Hesperus is Bosphorus

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The Liar and the Liar Denier – Or “Will the real Liar please stand up and then sit down where she’s told to?”

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Here are some thoughts (by a non-logician) on our recent workshop on semantic paradoxes.

Some Turkish philosophers have strange dreams. Erdinc’s are so weird and wonderful that he cannot even tell us about them. And after our two day workshop on paradoxes with Graham Priest and Stephen Read, Ilhan told us about a strange dream in which he met ‘The True’ who appeared as to him as a small talking metallic sphere. And I think it makes some sense to think of sentences as such spheres. So let’s suppose that sentences are small shiny metallic spheres that (a) can be named and (b) tell us what they mean. And let’s think of three such spheres. One of them is called “The Liar” and the second is called “The Liar-Denier” The third is called “The Liar-Affirmer”. The Liar and The Liar-Denier are twin sisters. The Liar-Affirmer is their younger sister. [Perhaps they’re all daughters of ‘The True’ who Ilhan met in his dream.] Anyway, this is what we know about each sphere:

(1) The Liar says: “What the Liar says is False”.

(2) The Liar-Denier says: “What the Liar says is False”.

(3) The Liar-Affirmer says: “What the Liar says is True”

Now, Stephen Read thinks that what The-Liar says is false, because while saying “what the Liar says is false” she says (probably very quietly under her breath, so we may not notice it), “What the Liar says is True” and also says “What the liar says is True and What the Liar says is false” – and Stephen thinks that what a sentence says is false (and not True) if anything the sentence says is false. So Stephen claims that what the liar says is false. Graham Priest thinks that what the Liar says is both true and false.

So what about her sisters? Well, according to Stephen, what the Liar-Denier says is clearly True (and not false), while what the Liar Affirmer says is False (and not True). But what about Graham? Well it seems to me that what he should say is that what the Liar-Denier says is True (and not False) and what the Liar Affirmer says is also True (and not false). But in our workshop he argued that what the Liar-Denier says is both True and False. Now I thought that, according to his account, what the Liar says is both True and False. So what the Liar-Denier says is thus clearly True, but it will only also be false if what the Liar says is both True, False and not-false, and as far as I understand his semantics being both true and false does not entail not being false. So I did not understand why he thought the liar denier was both true and false. I asked him about this and he explained that: “An atomic sentence  Pa is true if the denotation of ‘a’ is in the extension of ‘P’; and it is false if ‘a’ is in the anti-extension of ‘P’. By the Liar argument, your (1) is both true and false. The subject of (2) refers to the same subject as the subject of (1), and the predicates of (1) and (2) are the same. Hence (2) is true and false (2)… Note that, in general, though, if Qb  is both true and false, both T<Qb> and F<Qb> may be true only. They do not have co-referring subjects and

predicates.” But, given this, I’m wondering what it is, if anything, that makes the Liar and the Liar denier distinct sentences on his approach.

I have two big questions about this little story I’ve told: (1) What is it for two individual sentences to be distinct sentences? And (2) How do sentences get their names?

(1) One might be committed to the principle of the identity of indiscernibles for sentences, and so think that if two sentences say the same thing, they are the same sentence. But if this is right, then we might think that the Liar and the Liar-Denier are really the same sentence with two names. There is only one little metallic sphere which has been given two names. Or perhaps we have one little metallic sphere which is in two places at the same time? [and if this is the case then it looks like we have a problem analogous to Zeno’s problems with motion]. Now if Stephen is right on his account of what the Liar says, then we don’t have this problem as the Liar and the Liar-denier don’t really say the same thing at all, for the Liar does not only say “the Liar is false” but also says “the Liar is True and the Liar is False”.  Now one might think that the difference between what the the Liar and the Liar Denier say corresponds to the difference between :

(a) ‘This sentence is false’

(b) “’This sentence is false’ is false”

These do seem to be distinct sentences. But if we are thinking of sentences as small talking metallic spheres and we’re committed to the identity of indiscerbibles for sentences, then, unless we tell a story like Stpehen Read’s it is plausible to think that the Liar and the Liar Denier are really the same sentence. So, here’s a question, how many sentences you do think we have here? One or Two?

