Does Wittgenstein's Tractatus establish serious bounds for discussions of the supernatural from a modern point of view?

13

2

In today's mathematics, we have many variants of logic (propositional, first order, higher order, fuzzy logic, etc.). These are all self-consistent formal systems that are based on some set of axioms.

In Wittgenstein's Tractatus, he demands a logical structure for thoughts and basically says that only sentences that mirror such thoughts are valid.

However, it seems to me that he assumes there is one and only one real logic after which our thoughts can be ordered. On the other hand, in principle, the different logics could have been available to Wittgenstein before 1920.

I don't know if his considerations survive to the present day. I wonder if these problems have been discussed by other philosophers, and maybe even resolved. In particular, I'm curious what the modern relevance is of Wittgenstein's early claim regarding the usefulness of discussions about the supernatural.

Nikolaj-K

Posted 2012-04-01T11:29:01.853

Reputation: 1 125

These seem to me two different questions: (1) Universalist conception of logic vs. logical pluralism (2) Relevance of TLP to today's antimetaphysics. (Did I understand you correctly?) Quick comment regarding the first question: The existence of different logical systems does not force you to embrace logical pluralism. Quine's stance regarding the primacy of classical first order logic is a good example for this.

– DBK – 2012-04-01T20:14:30.377

@DBK: (I signed in from another account when I asked this) Yes, that's true, these are actually two issures. But the second would be to broad if I wouldn't explain where my motivations to ask it come from. I'm interested in both subjects, but I really only ask the second question with respect to the problems of the third. Btw. ich bin auch Wiener ;) – Nikolaj-K – 2012-04-02T08:33:56.060

@CodyGray: Okay, thanks Gray. Although sadly, in a physicists community it's not always a good move to disclose that you read books on philosophy. – Nikolaj-K – 2012-04-17T07:14:09.510

Really? How weird. :-( Sorry if that's not what you wanted then. I can delete your account on this particular site if you want to keep things hush-hush... – Cody Gray – 2012-04-17T07:16:02.800

@CodyGray: Haha, no it's good. I don't identify with internet accounts. And well, there are some people who think philosophy is useless, since I guess they espect a direct problem solving approach from all fields. But Wittgenstein is probably on the edge. – Nikolaj-K – 2012-04-17T07:20:29.190

Answers

3

In today's mathematics, we have many variants of logic (propositional, first order, higher order, fuzzy logic, etc.). These are all self-consistent formal systems that are based on some set of axioms.

True. Furthermore, some logics are classical, some are non-classical, and some are deviant-- but let's not let that detain us here.

In Wittgenstein's Tractatus, he demands a logical structure for thoughts and basically says that only sentences that mirror such thoughts are valid.

And, in the Philosophical Investigations he famously walked back from the absurdity of this claim, pointing to all kinds of thoughts and sentences that do not take the form of propositions. This does not mean that we necessarily need to follow the late Wittgenstein in rejecting the early Wittgenstein, but we should at least be aware of the critique, and be prepared to respond to it.

However, it seems to me that he assumes there is one and only one real logic after which our thoughts can be ordered. On the other hand, in principle, the different logics could have been available to Wittgenstein before 1920.

I don't recall him addressing this at all, nor do I see what the substitution of a different logical formalism would have on his project. Do you have a concrete example where the use of a different logic would result in a significant change to the system of the Tractatus? Or is this merely idle speculation?

I don't know if his considerations survive to the present day. I wonder if these problems have been discussed by other philosophers, and maybe even resolved. In particular, I'm curious what the modern relevance is of Wittgenstein's early claim regarding the usefulness of discussions about the supernatural.

Wait, what? How does "the supernatural" come into play here at all? At the moment, this appears to be a gross non sequitur. If you think there is an argument to be made which would link the substitution of non-classical or deviant logics into the schema of the Tractatus and "the supernatural", go ahead and make the argument-- I don't think you can expect us to connect those particular dots without a lot more to go on.

