Presentation on theme: "Catherine Legg What Achilles Did and the Tortoise Wouldn’t."— Presentation transcript:
Catherine Legg What Achilles Did and the Tortoise Wouldn’t
Agenda 1. Background: Semantics Metaphysics in Contemporary Analytic Philosophy Truth: Metaphysical Realism vs. Conventionalism Validity - ? 2. Carroll’s Fable of Achilles and the Tortoise What does this fable teach us? How might the puzzle be solved? Logical action: the “Hardness of the Iconic Must” 3. Peirce’s Sign Theory Icon, Index, Symbol Icons share properties with their objects: partial identity 4. What Peirce’s Sign Theory Has to Say re. Carroll’s Fable Partial identity between sign and required inference act 5. Semantics-Driven Metaphysics: A Reprise Beyond Metaphysical Realism and Conventionalism
1. Background: Semantics Metaphysics in Contemporary Analytic Philosophy Representationalist model of language: the primary purpose of language is to state “facts” in mind-independent reality. This naturally leads to a certain metaphysical realism: Term in language, e.g. ‘”cat” Thing in world DENOTES, REFERS TO Proposition in language, e.g. “The cat is on the mat” STATES Fact in world Dyadic structure Account of real objects No account of interpretation
But what makes it the case that a proposition is ‘fact-stating’? Early (strict) logical positivism: statements have “literal significance” by virtue of offering empirical hypotheses: Thus “the cat is on the mat” is literally significant because an appropriately cat-on-mat type experience might be had in relevant situations. However crisp criteria for genuinely empirical hypotheses were rather harder to find than logical positivists initially supposed. Quine (more purely semantic): a proposition is fact-stating if its bound variables have values: Thus “the cat is on the mat” is literally significant because in x(Cx & Oxm), suitably interpreted, x binds to George. George
Many philosophers find this view of language unsatisfying. This relation of ‘denoting’ or ‘stating’ seems too abstract, ‘supernatural’. (Putnam: ‘noetic rays’ between words and world) It is tempting to deny the reference, producing a conventionalism, according to which terms do not denote, but have other socially sanctioned and taught functions: “That is not a very funny joke” “John Key is the Prime Minister of New Zealand.” “Your RAE score is…..” Account of interpretation No account of real objects
Debates between metaphysical realism and conventionalism are usually fought out with respect to truth. But we don’t just use language to state facts. We also use language to reason. The study of valid reasoning is called logic. What (if any) metaphysics underlies this logic? Representationalists often talk of truth- makers for our truths: entities whose very existence somehow makes truths true. Are there ‘validity-makers’? If so, what could they be?
2. Lewis Carroll (Charles Lutwidge Dodgson) 27 January 1832 – 14 January 1898 English author, mathematician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems: “The Hunting of the Snark” and “Jabberwocky”. But he was also, of course, an extremely talented logician.
Carroll’s Puzzle of Achilles and the Tortoise The great warrior and his friend with a shell together examine a clearly valid argument. Something like this: ARG) Socrates is a human being. PREMISE: P1 All human beings can be killed. PREMISE: P2 Therefore Socrates can be killed. CONCLUSION: C Most of us* see a pattern in ARG) which makes us inclined to do something. What? If we believe P1 and P2 are true, infer that C is true too. But how does this work? What makes it happen? And what do we mean by make? * English speakers who are rational
ARG) Socrates is a human being. PREMISE: P1 All human beings can be killed. PREMISE: P2 Therefore Socrates can be killed. CONCLUSION: C This looks good on the page. I do believe P1 and P2. But I don’t see why I have to believe C. Please explain ?! You’re kidding me. What do you mean, you can’t see why? It’s totally obvious! No actually, it’s really not obvious to me. I’m a tortoise so I’m a little slow. Please explain it to me. Good grief! Well it happens to be objectively true that: If P1 and P2 are both true, then C is true also. So we can add this to the argument.
ARG) Socrates is a human being. PREMISE: P1 All human beings can be killed. PREMISE: P2 If P1 and P2 are true then C is also. PREMISE: P3 Therefore Socrates can be killed. CONCLUSION: C Tortoise Achilles Can you see it now? Um, well, no actually. I accept P1 and P2, and P3. But I still don’t see why all of that means I have to accept C. I’m a tortoise so I’m a little slow. Please explain it to me. You’re kidding me!!! No I’m not, honestly It looks as though something else needs to be added to the argument…
ARG) Socrates is a human being. PREMISE: P1 All human beings can be killed. PREMISE: P2 If P1 and P2 are true then C is also. PREMISE: P3 If P1, P2 and P3 are true then C is also. PREMISE: P4 Therefore Socrates can be killed. CONCLUSION: C Tortoise Achilles Can you see it now? Um….. …to be continued. (What should Achilles have said to the Tortoise?)
It adroitly highlights both the existence and the puzzlement of a certain feature of our necessary reasoning which representationalism encourages us to miss: its link to action. The fable exposes a bindingness on the actions of rational agents (specifically their inferencing) which appears a-causal, yet nonetheless intriguingly compelling. Here one glimpses an internalism about logic, whose analogy to metaethics is arguably no accident. If one is not motivated to act by logical norms, it seems that one does not fully understand them. Via his recalcitrance the Tortoise usefully makes the bindingness of valid argument on action normally invisible due to its ubiquity visible. What does this fable teach us?
