• frank
    17.9k
    I'm reading Davidson's Rational Animals, and I fell down the rabbit hole of referential opacity, which is about situations in speech that defy Leibniz' Law, which is that “if x and y are the same object, then x and y have the same properties"

    A typical example involves Lois Lane believing that Superman can fly, but she doesn't believe Clark Kent can. Yet Superman=Clark Kent.

    a. Superman is Clark Kent. Major
    b. Lois believes that Superman can fly. Minor
    c. ∴ Lois believes that Clark Kent can fly. a, b =E
    IEP

    From two true statements, we get an untrue conclusion.

    Is it that we're misapplying Leibniz's Law? Let's look at some cases of that:

    a. Istanbul is Constantinople.
    b. “Istanbul” has eight letters.
    c. ∴ “Constantinople” has eight letters.
    IEP

    In this case, the problem is coming from the use of Tarskian quotation, which means the quoted part is a word, not a city.
    -----------------------------------------
    a. Giorgione is Barbarelli.
    b. Giorgione is so-called because of his size.
    c. ∴ Barbarelli is so-called because of his size.
    IEP

    The flaw here is equivocation. The "so-called because of his size" can't skip from one name to the next.
    --------------------------------------------

    a. The number of planets = 3 squared
    b. It is contingent that the number of planets = 9
    c. ∴ It is contingent that 3 squared = 9.
    IEP

    There a long drawn-out answer to what went wrong in this example. See next post.
  • Leontiskos
    5.1k
    “if x and y are the same object, then x and y have the same properties"frank

    In each case you are dealing with mental or intentional objects, and therein lies the confusion. Things like belief or the number of letters that any given language uses for a word have to do with our thinking, not with objects in themselves. In an Aristotelian sense an accidental property is being confused with an essential property. For example, it is only an accidental property of Istanbul that its English name has eight letters. Leibniz' law was never meant to track accidental properties deriving from mental objects.
  • T Clark
    15.2k

    Superman is not Clark Kent.
    Istanbul is not Constantinople.
    The number of planets is not three squared.
    It is not contingent that the number of planets equals nine, even if there were nine planets.
  • frank
    17.9k
    Superman is not Clark Kent.T Clark

    He's not?
  • T Clark
    15.2k
    He's not?frank

    He's Jor-el. Also - Lois Lane believing Clark Kent can or cannot fly is not a property of Clark Kent. It's not a property at all.
  • wonderer1
    2.3k
    Lois Lane believing Clark Kent can or cannot fly is not a property of Clark Kent. It's not a property at all.T Clark

    Not a property at all, or a property of Lois rather than a property of Clark?
  • frank
    17.9k
    :grin:
    A little more formally, the rule of inference =E can be stated as:

    Identity Elimination Schema

    Major: t1 = t2

    Minor: ϕ(t1)

    Conclusion: ϕ(t2)

    Here t1 and t2 are expressions which refer to entities (for example, proper names of people or cities). ϕ(t1) is a sentence containing at least one occurrence of t1, and ϕ(t2) is a sentence that results from replacing at least one occurrence of t1 in ϕ(t1) with an occurrence of t2, eliminating the “=” of t1 = t2. Recurring ti presumes that ti is univocal throughout, and recurring ϕ presumes that the sentential context ϕ is not altered, syntactically or semantically, by the replacement. If these uniformity conditions are not met, then the inference scheme is being misapplied, and it is no wonder that false conclusions are derivable. For example, in the inference “The man behind Fred = the man in front of Bill; the man behind Fred saw him leave; therefore, the man in front of Bill saw him leave,” the context “saw him leave” is not uniform, since substitution of “the man behind Fred” by “the man in front of Bill” changes the reference of “him” (Fine 1989:222–3; Linsky 1967:104).

    In discussing the problem with apparent substitution-failure by using =E, many examples will be drawn from the fictional story of Superman, treated as if it were true. In the story, a child from the planet Krypton, Kal-El, is sent to Earth, where physical conditions cause him to acquire superpowers. Wearing specific clothing (red cape, blue jumpsuit), Kal-El prevents disasters, rescues endangered innocents, and foils would-be perpetrators of crimes, such as Lex Luthor. People call Kal-El “Superman” when talking about Kal-El’s actions of this kind.