(2) Perhaps we can answer this question by thinking a bit more about how sentences get their names. It seems to me that there are two options here: either they are named by someone else, or they name themselves. So one story is would be that the Liar and the Liar Denier were named at birth by their mother, The True. This is an odd story. It sort of commits us to the view that individuals have real names, that are perhaps unknowable by anyone. Perhaps The True names her daughters, but how does she tell them apart when she bumps into them? They say the same thing, and so seem to be indistinguishable. So perhaps they have the names they have, but once they’ve been named there is no way, in principle, of telling them apart. So I think it makes more sense to think that these sentences name themselves. And if this is the case it looks like we have two sentences that are not indiscernible:

(a) one sentence says: “I am called the Liar and what the Liar says is False”

(b) another sentence says: “I am not called the Liar and what the Liar says is False”

Now, what are we to make of what the first sentence says? When she claims that “I am called the Liar” is she saying something true? There is no fact of the matter that makes this claim true. So perhaps we should take it as something more like an order or a stipulation: “Call me the Liar!” And it seems to me that perhaps the proper response to this order is to say “I can’t do that”, because it forces us into a performative contradiction. If someone tells you “Call me Lucas and don’t call me Lucas” what they are saying is not paradoxical, they’re just telling you to do something that you don’t know how to do. It is difficult to see how the liar can succeed in naming herself. But what about the second sentence? Well, this now appears to be a sentence containing a name with an unknown reference, so it looks like we just don’t know its truth value. But what about the following sentence:

(b’) “I am not-called the Liar and what the sentence who claims to be called the liar says is False.”

Given my account of (a) this might look like a way of referring to (a) and so given the fact that (a) is false this sentence is saying something True. Unfortunately, this suggests a way of constructing a stronger version of (a):

(a’) “I am the sentence that claims to be called the Liar, and what the sentence that claims to be called the Liar says is false.”

Now, with this sentence the question is whether the term “the sentence that clams to be called to Liar” should be read as a name or a definite description. If we take it as a name we get the following sentence:

(a’n) “I am called ‘the sentence that claims to be called the Liar’ and what the sentence called ‘the sentence that claims to be called the Liar’ says is false.”

If we read the sentence in this way, then it seems to me that I can give the same sort of analysis as before which is that the whole sentence is false because either (a) the first of the conjuncts is false or (b) because the sentence commits a performative contradiction by trying to do something that it cannot do. Or perhaps (b) is the explanation of (a).  But what if we take “the sentence that claims to be called the Liar” as a definite description? Here things are more difficult. But one thing to bear in mind is that “I am the x” will be false if there is more than one x. So if there is more that one sentence that claims to be called the liar then a’ will be false because the first of the conjuncts will be false. So to avoid paradox, The True just has to give birth to at least two daughters who claims to be called the Liar.

(3) Anyway – Perhaps it’s a mistake to think of sentences as small talking metallic spheres. So lets supposed that sentences are strings of words written on bits of paper, and let’s suppose that there are five of them in a hat and we’re told to firstly look at them individually and secondly to take them out one by one and put them in random order – and we produce the following list:

(1) “2+2=5” (F)

(2) “The second Sentence consists of five words” (F)

(3) “The third sentence consists of seven words” (T)

(4) “The fourth sentence is false” (F?)

(5) “The fourth sentence is false” (T?)

The fourth sentence seems to be the Liar –if it is True it is False and if it is False it is True, and the fifth sentence seems to be the Liar-Denier. Now what truth values do these sentences have? Now I think that this is a trick question. If we just randomly look at a sentence while they are still in the hat the only sentence that clearly has a truth value is the first sentence. While they are in the hat none of these sentences are paradoxical. It’s only when we take them out and put them in a certain order that paradox arises. Another strange thing is that when we look at the sentences in the hat we are are unable to distinguish between the liar and the liar denier. If we switch the positions of the 4th and 5th sentence the liar sentence becomes the liar denier and the liar denier becomes the Liar. Which one is which depends upon its order in the list. So perhaps we don’t really have 5 sentences in the hat, but only four – one of which we copy down twice.

Now it seems to me that that the paradox here only arises because we take a set of sentences and try and put them in a certain order. And so my suggestion for blocking the paradox is to revise our theory of order and position. We have assumed that when we are told to randomly take five sentences out of a hat and put them in order this is something we know how to do, and that we will end up with a list with five members. But this is an assumption that we can reject. We have no problem with taking our the first three sentences and putting them in order. But when we take out the next one, something strange happens – our theory of order breaks down. The rules of our game are set up in such a way that when we try and put the sentence “the fourth sentence is false” in the fourth position on our list it ends up somewhere else, and the fourth position is filled by the empty set. We try and put the sentence we’ve just pulled out of the hat just after the third sentence, but instead we put nothing there and the sentence we try and put there ends up somewhere else.