The disparity in understanding between Achilles and the Tortoise cannot be remedied by further explanatory signs. For as Achilles’ extra conditionals tend to infinity, no progress is made. But if the Tortoise is not lacking further signs in his failure to grasp the relationship between P1 and P2 and C, what is he lacking? He is surely lacking something! He is failing to see a structural isomorphism shared by the original sign (ARG)) and an act (inferring C from P1 and P2). A structural isomorphism between a written sign and an act might seem to be a curious idea. And how can we explain Achilles’ grasp of it? Arguably, by recourse to a kind of sign which current representationalist semantics overlooks. How might the puzzle be solved?
Charles Sanders Peirce Sep. 10, 1839 – April 19, 1914 American philosopher, logician, mathematician, scientist… In 1934, the philosopher Paul Weiss called Peirce: “the most original and versatile of American philosophers and America's greatest logician”. Peirce placed logic within the broader context of a theory of signs, or semiotics.
unit (in itself) correlate (to another) medium (bringing into relation) 1 2 3 REPRESENTAMEN e.g. “cat” OBJECT INTERPRETANT Uses of “cat” to refer to cats The structure of the sign Account of real objects AND account of interpretation
(icon) index symbol 1 2 3 Picks out its object by resembling it. E.g. map of NZ Picks out its object by brute denotation (direct reference) E.g. “Gordon Brown” Picks out its object by arbitrary convention E.g. “train” Three kinds of sign (Mixed forms are most usual) This kind of signification best suits discrete particular objects. Metaphysical realism arguably treats all signification on this model This kind of signification best suits general terms. Conventionalism arguably treats all signification on this model What does this kind of signification best suit?
An icon and its object share a property (thus partaking in partial identity) Since indices serve as pure pointers, whatever internal properties they have are irrelevant to their signification. Symbols have nothing in common with their objects by definition since their establishing convention is arbitrary. But as icons represent their objects by resembling them, the basis of that resemblance must be some shared property. Thus Peirce wrote: This claim is made within a broad framework of scholastic realism (realism about universals) “…a pure icon does not draw any distinction between itself and its object… whatever it is like, it in so far is.”
How do we apprehend the validity of this argument? Plausibly, by drawing a kind of diagram in our heads, something like this: This diagram is an iconic sign insofar as the parts of an icon, in Peirce’s words “…bear the same relationship to one another as the parts of the object they represent”. The object in this case is logical form. ARG) Socrates is a human being. PREMISE: P1 All human beings can be killed. PREMISE: P2 Therefore Socrates can be killed. CONCLUSION: C All things that can be killed All humans Socrates is in here So he can’t be out here
4. What Peirce’s Sign Theory has to say about Carroll’s Puzzle Written signs such as ARG) represent logical form to the human mind so that it can be understood and acted upon. And what more could we ask to say that a system of signs has genuine content? Yet ARG) does not state logical form in any way understood by contemporary mainstream philosophy. ARG) does not denote logical form in a metaphysical realist sense. There are no further objects (validity-makers) picked out, over and above the objects picked out by ARG)’s individual sentences (i.e. Socrates, humans, dead people). ARG) does not fit the conventionalist picture either, though, because logical form does not rest on, and cannot be altered by, arbitrary convention. Its necessity is directly seen. (I call this “the hardness of the iconic must”.)
And insofar as the implications for action are isomorphic with the written sign, these are directly apprehended also. Thus there is an important sense in which the Tortoise fails to read the argument at all. He reads and accepts P1, P2 and C, but he fails to see the structure which upon acceptance of P1 and P2 compels recognition that C must follow. And it is this (iconic) structure that makes the sign ARG) what it is. Thus, further, what explains the intriguing bindingness between sign and inference which Achilles grasps but cannot explain to the Tortoise is identity. What else could explain it? DD
We may understand Quine’s ‘bound variable’ criterion of ontological commitment in Peircean terms as an attempt to place the full burden of representation on indexical signs. This leads realist philosophers to ask questions such as: “Does term X denote an existent object?”, and it often seems hard to answer “yes” for key terms in manifestly important human discourses [e.g. “the Good”, “God”….] On the other hand, we have seen that those unsatisfied with metaphysical realism’s problematization of such terms often counter with a conventionalism arguing that the term does not denote but has some other socially sanctioned and taught function. We may see such conventionalism in Peircean terms as trying to understand all representation as symbolic. 5. Semantics-Driven Metaphysics: A Reprise
Metaphysical realism and conventionalism are too often taken for polar opposites in philosophy: an argument against metaphysical realism is frequently assumed without question to be an argument for conventionalism, & vice versa. This dichotomy is false. A third kind of representation exists, which does not consist in brute denotation or arbitrary convention, but presents structure directly to the mind’s eye. It is iconic It is barely glimpsed in formal semantics today. Yet it is this kind of sign that represents logical form – hardly a trivial part of our conceptual scheme. If we could only recognize that the symbol, index and icon all have a unique, irreducible semantic role, and reality correspondingly comprises real habits, real particulars and real structures, we could take an unanticipated leap towards understanding this most contested term.