    But Kal-El also takes a day job as a reporter, using the name “Clark Kent.” A coworker, Lois Lane, treats him with indifference in the office, but has a pronounced crush on, as she would put it, Superman, unaware they are the same individual.

    The problematic examples discussed below involve ascriptions of mental states to Lois (or occasionally Lex), arrived at by applying the rule =E to the major premise “Superman is Clark” and a carefully chosen minor premise. Lois has a crush on Superman (minor premise), so, by =E, Lois has a crush on Clark. But this latter seems false, and would certainly be rejected by Lois herself. Also, Lois believes that Superman can fly, but does not seem to believe that Clark can; she hopes to see Superman again soon, but seems not much to care when she next sees Clark; she would like a date with Superman, but apparently has no interest in one with Clark; and so on
    IEP
  • frank
    17.9k
    a. The number of planets = 3 squared
    b. It is contingent that the number of planets = 9
    c. ∴ It is contingent that 3 squared = 9.
    IEP

    This substitution failure results from the fact that the number of planets isn't a rigid designator. It's a singular definite description.
  • T Clark
    15.2k
    He's Jor-el.T Clark

    Sorry - Kal-el.
  • Banno
    28.5k

    Referential opacity occurs between contexts. Indeed, it can be considered part of what defines a context. Getting the scope right clears up the mess.
  • frank
    17.9k
    Referential opacity occurs between contexts. Indeed, it can be considered part of what defines a context. Getting the scope right clears up the mess.Banno


    Look at this example.

    a. Superman is Clark Kent. Major
    b. Lois believes that Superman can fly. Minor
    c. ∴ Lois believes that Clark Kent can fly. a, b =E
    IEP


    We aren't really worried about how we know what Lois believes, whether it was from observing her behavior, or she told us, or we have a mind-reading machine. We just know that she believes Superman can fly. There's a magical thing about belief: that it causes referential opacity.

    But if we attribute propositional attitudes to a dog, do we still get referential opacity? We can't substitute a dog in the above =E because we aren't likely to just know specifically what the dog believes. We're just guessing from a afar, and so all our attributions will have extensional definitions, right?
  • Banno
    28.5k
    Not sure here.

    "Superman is Clark Kent" is a straight forward identity - one may be substituted for the other. Superman can fly, hence Kent can fly.

    "Lois believes that Superman can fly" is not directly about superman - this by way of giving a sense to "directly". It's about Lois, and something else... that we call a belief.

    Whatever sort of thing that belief is, it doesn't allow the sort of substitution we are envisioning.

    But we should not jump the gun. Perhaps a slower reading of the article is called for?
  • frank
    17.9k
    Perhaps a slower reading of the article is called for?Banno

    True. Davidson uses referential opacity to make his case that language is required for rationality. So I was just contemplating the background of propositional attitudes.

    In the example of Superman, we know what Lois believes because it's a fictional story and we have a God's eye view. That Lois believes Superman can fly is not a speculation, it's one of the central columns of the story. I'm thinking we'd want to keep that in mind when using referential opacity as an element of an argument. It's going to be dragging that God's eye view in with it.
  • Banno
    28.5k
    Why introduce "god's eye view"?

    If you and I agree that Superman can fly, why should we concern ourselves with god's opinion on the topic?

    Seems out of place.
  • frank
    17.9k

    How do you know Lois believes it?
  • Banno
    28.5k


    You stipulated that she does. I trust you. If you now want to bring that in to doubt, go ahead, but I don't much see the point in doing so.
  • frank
    17.9k
    You stipulated that she does. I trust you. If you now want to bring that in to doubt, go ahead, but I don't much see the point in doing so.Banno

    I don't think it's a stipulation in that context. We know what Lois believes because we know the story. It's from the narrator's point of view. That isn't available in real life.

    Another angle on the same question would be: how do you ever know what other people believe? If it's charity, do you extend that charity to dogs? Why or why not?
  • Banno
    28.5k
    Well, seems to me that if you are unsure that she believes what you suggested, we can't proceed.