My suggestion for solving this paradox, then, is to claim that what I have been calling the “fourth sentence” is false because there is no fourth sentence. If we think that “The King of France is bald” is false because there is no King of France, then if there is no 4th sentence then “the fourth sentence is false” is false for the same reason. But why would one think that there is no 4th sentence? My thought here is that when we try and put the sentence “The Fourth sentence is false” in the 4th position we necessarily fail. Just as an attempted act of self-naming is not guaranteed to succeed, an attempt to put a sentence in a certain place on a list does not necessarily succeed either. Sometimes, however hard you try, you just can’t get seven people into a taxi, they just don’t fit.

So when we play our game, the list we end up with actually looks more like this:

(1) “2+2=5” (F)

(2) “The second Sentence consists of five words” (F)

(3) “The third sentence consists of seven words” (T)


(5) “The fourth sentence is false” (F)

(?) “The fourth sentence is false” (F)

I’m not even sure that we can say how many things we have on this list. But the fact that we’re told to take a bunch of things and put them in arbitrary order doesn’t mean we can necessarily do it. Where on our list is the sentence marked (?)? I think the best answer is: We just don’t know. [So the suggestion I’m making here is that we can avoid the paradox by questioning the assumption that sets of sentences can necessarily be well ordered.]

In the case of the sentence who claims to be the Liar, we really don’t know who she is. In this paradox we really have no idea where the sentence is on the list. The Liar is not paradoxical; She’s just very naughty. She won’t tell you who she is, and she refuses to sit where you tell her.


Written by Lucas Thorpe

April 15, 2012 at 2:27 pm

8 Responses

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  1. Comment on the first paragraph: This isn’t quite what I said. I said a sentence is false if anything it says does not hold. Sentences are either true or false; what a sentence says either holds or does not hold. See discussion of connecticates in my fourth lecture and the quotation from Prior. There shouldn’t really be a verb on the RHS – what a sentence says already has a verb. ‘hold’ is a dummy for a verb. But we wouldn’t want to use ‘is true’ for that dummy, on pain of circularity.

    (By the way, I assume there’s nothing significant in the capital ‘T’s and ‘F’s in (2) and (3).)

    Another thought, concerning the five sentences in the hat. Why can’t sentence (1) go in the fourth place, e.g., list them (4), (5), (3), (1), (2)?

    Stephen Read

    April 16, 2012 at 5:07 pm

    • Hi Stephen,

      (1) I guess on in terms of my first point, I was just sloppy. But I think the metaphysics of your position might get quite complicated – as you want to make a distinction between a sentence being true or false, and what the sentence says holding or not. But I’m not exactly sure how this distinction is supposed to work – It seems quite natural to think that we express ‘what a sentence says’ in terms of the sentences that are entailed by the original sentence – and so I’m worried that we might ultimately want to cash out “whether what a sentence says holds or not” in terms of whether or not all the sentences entailed by the (original) sentence are true (or not). Does this worry make any sense to you? Perhaps I’m not expressing it very well. But before you came to Istanbul I read your paper and told you that I guessed that Bradwardine was some sort of nominalist. And you said not. I thought at the time that perhaps my conception of nominalism and yours are quite different. So on the sort of nominalism that (I suspect) I’m mistakenly attributing you, ‘what sentences say’ are themselves sentences. So I’m thinking of what it is for ‘what a sentence says’ to ‘hold’, in terms of ‘what the sentence says’ [i.e. all the sentences entailed by the sentence] ‘being true’. So I guess I’m not really sure that I get the distinction between ‘being true’ and ‘holding’. Does this question make any sense to you? I think I’ve misunderstood something about your position – but I’m not sure what.

      (2) Nothing significant about capitals. I thought I’d fixed that in the version I posted. Too many things to do and not enough time.

