the people conversing, or others who may be just reading?

j..