Michael Dorfman

Posted 2012-04-01T11:29:01.853

Reputation: 22 863

(i) A different logic B would make any conclusion in his logic A, which couldn't be drawn in B not a valid in B. Therefore different underlying logics (if they really differ) mean different legal thoughts. (ii) The supernatural is related because according to Wittgenstein many concepts, which relate to e.g. god (e.g. Good and evil) are not to be talked about. The question asks to what extend it is today reasonable to discard all the things he wants to discard on the last page of the book. PS: I really like the "What would you like to know?" question on your page, given that one can't answer. – Nikolaj-K – 2012-04-17T08:49:45.883

>

  • may be true, depending on the logics, etc.-- this is why I asked the OP for an example; 2) Wittgenstein did not identify the supernatural as "that which must be passed over in silence"-- furthermore, his later work consisted largely of attempting to say precisely those things. re: P.S.--- Glad you liked it, I chose it (in part) because of the number of ways it can be read.
  • < – Michael Dorfman – 2012-04-17T09:13:54.190

    @MichaelDorfman: I interpreted "the supernatural" as "the divine" which is not really all that supernatural, it doesn't require lightning smiting down sinners. The late Wittgenstein change of heart is just him renouncing logical positivism, which is unfortunately easy enough for him, because he was never really involved in the heroic task of erecting the modern structure of logic and computation in the first place, he just happened to be the go-to guy when people wanted to find a philosophy which works with predicate calculus. So Wittgenstein can sell out the ideas when fasions change. – Ron Maimon – 2012-04-18T03:32:05.030

    ... regarding the issue of predicate definition of all statements, you can do it, but the predicates won't resemble anything intuitive. A statement like "Hey, that's my grandmother there!" Can be formalized by a facial recognition software that recognizes your grandmother as well as you, and then there is a first order sentence that tells you whether this face-recognizer is seeing grandma. The naive view that most discourse can be easily formalized in intuitive recognizable first-order predicates is likely less true, considering the difficulty in programming computers to do everyday tasks. – Ron Maimon – 2012-04-18T03:34:18.443

    @RonMaimon: I didn't interpret "the supernatural" as "the divine"-- I assumed that if the OP had meant "the divine", he would have said so. Personally, I find the late Wittgenstein to be far more than the "selling out" of "the heroic task" of logical positivism; rather, it is a recognition of the (crippling) limitations of that project, and an attempt to go beyond it. Furthermore, I believe that Wittgenstein makes an indisputable case that there are statements that are not predicate definitions-- one need look no further than the Sraffa gesture. – Michael Dorfman – 2012-04-18T06:35:41.817

    @MichaelDorfman: To give this gesture logical positive form, as a first order predicate sentence, you need a good enough AI to do visual images and extract gestures, and understand disgust from these. Then the embeddability of computation guarantees that the AI's program's output can be expressed as a (very long) logical sentence on the visual input. There are no "crippling limitations" of logical positivism, there are only barriers to understanding caused by lack of mathematical training among philosophers, and this includes Wittgenstein. – Ron Maimon – 2012-04-18T11:03:52.577

    Why would people believe something so simple looking as predicate calculus can express all of knowledge in the first place? It's not because it is obvious the "Sraffa gestures" (emotional gesticulation) can be encoded, it is because there is a proof that all of mathematics, including the structure of a computer, can be encoded. The universality of computation guarantees that any observed physical computation can be too (you might need to add stochasticity--- a true random number generator), and it is a coincidence that many of the simplest questions beloved of philosophers... – Ron Maimon – 2012-04-18T11:08:45.940

    like precise language processing, or relationships beween objects, can be easily encoded in first order logic. There is no reason that complex things, like day-to-day life, can be so easily encoded, and in fact, AI projects are the formalization of day-to-day life, and they have the hardest time in the simplest tasks, not the traditionally most sophisticated ones. The early Wittgenstein was getting his philosophy from the Zeitgeist, as young people do, and it was the people building the Zeitgeist who understood these things. As he got older, he realized just how counterintuitive this idea is – Ron Maimon – 2012-04-18T11:10:04.707