      (3) Of course sentence #1 can go in the 4th place. And then you’d have no paradox. But the rules of the game are that you take the sentences out in random order. So imagine you have firstly taken out sentence (1), secondly sentence (2) and thirdly sentence (3) and the next one you take out says ‘the 4th sentence is false’. My suggestion is that we may thing that this sentence is the 4th thing we have put in the list – but actually we have put nothing in the 4th place. If this sentence really was the 4th sentence I think you’d have a paradox. My thought is that although this sentence may appear to be 4th in the list, appearances can be deceptive. I could just chnge the game – imagine 5 sentences in a hat – each one says ‘The 4th sentence is false’. Now take them out and put them in random order.

      The thought behind this is that when I ask logicians how one introduces self reference into a formal language, the reply they give is in terms of assigning Godel numbers to sentences/propositions. So the idea seem to be that we cash out self reference in a formal language in terms of naming, and we explain naming in terms of assigning Godel numbers to sentences – so the suggestion is that if we we are thinking of self reference in terms of naming and naming in terms of assigning Godel numbers, the paradox only arises if we assume that each sentence can be assigned a Godel number and that Godel numbers are well ordered. And this is just an axiom. Something has to give – so why not give up on the (total) consistency of arithmetic, or at least on the assumption that all sets of (sentences) can be well ordered? I guess I’m thinking of the axioms of arithmetic as something like the constitution of a legal system – and (inductively) we know that all the legal systems we have ever met are not consistent. So the thought is to reject the assumption that all sets of sentences can be well ordered.

      Lucas Thorpe

      April 17, 2012 at 3:19 am

      • Hi Lucas, ( in the following comment i’ll take what you call ‘says’ to be exact equivalent of Read’s technical ‘signifys’ relation)

        I agree with you about the appearent naturalness of cashing out what a sentence signifies by what it entails. However, in order for the Bradwardine’s solution to work, at least some sentences (paradigmatically Liar sentence) must signify things that it does not entail.

        Moreover, it turns out all sentences signify truth of themselves, and since this solution rejects T-in ( p entails T) that means all sentences signfy something that they do not entail. So, cashing out what a sentence signifies by what it entails is exactly what Bradwardine forces us to reject.

        However, consider following definitions of two entailment relations.

        (E) p entails(1) q iff whenever p is true, q is also true.

        However by reflexivity of signification, and by the truth principle, –if we use full T-schema–, it becomes equivalent with:

        (E’) p entails(2) q iff whenever p is true, q holds.

        Observe that equivalence of (E) and (E’) depends on full T-schema. if we reject T-in (E’) is weaker than (E) in the sense that ‘p entails(1) q’ implies ‘p entails(2) q’ but not vice versa. (Isn’t it? I may be mistaken since the whole point of my comment is that I do not understand ‘entailment’ in the new system, and I ask for an explanation or definition)

        Now consider I work with weaker (E’) and assume q is an arbitrary item that p signifies. Then if p is true, since p signifies q, q holds. Therefore whenever p is true, q holds. By (E’) p entails q. since p and q was arbitrary, all sentences entail all the things they signify… !?

        But I said that Bradwardine’s solution requires sentences to signfy things that it does not entail. There must be something wrong here, either I did not understand Bradwardine’s solution at all or definition of entailment I am working is defective. I would like to believe that I understand Bradwardine, so what is the correct definition of entailment. (E) is the definition we commonly use and (E’) was its equivalent in the good old days of full T-schema. So what is the revised version of entailment?

        So, I agree wiht you we need explicit new accounts the terms signification, entailment, being true and holding, because in the orthodox account they are interdependent and symetric, and we understand some of them to be nothing more or nothing less than some other.( i.e your example of ‘being true’ and ‘holding’) Breaking one symetry (T-schema) leaves us with a mess if we do not revise other concepts.

        For the last part of your reply, it is quite interesting, but I am not sure well-ordering of natural numbers plays an essential role on fixed-point theorem. If it does I would like to hear more, what is the exact relation between two? And I do not understand how you plan to give up from naming sentences, because he does not assume a given naming, but he gives names by Gödel-numbering and moreover he proves their properteies can be represented in the system. For example there is a predicate in the formal system Sent(x) which expresses the property of being a sentence and if p is a sentence PA proves Sent([p]). So he shows that they can be named, and that it works.I do not understand what is the thing that you want to give up.


        April 18, 2012 at 12:36 am

        • Hi Adil,

          Thanks for the reply. Here are some thoughts:

          (1) I had not thought about your the point that as “all sentences signify truth of themselves, and since this solution rejects T-in ( p entails T) that means all sentences signfy something that they do not entail.” Nice point. I think Stephen is committed to the claim that all sentences signify their own truth and so signification and entailment do seem to come apart.

