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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?

Geoffrey Thomas
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Niwilger
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    "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
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    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
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    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
  • logical neccesity that wants to be of the form x is P can only affirm self identity. 2/2 – Niwilger Nov 14 '17 at 16:07
  • Exactly; "2 is necessarily Odd" is NOT a "logical truth". It is true only in the "worlds" where the axioms of arithmetic and the definition of odd number hold. – Mauro ALLEGRANZA Nov 14 '17 at 16:12
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    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
  • "All contingent facts", "all possible worlds", etc., are relative terms, one is free to select their notion of what counts as possible, and that in turn determines what counts as necessary. If one selects the broad notion of possibility then nothing will remain necessary, but that is not a very interesting notion. With logical necessity one is not allowed to vary logical constants across possible worlds, so logical truths remain necessary. – Conifold Nov 14 '17 at 18:45
  • I would appreciate it very much if you elaboratred. I'll toss something that might be a reason for any conflictions. I do not reject the logical necessity of the whole "If x is defined this way and P is defined this way then x is necessarily P". But I reject its equivalence with just "x is necessarily P", and hold that if we removed the introduction of their definitions they could not be logical truths, unless they claimed self-identity. – Niwilger Nov 14 '17 at 19:23
  • I am not sure what you mean but logical constants (like or, and, etc.) are not defined at all, one simply fixes the rules of their manipulation. Also, "x is necessarily P" is a conventional expression, so there is nothing for you to reject. You are free to adopt your own convention, but if you want to be understood by others it should not stray too far from the usual ones. There are philosophers who dismiss possible world interpretations of necessity altogether, see Is there modal logic without possible worlds? – Conifold Nov 14 '17 at 23:47
  • @Conifold Take the above example by Mauro Allegranza. When is "2 is necessarily odd" true? It is true only in the possible worlds where the axioms of arithmetic and the definition of odd number hold. It's not a logical truth. If it's only true in the possible worlds where their definition holds, an implicative form that captures this will evaluate as a truth of every possible world. I do not believe that I could treat even our understsnding of "possible" as a contingent fact since from every possible world what is possible should be the same for us to treat it as a possible world. So I do 1/2 – Niwilger Nov 15 '17 at 00:26
  • not quite understand what we disagree about. I apologize for this. – Niwilger Nov 15 '17 at 00:30
  • The problem is that you are unfamiliar with the formalism of modal logic. There is a number of things including logic, accessibility relations, and often some portions of mathematics, which remain outside the possible worlds and which one does not get to vary, they are part of the "framing" so to speak. So some "definitions" hold everywhere by convention, and which determines one's understanding of "possible". Your absolutist understanding of it is not what most people mean, mostly because it is of little interest. – Conifold Nov 15 '17 at 01:09
  • @Conifold I think I am beginning to understand what you are saying. Those definitions that determine our understanding of "possible" are taken as necessary truths. Since they cannot be varied and since they hold everywhere, we can affirm them as necessary truths that are not in the form of asserting self-identity, which answers my question. Would this be correct? – Niwilger Nov 15 '17 at 02:06
  • Roughly, yes. What I described is called "analytic truths" and they are usually taken to be necessary by convention. In some applications people add additional necessary truths which lead to so-called physical and metaphysical necessities. – Conifold Nov 15 '17 at 20:39
  • @Conifold Thank you, this conversation has been very helpful. – Niwilger Nov 15 '17 at 21:34
  • OP you are using the term contingent differently from how the term contingent is used in logic. In logic a proposition is contingent when the truth value is not certain. So some days it rains. It is not always raining. So a proposition about a rainy day will be false at times and true at times. There are no contingent facts. Facts happen to be certain which is the reason why you should use that term. If you are not certain then don't use the word fact. Because you don't know something also is not an excuse to say something is not a fact either. – Logikal Mar 16 '18 at 03:18
  • @Conifold and the OP, I highly doubt you mean that about logical necessity. For instance a woman being a human being is logically necessary but yet no self referring. If something is not a human being it is impossible to be a woman. Of course we are using standard language rules here. If I said a triangle had three sides you would say that is referring to the thing itself. That is an analytical truth. A woman being a human being is not analytical. – Logikal Mar 16 '18 at 03:28
  • @Logikal I am not sure I follow, "woman is a human being" is analytic on the traditional understanding of "analytic" ("true in virtue of meanings"). "Analytic" does not amount to "self-reference", semantic conventions are far more complex than that. I think you may have in mind something like Kant's original narrow sense of "analytic", but it is rarely used today. – Conifold Mar 16 '18 at 22:07
  • No I am not referring to Kant or older definitions. Kant had different context for the terms analytic and synthetic. I am using standard logic context. You are not. Analytic statements are only two kinds logically necessary and self contradictory. Synthetic statements can be logically necessary because of our knowledge of the world. Analytic statements are true or false based on definition alone. So a triangle has three sides is true without having knowledge of the world. By definition. Or rules alone one can have true knowledge. Synthetic requires external knowledge to know truth. – Logikal Mar 16 '18 at 22:36
  • We know all women must be human beings not by definition alone. Men are also human beings but not women. So the claim is logically necessary but is also not analytic. – Logikal Mar 16 '18 at 22:38
  • At the start it looks as if you are using the 'is' of predication (e.g. a square is necessarily a four-sided figure in plane geometry) and the 'is' of identity, which self-identity requires. – Geoffrey Thomas Jun 17 '18 at 19:45
  • To me this sounds like you are asking whether a logic and its set-theory are dual. They are. All logically meaningful statements, not just the necessarily true ones, are claims that some class equals itself when it is expressed with two different intensions. And you can turn that into a statement about the universe containing a given set that is the set satisfying both intensions. So every statement asks whether your universe is like itself, which is a question of self-identity. –  Dec 14 '18 at 18:43

4 Answers4

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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?

Allen More
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  • 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 03:35
  • 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
  • It seems that you are working off of the idea that a proposition is a logical representation of a possible state of affairs, in which case, yes, many sentences can express the same state of affairs. These different methods of describing a state of affairs can inform a speaker in different ways about that state of affairs. The original question uses the symbols x and P which are different methods of referring to the same thing since 'x is necessarily P', and OP seems confused how x are P and x are x (identity) could express the same proposition. (Continued...) – Allen More Mar 19 '18 at 19:49
  • This is a sensible question to ask; how can we make deductions is all we ever assert is identity? Mention of linguistic concepts like sense and reference is needed to dispel this confusion. If the question is purely logical like you say, then OP would essentially be asking, 'Can I derive x is x from x is P' which I think is probably not what was asked. – Allen More Mar 19 '18 at 19:49
  • I get what you are saying. The problem then is one must be careful how propositions are expressed. There are rules to that as well. To say x is p and x is also something else may be too vague. Using specific concrete nouns would remedy that vagueness. Is it that x could be multiple things simultaneously or is the expression ill formed. Using shorthand should not be an excuse. The shorthand is only to save time. The variable should still stand for a real proposition. Some statements are not propositions. To get into sentence structure is more linguistics than logic. – Logikal Mar 19 '18 at 20:34
  • Here's a question that might help: When expressing propositions in symbolic logic, why use different symbols to represent the same thing? – Allen More Mar 19 '18 at 20:43
  • You are not supposed to use the same SYMBOL for distinctly different things. You should use a unique identifier for every distinct thing. Symbolic logic should be the shorthand for classical logic. Otherwise you are using another type of logic. Logic is not logic. There are differences in the types . – Logikal Mar 19 '18 at 20:47
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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."

SunGunRun
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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.

lukuss
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Ethan NOPE
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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