    That it is still true, despite being counterintuitive, is a testament to those philosophers who understood computation and built positivism, not to Wittgenstein, who didn't ever fully understand it, and sold it out in later life. – Ron Maimon – 2012-04-18T11:12:45.873

    1Visual images and gesture extraction isn't the point-- it is that the gesture does not translate simply to "disgust". Furthermore, meaning is always understood within a context, and the context is never saturated. There is more to the world than mathematics or computation. and many things which resist formalization. Finally, as far as I recall, Wittgenstein was not by any means lacking mathematical training. – Michael Dorfman – 2012-04-18T11:25:25.403

    1Also - even if 'something so simple looking as predicate calculus can express all of knowledge in the first place' were true (which is dubious as Michael notes), are we assuming there is something defective in natural language? That the formal expression is the correct one? Just what is it about the formal expression that makes it better than the original, informal expression? 'I asked him for a breadknife, and he gives me a razorblade because it is sharper'. – adrianos – 2012-04-20T19:44:50.120

    @MichaelDorfman: Wittgenstein wasn't particularly mathematical--- he had enough training to know FOL, but not the compelling arguments for computational universality. This is why he could sell it out. The formalization of contexts and backgrounds requires a background computation of large complexity, and it is naive to think that the formalization will resemble first order sentences about hard relationships. But you can code any computational model, including a full biological one, as a first order sentence. The sentene would be enormously long, and bear no relation to the intuitive meaning. – Ron Maimon – 2012-04-22T04:13:17.390

    @adrianos: This is a misunderstanding of the type of sentence one is talking about: the FOL sentence corresponding to "this JPG is of my grandma!" is a horrendously complicated sentence on pixel-values that encodes the running of a facial recognition software. The formal expression is only better because it is formal, and precise. If you have a good language processing program, natural language is equally good. The defective thing in natural language is that it makes Hegel look smart. Obscurantism and meaning-shifting is encouraged as poetic expressions, and this is the opposite of knowledge – Ron Maimon – 2012-04-22T04:15:32.770

    Meaning-shifting is not the opposite of knowledge; it is a recognition that the map is not the territory, that words rarely align perfectly with meaning, and that words and contexts shift over time. – Michael Dorfman – 2012-04-22T09:55:16.353

    1@RonMaimon Can you explain why formal and precise is "better"? Wittgenstein's point about the knife/razor shows that 'better' is purpose relative. Similarly, what exactly is imprecise about 'this JPG is of my grandma'? Isn't the point of saying it just to say who the image is of, or perhaps to make a joke? How does your formal language do that better than natural langauge? – adrianos – 2012-04-23T12:48:24.497

    2

    The existence of different logics is interesting, but not particularly relevant, because of Gödel/Turing universality. If you have a statement about possibilities, a statement in modal logic, you can encode it in a semantics about possible worlds, in a first order logical form about an expanded universe of discourse (see Kripke semantics). Further, if you have a "fuzzy logic", you can speak about it in an appropriate axiomatic mathematical system which includes real numbers, and makes a map between propositions and fuzzy values.

    There are also Bayesian probability calculi which can be thought of as a different logic, some people regard quantum amplitudes as a logic, while other schemes regard permission as in the logic. What you put in the logic and what you put in the axioms is largely up to you.

    But the main point is that the ordinary first order logic is complete, it will produce any logical consequence of any axioms, and this was proved by Gödel. This means that if you have a mathematically precise description of some other logic, you can always talk about this logic in terms of first order logic, and consider the other logic as axioms on top of first order logic. This is not a natural point of view, but it is a possible point of view.

    The universality of first order logic is the logical analog of Turing universality--- that a finite complexity computer with unbounded memory can simulate any other computer with suitable programming. The formalism of logic is like the instruction set, the axioms are like the instructions of the program, and the deductions are the running of the program. A Turing machine can do Gödel deduction (you can program a computer to deduce in first order logic) and Gödel deduction can describe a computer, so the two results are essentially equivalent, and anything that can be stated in any coherent logical system is something that is meaningful for a computer to analyze and interpret.

