# Are all logically necessary statements self identity claims?

When we say that x is necessarily P, are we not asserting that this is the case regardless of all contingent facts, so regardless of what x and P are? And if x was P regardless of what x and P are, are we not just asserting self identity?

• "regardless of what x and P are?" What are x and P ? Is "x" an object and "P" a property ? – Mauro ALLEGRANZA Nov 14 '17 at 15:35
• I may say "2 is necessarily Odd" (by def of odd number) but in what sense I may assert it "regardless of what 2 and Odd are" ? – Mauro ALLEGRANZA Nov 14 '17 at 15:36
• I'm afraid I don’t get it, either. Does it have to do with the fact that reference is contingent; i.e., with the fact that ‘2’ and ‘even’ only contingently denote the number two and the property of being even? – MarkOxford Nov 14 '17 at 16:01
• What I am asking is, why are you allowed to claim that "2 is necessarily odd" and assert this as a logical truth, true in every possible world, when the definitions of two and being odd could have just changed between possible worlds, making this statement moot? If I am not mistaken, Kripke argued against Quine that we are interested in evaluating certain meanings across possible worlds, but that would not be a logical necessity, since it did not span all possible worlds. My question was if, since we must abstract from all contingent facts, so even from the determination of terms, a 1/2 – Niwilger Nov 14 '17 at 16:06
• Let S be a sentence of language L. Then its modal status is assessed in two stages. First, determine the content that S expresses according to the actual rules of L. Second, find out whether that content/proposition is true in all worlds. More simply, to say that a sentence is necessary is to say that given the way we use the sentence*, it expresses a necessary truth. We could define necessity differently; but then no sentence would be necessary any more. Even ‘a = a’ would be contingent, as ‘=’ doesn’t express identity in all worlds. – MarkOxford Nov 14 '17 at 16:37

This is an issue Frege dealt with. If I told Lois Lane that Clark Kent is Superman, she would be very surprised. Thing is, Clark Kent and Superman both refer to the same thing, so it seems as though I'm just asserting identity. From this perspective the phrase should be as informative as saying Superman is Superman which would not surprise Lois. Frege describes the concept of "Sense" which means the "Method of reference" used by a word or phrase. I can refer to the same object with Clark Kent and Superman, but each has a different sense. Superman refers to that really strong flying guy, Clark Kent refers to that really boring nerdy guy. The extra info offered by "Superman is Kent" is that the really strong flying guy is also the boring nerdy guy, which is what surprises Lois. This exemplifies the difference between propositions of the form A = A and A = B: A and A have the same sense, A and B have different senses. Make sense?

• Are you not referring to synonyms? Saying the same idea with different words does not change the message. I get it that the other person might not KNOW the terms are synonyms and you are just making the connection using the other words. The OP thinks that all necessary claims are self referring claims and you seem to support his original view. Would you agree? – Logikal Mar 16 '18 at 3:35
• The claim "Saying the same idea with different words does not change the message" begs the question. I would argue that "Superman is Kent" and "Superman is Superman" do not "say" the same thing, they just refer to the same thing. "Superman is Kent" is contingent because there are possible worlds where someone else might be Superman, Peter Parker for instance. "Superman is Superman" is necessarily true in all possible worlds. (Continued...) – Allen More Mar 19 '18 at 17:00
• Another way of establishing a difference between the statements is that "Superman is Kent" can be wrong, "Superman is Superman" is analytically true no matter what. This difference shows that the statements do not "say the same thing" because the conditions for being false differ. The thing that creates the difference between these statements is not their reference, but something Frege called "Sense" which might be described as their "means of reference". – Allen More Mar 19 '18 at 17:00
• @AllenMoore, your reply may be acceptable in ordinary language but not in deductive reasoning. In philosophy words and statements are not the same as "Propositions". Propositions are identified by what is being expressed alone and not word order or syntax. Thus you can express the same proposition in ten distinct languages but only one proposition is expressed. So statements expressing the same idea are only one proposition. Proposition definition in philosophy is pretty standard. – Logikal Mar 19 '18 at 17:47
• @AllenMoore, what your second comment refers to is what philosophy identifies as different TYPES of propositions. There are Analytical propositions and Synthetic propositions. I do not refer to how Kant used those exact terms. Synthetic propositions require knowledge of the world to know that a proposition is true. Analytic propositions are determined by definitions or rules that DO NOT require worldly knowledge. So superman is Clark Kent could be false if he were REALl. Superman is currently only a concept in our world & this concept is linguistic only so it is equivalent to Clark kent. – Logikal Mar 19 '18 at 18:09

Consider this logically necessary statement: "If everything is red and round, then everything is red and everything is round."

This sentence makes no mention of identity. It does not claim that two things are identical. And it certainly does not claim any kind of self-identity, whatever that might mean.

So, no, not all logically necessary statements "claim self-identity."

Consider: Something(x) must have some quality(P) to indeed be that thing. : Identifying an attribute(P) of something(x).

Your question is: "Regardless of what x and P are, are we not just asserting self identity?"

To give you an answer to this question, we must only show one case of x and P which is not 'just asserting self identity' -- bugger all the logical hoop jumping.

Self identity has the property that, in it's statements, you can reverse the identified terms and still get a true proposition.

Let's use your form: "x necessarily is P".

Our x is say 'A Louise Ville Slugger', and our P is the quality 'wooden'.

This gives us: A Louise Ville Slugger is necessarily wooden.

Can we reverse the terms without getting something absurd?

Nope, so for all x's and all P's, there are some possible cases in which self identity is not being expressed; the answer to your question then being: no. In all statements were P is a quality, self identity is not being expressed.

The verb " to be " has standardly 3 meanings

• identity : a = b

• membership : a is a B ( that is: a is a member of the set of B's)

• inclusion : A's are B's ( A is a subset of set B)

Examples:

• The morning star is necessarily the evening star ( for these "two" stars are in fact one and the same).

• Felix ( my cat) is necessarily a mammal.

• The Cat ( taken as a species) is necessarily a mammal.

So " X is necessarily Y" does not necessarily mean : " X = Y", for the " is" is not necessarily an " identity - is" ; it can also be a " membership-is" or an " inclusion -is".

As to the question of knowing whether all identity statements are logically true, I think that one could answer that

• yes, from an extensional point of view

• no from an intensional point of view.

Necessarily " the person who won the elections against Hilary Clinton" is " the man that built an anti-immigrant wall" : this is true if I mean by this that the person denoted by the first expression is necessarily the same as the person denoted by the second.

However, the two expressions are not logically equivalent, for they do not express the same concepts: " winning against Hilary" does not logically imply " builing a wall" ( and reciprocally). So, the " person that won against Hilary " could have not been " the person that built the wall".

Note : on the distinction between denotation ( extension) and sense ( intension), and its use in the analysis of identity statements, , you may have a look at Frege https://plato.stanford.edu/entries/frege/#FreTheSenDen