    If we are going to get somewhere we may need to focus?
  • frank
    17.9k


    I'm going to be examining an argument that says language is required for rationality. It's going to be rejecting the idea that dogs have beliefs, specifically because we have no way to be sure what they believe.

    If referential opacity is drawn into the argument, which it is, then it's fair to tinker with the gears in that object.
  • Leontiskos
    5.1k
    I don't think it's a stipulation in that context. We know what Lois believes because we know the story. It's from the narrator's point of view. That isn't available in real life.frank

    I don't see why it can't be recast as a question of what follows from belief. For example, you could avoid this by rewriting b. "Suppose Lois believes that Superman can fly." It seems that the "God's eye view" comes not primarily in premise (b) but rather in premise (a), yet that too can be recast as a supposition, thus achieving the central Analytic shift from inference to consequence.
  • flannel jesus
    2.9k
    “if x and y are the same object, then x and y have the same properties"

    A typical example involves Lois Lane believing that Superman can fly, but she doesn't believe Clark Kent can. Yet Superman=Clark Kent.

    a. Superman is Clark Kent. Major
    b. Lois believes that Superman can fly. Minor
    c. ∴ Lois believes that Clark Kent can fly. a, b =E
    — IEP
    frank

    Allow me to risk being idiotic, but perhaps part of the solution lies in thinking "Lois believes that Superman can fly" is not a property of Superman. It's a fact that you can say, but it's not a property as such.

    Seems more like that statement is about a property of Lois lane
  • Banno
    28.5k
    Don't Lois's beliefs belong rather to Lois?

    Superman can fly. Lois believes that.
  • frank
    17.9k
    Allow me to risk being idiotic, but perhaps part of the solution lies in thinking "Lois believes that Superman can fly" is not a property of Superman. It's a fact that you can say, but it's not a property as such.

    Seems more like that statement is about a property of Lois lane
    flannel jesus

    Yes, I misspoke. Leibniz's Law gives us the expectation that we can substitute t1 and t2 in the Identity Elimination Schema (here)

    The schema itself isn't an expression of Leibniz's Law.
  • bongo fury
    1.8k
    There's a magical thing about belief: that it causes referential opacity.frank

    Wouldn't it be more a cause for wonderment if it created referential transparency?

    Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one?

    Granted that would spoil story-telling, and perhaps also Davidson's proposed intentionality test.
  • frank
    17.9k
    Wouldn't it be more a cause for wonderment if it created referential transparency?

    Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one?
    bongo fury

    It depends on how you explain belief. A behaviorist would say that what we call belief reduces to certain actions. Since Clark is Superman, we can substitute all day long, because there is no hidden object in Lois's head. There is no opaque reference. The behaviorist goes with the de re reading:

    Normally, we understand such ascriptions in the way that does not, which is why we reject (2b), but if cajoled enough (“look, she does believe Clark can fly, she just wouldn’t say it like that”), we may switch to a reading that allows substitution. In the usual terminology, this is called the de re reading, contrasting with the more common de dicto reading, which disallows substitution. Other terminology for this reading is relational, contrasting with notional; transparent, contrasting with opaque; and wide scope, contrasting with narrow scope. We turn now to explaining what distinction these labels attempt to mark.IEP
  • Leontiskos
    5.1k
    Wouldn't it be more a cause for wonderment if it created referential transparency?

    Then the Superman of Lois' beliefs could be relied on to share all his properties with the actual fictional one?

    Granted that would spoil story-telling, and perhaps also Davidson's proposed intentionality test.
    bongo fury

    Wouldn't it also mean that the believer is omniscient, lacking no knowledge about identities?
  • bongo fury
    1.8k
    A behaviourist wouldn't necessarily deny belief or opaqueness, though? Belief can be a disposition to assent to sentences, and opaqueness will be a natural affliction, given imperfect information? My point was merely that the opposite would be more surprising?

    Edit: @Leontiskos exactly :ok:
  • bongo fury
    1.8k
    the de re reading, contrasting with the more common de dicto reading, [...] relational, contrasting with notional; transparent, contrasting with opaque; and wide scope, contrasting with narrow scope.IEP

    Also reference, contrasting with sense? (I wonder.)
  • Leontiskos
    5.1k
    - Yeah, I think you're making a really salient point. :up:
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.