    So there really is only one type of logic, and Wittgenstein is mostly right. Although it is a mistake to attribute this to Wittgenstein, who was not as mathematically or logically precise at the mathematicians and logicians of the early 20th century in whose footsteps he followed, not as precise, nor as iconoclastic, as Russell, and did not contribute commensurately to the formal developments as Russell did. Further, one may say that Wittgenstein's ideas have a sonority and a lack of mathematical precision that leads those in technical fields to perhaps use the phrase "running one's mouth". The proper attribution of first order logic, the recognition of its importance in philosophy, and the associated logical positivism, better belongs to Hilbert, Frege, Boole, Quine, Gödel, Turing, Russel, Whitehead and others who come before. It continued with those who built the Vienna school, including Carnap, which made logical positivism the ascendant philosophy until the 1970s.

    The use of predicate language to remove ambiguity, and the thesis that all statements should be formulated in some predicate language about precise observable criteria, is the central tenet of logical positivism, which flourished in the mid-20th century, but took a beating in the 1970-90s.

    Ron Maimon

    Posted 2012-04-01T11:29:01.853

    Reputation: 1

    @RonMaimon

    "it will have a well defined computer program to do deductions"

    This is a property of logics known as computability and closely related to decidability. I'm not sure what you mean by "well defined" here, but since neither first order logic nor ZF is decidable, I don't know why an imbedded dialetheistic logic should be presumed to be decidable. Do you have any reference to a place where a dialetheistic logic (such as Priest's Logic of Paradox) is proven to be decidable? I would be very interested to see such a proof. Thanks!

    – Dennis – 2013-01-07T18:06:42.070

    @Dennis: The only point is that if your logic makes sense as a system, then it is embeddable inside a first order system, by just formalizing the terms in ZF. It's like universality, once you have one computer with one instruction set, you can simulate any other computer, and that computer can simulate yours back. Likewise, once you have one logic, the standard choice is first order logic, you can simulate any other, by modeling it with axioms, and vice versa, the other logic can include first order logic, or at least should. – Ron Maimon – 2013-01-22T20:53:52.310

    For Priestly's specific logic (I looked at Priestly's "The Logic of Paradox"), the tautologies are given by 3-valued truth tables, true, false, paradoxical, and the decision algorithm for deciding tautologies by truth table is given algorithmically in the paper (the matrices for the elementary logical operations are all given), then the deduction steps are spelled out in a list of transformation rules on page 230, which means you can write a program to deduce, so it's computable. The system includes first order logic as a subset, so it is Godel-complete (just make true/false axioms). – Ron Maimon – 2013-01-22T20:57:11.190

    1Thanks for clearing up some of the logic points. The other (main) question remains to be answered. And I have yet to understand how first order logic encompasses the others... I'll look into it. And it's funny, I really only wrote the "On the other hand, in principle the different logics could have been available to Wittgenstein before 1920." line only because it seems to me that he basically tries to translate Gödels semantic considerations to truth of statements in common language. In any case, I don't value truth as much as many others, so I regard many philosophical questions as sensible. – Nikolaj-K – 2012-04-02T08:44:43.347

    How does ordinary first-order logic deal with paraconsistent logics such as dialetheism? – Michael Dorfman – 2012-04-17T08:37:10.090

    1@MichaelDorfman: You write down the axioms of Peano Arithmetic, or some set theory, say, ZF, in first order logic, so that you can talk about mathematics. Then you define the statements of dialethistic logic as text strings (integers), and the deduction rules as manipulations of these (recursive functions, i.e. computations). If the dialethistic logic is well defined, it will have a well defined computer program to do deductions, and this means it can be modelled in PA or ZF or any other reasonable axiom system. Now any statement about the other logic is a first order statement in PA. – Ron Maimon – 2012-04-18T03:27:21.430

    1

    However, it seems to me that he assumes there is one and only one real logic after which our thoughts can be ordered. On the other hand, in principle, the different logics could have been available to Wittgenstein before 1920.