          I like the sort of paradox you develop using E and E’. But perhaps it only works because your notion of entailment seems to be a material entailment. Perhaps one might want some sort of relevant entailment, and so reject the claim that ‘today is Wednesday’ entails “2+2 = 4”. But I guess this might not be enough. p and T(p) seem to share a propositional variable. And so one might think that p entails T(p) is a relevant entailment. But do they really share a propositional variable? (p) is not p, but the name of p. And so do they really share a propositional variable?

          But even if we do this – it seems to me that we still do not have a well defined notion of signification. I like Bradwardine’s solution as Stephen explained it – but can’t buy it until I get a better idea of the signification relation. And there are two questions I have: (a) What sort of things does is relate? On the left hand side we have a sentence. What do we have on the right hand side? A set of sentences? Propositions? (b) How does it relate them?

          (2) In terms of your final paragraph: I’m at he edge of my competence here. But I think that what I’m suggesting is that one way of blocking the semantic paradoxes (at least for formal languages – what I have to say may not be relevant for paradoxes in natural languages where one has demonstratives and indexicals) might be by giving up on the well-ordering theorem – and I’m not sure why this is called a theorem rather than an axiom. http://en.wikipedia.org/wiki/Well-ordering_theorem. Anyway – I guess I have two questions to myself: (a) is this a possible solution? (b) Is it a good solution? (what are its costs?)

          (a) I have a feeling that all ways of setting up the paradox for formal languages make some sort of implicit appeal to the well-ordering axiom. Perhaps I’m wrong about this. I don’t really understand how the naming of sentences is introduced into formal languages. People introduce new symbols, such as ” ” – but I’ve never really worked through the technical details of how these new symbols function. As far as I understand, “p” is a godel number, which is a structural descriptive name of p. And my suspicion is that there are assumptions at play here about godel numbering that can be rejected, and if we reject these assumptions we can avoid the paradoxes. But I have a feeling that the assumptions we need to reject to block the paradoxes will entail rejecting the well-ordering axiom. But I’m really not sure if this is right.

          (b) But assuming we can avoid the paradoxes by rejecting some assumptions about the naming of sentences. What are the costs? One should do things as cheaply as possible. My gut feeling here is that any solution that trys to solve the paradoxes by questioning the technical details of how naming of sentences works for formal languages will probably have to reject the well-ordering axiom. But I’m not at all sure about this.

          Now, as far as I understand number theory (which is not very much) – rejecting the well ordering axiom pushes us to reject the 5th axiom of Peano Arithmetic, the axiom of induction: “Let P be a set. If P contains zero as an element, and if “n is an element of P” implies “n+1 is an element of P” for all natural numbers n, then P contains the entire set of natural numbers.”

          Now, I guess this is a price most people today would not want to pay. However, it’s (at least epistemically) possible that it might not cost anything as some mathematicians think that the consistency of peano arithmetic is an open question, and trying to prove the inconsistency of peano arithmetic is an active research project (see the links below). If this project succeeded, and a consensus arose amongst mathematicians that peano arithmetic was inconsistent (which is imaginable, although perhaps not conceivable), this this type of solution might be quite cheap.

          Here are some interesting discussions about some of the discussions amongst mathematicians concerning the about the (1n?)consistency of peano arithmetic:




          Lucas Thorpe

          April 18, 2012 at 2:41 pm

  2. There are many issues now in play, but I’ll just concentrate on one of them, namely, saying that or signifying that (strictly, people says that … and sentences, or “propositions” in the medieval sense, signify that …, but I’ll treat them as the same). First, the grammar of ‘says that’. Here I referred in lecture 4 to Frank Ramsey and Arthur Prior (see slides 7 and 9). The Ramsey quote comes from ‘Facts and Propositions’ (p.143), which Prior discusses in Objects of Thought at p.19 (see also p.135). Lucas asks, what sort of things does signify relate? Prior’s point is that it is NOT a relation, but a connecticate – a predicate at one end and a connective at the other. I alluded to Ryle’s complaint about ‘Fido’-Fido theories of meaning (see his review of Carnap’s Meaning and Necessity), rejecting the idea that all expressions name something, in the way ‘Fido’ names Fido. Sentences (contra Frege and Ilhan) don’t refer, and in ‘s says that p’, ‘p’ is not a referring expression. So ‘says that’ is not a relation between two things, a sentence and its meaning.
    Signification and entailment certainly do come apart, as is shown by my (and Bradwardine’s) rejection of CBP, Spade’s Converse Bradwardine Principle (see lecture 1, slides 11 and 18). P2 and BP says that if entails and s says that p then s says that q and says that q (here forming names of sentences). But the converse is false, and as Adil notes, the Liar is a counterexample. What then, asks Adil, is the definition of entailment? What I noted in lecture 3 (slide 19) is that many medieval authors (possibly including Bradwardine) rejected the account in terms of truth-preservation. Rather, they said, the premises entail the conclusion if and only if things cannot be as signified by the premises unless they are as is signified by the conclusion. (This might appear circular, but maybe no more than the truth-preservation criterion, given that truth is defined in terms of signification).
    These are tricky issues, and I don’t claim to have a definitive answer to them all, but I’m delighted to have started a debate about them.