    Wittgenstein's early and later view of logic entails that there cannot be multiple logics. A calculus is a means of transforming symbols, and there can be as many of these as one has transformation rules. Logic however, in Wittgenstein's sense of the word, is different. He regarded propositions as bipolar (Tractatus) and, later, bivalent (Investigations). He rejected Brouwer's view that there are propositions with no truth value and Lukasiewicz's multi-valued logics (in the 1932-1935 Cambridge lectures). Their systems are calculi which specify alternative transformation rules, but these are not the rules of language and not, therefore, the rules of logic in the required sense. A language can be governed by these rules only by altering what it means to be a proposition, and therefore what it means to have a language. Logic, proposition and language are all internally related concepts.

    I don't know if his considerations survive to the present day. I wonder if these problems have been discussed by other philosophers, and maybe even resolved.

    These considerations have very much survived. Michael Dummett in particular has argued that alternative logics (such as dropping LOM or multiple truth values) entail alternative metaphysics. This has led to much discussion about how we could build a 'theory of meaning' for language such that the answers to metaphysical questions would all be determined by the right meaning theory. This actually goes against both the early and later view of Wittgenstein that logic does not entail any metaphysics at all, for the propositions of logic do not correspond to any state of affairs. They are rules which are tautologies (in the Tractatus) or grammatical rules (Investigations).

    There is a modern resurgence of interest in metaphysics that is profoundly un-Wittgensteinian. The problems have not so much been resolved as exacerbated, and a return to Wittgenstein's penetrating solutions (in the later philosophy) would be very helpful.

    In particular, I'm curious what the modern relevance is of Wittgenstein's early claim regarding the usefulness of discussions about the supernatural.

    There are a number of comments on the 'mystical' in the Tractatus which are related to the doctrine of showing what cannot be said, but this doctrine was abandoned by the later Wittgenstein as confused. There is no such thing as ineffable metaphysics. Those modern philosophers however, like Dummett and Davidson, who have revived the old Tractatus approach to philosophy, could well be said to be committed to mystical, or supernatural views, about the nature of the world, reality etc. I do not see, though, that they have solved any 'problems' in these areas any more than Plato, Aristotle, Aquinas or Descartes solved them.

    adrianos

    Posted 2012-04-01T11:29:01.853

    Reputation: 1 212

    1

    There is a large literature on this: priest has two relevant chapters in his doubt truth to be a liar.

    It is true that there are many logics, all of which are more suited to some purposes than others. However, this does not preclude there being one true logic in W's sense of the term.

    The thing to bear in mind is what the purpose of logic is. The philosophically interesting one, which W plausible held, is to capture logical consequence (See Dummett's Justification of Deduction for an argument that this must be prior to any other concept).

    Hence, if we are not pluralists about logical consequence (Beall and Restall are an example of such pluralists) we should think that there is a single notion of logical consequence we are attempting to capture. The logic that does this would be the one true logic.

    The other logics we have are appropriate for other purposes, or where the domain allows us to add further restrictions on the consequence relation. But from the mere fact that there are different logics we are unawarranted in concluding that there is no one true logic.

    I think this is all irrelevant to concerns about the supernatural. One should always, in my view, be careful about reading too much into logic -see for example those that misuse Goedel's Incompleteness Theorems.

    Carlo Lori

    Posted 2012-04-01T11:29:01.853

    Reputation: 422

    Seems like you want to believe in one true logic, but I feel like that would could never address notions such as morality - they are supernatural enough from that perspective, I think. (Hard to believe the question was asked 4 years ago, pew) – Nikolaj-K – 2016-04-13T21:39:30.393

    Not necessarily: my point was merely that the existence of multiple formal systems does not show that there is no one true logic. What do you mean about addressing notions such as morality? – Carlo Lori – 2016-04-13T21:50:35.670