    Stephen Read

    April 19, 2012 at 12:01 pm

  3. Apologies for the typos. But in the second paragraph, something went badly wrong with the software, when I typed ‘left angle bracket p right angle bracket entails left angle bracket q right angle bracket’ and it came out as entails “. Perhaps that sentence will come out more readably as:

    P2 and BP say that if ‘p’ entails ‘q’ and s says that p then s says that q and ‘p’ says that q (here forming names of sentences).

    Stephen Read

    April 19, 2012 at 12:08 pm

    • Hi Stephen,

      This will have to be quick as I’m on a break between classes. I guess I won’t be able to give a proper response until I’ve looked at the references you supplied.

      But I have one quick question: Last week we had two interesting talks by Brendan Larvor (Hertfordshire). Both were in some sense an attack on formal reasoning – the second was about non-formal reasoning in mathematical practice (he’s quite influenced by Lakatos). Anyway he convincingly argues that much mathematical reasoning is material, and cannot be reduced to inferential relations between propositions. He’s particularly interested in the role of diagrams and symbols in mathematical reasoning. [there are some inferences that we can only make once we’ve introduced brackets into our language, but once we have brackets it is easy to see the inference]. Another example of a material argument: A claims: A woman cannot be a doctor. A woman can refute this claim by becoming a doctor.

      Anyway – thinking about your talks in the light of his talks – I’m wondering whether you think that Bradwardine’s logic can be (fully) formalised? One might think that ‘signification’ is not something that can be fully cashed out formally. So for example one might think that smoke signifies fire. And this is not primarily a relationship between two propositions. I don’t know how you would answer this question. But if Bradwardine’s logic is not attempting to be fully formal logic, this may explain some of the misunderstanding between us. So I’m wondering whether you are ultimately thinking of Bradwardine as offering the tools for developing a more plausible formal logic, or whether you think that his logic is ultimately nor fully formalizable (in the way, say, Frege-Russell logic is)? Are you trying to compete directly with these guys, or suggesting that we play a different ball game?

      Lucas Thorpe

      April 19, 2012 at 1:14 pm

  4. A similar puzzle is discussed by John Buridan in the 8th chapter of his Sophismata. In sophism 8, he considers the mixed liar:

    “Socrates utters this proposition: ‘Plato says something false’, and none other, and, conversely, Plato utters this: ‘Socrates says something false’, and none other.”

    The initial problem is that there is no way to distinguish these when determining truth values: “for there is no reason why Socrates’ proposition should be true or false rather than Plato’s, or conversely, for they are related to each other in exactly the same way. Therefore, if one is true, then so is the other, and if one is false, then so is the other.”

    But then another participant, Robert, arrives, and

    “along with Socrates, Robert says that Plato says something false, and I also posit that Socrates and Robert say these propositions with the same intention and they think they say something true, for they think Plato says: ‘God does not exist’. Then it is clear that Socrates’ proposition and Robert’s proposition are entirely alike, both in utterance and in intention, both for the speakers and for the listener’s; but Robert’s proposition is true, since we posit that Plato says something false; therefore Socrates’ proposition is also true.”

    (And then John appears, and he wants to contradict Socrates by saying that Plato does not say something false…)

    Buridan’s analysis of this is quite interesting and highly recommended!

    (Quotes from G. Klima’s translation of the Summulae de dialectica (Yale, 2001), p. 971).

    Sara L. Uckelman

    April 19, 2012 at 5:42 pm

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