Mini Symposium on Truth: Quid Est Veritas?

by E. John Winner


Most of what I know about logic I learned studying Aristotle, Kant, and Peirce.  However, I did take an introductory undergraduate course in symbolic logic.  The surprising take-away was that with a properly formed compound sentence, one could assert just about anything, and still hold the assertion, as a whole, to be true.  In short, the standard symbolic logic course of the 1970’s was an indoctrination in epistemic relativism, and in a certain kind of rhetoric.  A simple course in truth tables can contribute to public skepticism, which can then be manipulated rhetorically. So much for truth! [1]


In 1963, Edmund Gettier caused a minor controversy with a brief paper [2] demonstrating that certain rules governing the truth values of conjunctive propositions and disjunctive propositions effectively undermined the understanding of knowledge as “justified true belief,” for which he provides the generally accepted formula:

S knows that P IFF

P is true,

S believes that P, and

S is justified in believing that P.

“Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:

(d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

(…) Proposition (d) entails:

(e) The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true.

The evidence is that the prospective employer has told Smith that Jones would be hired, and for reasons unknown, Smith has counted the change in Jones’ pocket.  Unfortunately, the employer changes his mind and hires Smith, who has apparently forgotten that he himself has ten cents in his pocket. The proposition he believes before the hiring is announced is true, but not based on the logical justification he presumes for it. And if he doesn’t even know that he has ten cents in his pocket, he can no longer believe (e), so obviously this true proposition cannot be knowledge.

In the present case (known as “Gettier 1”), we immediately notice the clear lack of any sort of temporal verification process that we would expect in the real world.  E.g., in the real world, at time X-1 (prior to the hire being announced), Smith would not know that “the man hired will have ten coins in his pocket.”  He only has a hypothesis that this will be the case.  Even if at X+1 (after the hire has been announced) he discovers the ten cents in his pocket, and thus may rightly claim that “the man hired has ten coins in his pocket,” he may also be aware that this had no dependence on his prior beliefs that Jones would get hired and Jones has ten coins in his pocket.  The logical structure, reassuring Smith of his claim to knowledge, has completely broken down.  But it was wholly artificial anyway, so such was inevitable.

The world of which Gettier writes is not the real world but a possible world, governed by the rules of a given logic.  A real world Smith would not be too troubled about whether he holds a “justified true belief.” He’s just happy to get a job!  And that he has ten cents in his pocket … well, there’s nothing much one can buy with ten cents these days.  Maybe he’ll feel charitable and give it to Jones.

But in the logically possible world of the example, none of this matters.  Motivation, emotional response, charitable behavior…all of these count for nothing.  (Any method of verification or falsification would matter IFF we accept that Smith begins with a hypothesis, not a knowledge claim, and this isn’t allowed in terms of the given example.)  Of course, Gettier doesn’t have to explain all of this in the context of his assumed readership.

The community of epistemologists for which Gettier was writing, trained in formal logic and having inherited many of their questions from the project of Logical Positivism, would have understood that Gettier’s cases are not problematic because of their “real world” application, but because of the formal-logic problems they pose.  We can see this when Gettier remarks that knowledge is understood as “someone’s knowing a given proposition.”  Note that what is known (or not) is not a thing, nor an idea, nor a theoretical model, nor anything other than a statement.  This means in the case given that what Smith claims to know is not that the man getting hired has ten coins in his pocket, but the proposition “The man who will get the job has ten coins in his pocket,” which turns out to be true; but since it is derived from false inferences, Smith’s initial belief has no logical ground, and cannot be knowledge.

We can see this problem better in Gettier’s second example (“Gettier 2”):

“(f) Jones owns a Ford.

Smith’s evidence might be that Jones has at all times in the past within Smith’s memory owned a car and always a Ford and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:

(g) Either Jones owns a Ford, or Brown is in Boston.

(h) Either Jones owns a Ford, or Brown is in Barcelona.

(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is entailed by (f).”

Here Gettier gives an empirical justification for (f); but the only justification for (g), (h), or (i) is the logical entailment made viable by its disjunctive truth-value:

A          B          A or B

T          T          T

T          F          T

F          T          T

F          F          F

(As long as one statement is true, the proposition is true.)

“But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.”

What Smith asserts is not who owns a Ford, and who is in Boston/Barcelona/Brest-Litovsk; he asserts the proposition “Jones owns a Ford OR Brown is in Barcelona,” which just happens to be true, and is empirically justifiable.  That the first statement is false and any justification of the second statement are both unknown to him, however, so his assertion cannot constitute knowledge.

Notice that this also has little real world applicability.  Why would a real world Smith be doing this?  Is he making a bet?  No, but logically-possible-world-Smith is testing the relationship between what logic says should be the case, and what the logical principle of knowledge says cannot be the case.  The problem has to do with the formal structure of knowledge claims.


All of these problems can be traced back through the tradition that – thanks to promotions by Bertrand Russell and others – finds its main progenitor in Gottlob Frege.  One of Frege’s key texts influencing that tradition was “On Sense and Reference” [3], and one finds in it several strategic missteps that played a significant role in the ultimate failure of the Logical Positivist project.  Indeed, the very project itself was misguided.  The Logical Positivists seemed bent on developing a “logically perfect language,” through which mathematics and the natural sciences could establish their claims: mathematics through a purified, deductive logic and the natural sciences through theories composed of true sentences concerning empirical reality.  It never occurred to the Positivists (as it did to the Pragmatists) that mathematicians and scientists could develop their own logics and methodologies and their own languages for communicating their discoveries and inventions.  When physicist Richard Feynman famously dismissed philosophers’ claims to provide explanations for the physics of the post-Einstein universe, he may have been thinking of some phenomenologist’s obscure ontological ramblings, but his remarks apply equally to Russell and Carnap. [4]

But this project, embedded implicitly in Frege’s text, is not its worst strategic error.  That would be the decision to treat the sentential proposition as the principle bearer of truth, and the necessary object of logical analysis.  In the development of logic after Frege, this decision has had beneficial consequences, including the development of symbolic logic and formal logic and computing languages.  But this is a completely wrongheaded way to think of any language, including artificial or formal ones.  A sentence has little meaning outside the context of a paragraph, which may itself have meaning, but more often requires the even larger context of the whole text. And in any case, it will require the context of a community of readers and writers to even make sense of it (even using Frege’s sense of ‘sense’).

This is made evident in Frege’s decision to draw many of his sentences for analysis from the texts of history.  His remarks on the sentence “Napoleon, who recognized the danger to his right flank, himself led his guards against the enemy position,” is particularly embarrassing.  It takes Frege some three paragraphs to admit that there is an implication in the sentence that Napoleon’s recognition of the danger to his right flank motivates his decision to lead his guards against the enemy position.  Yet any reader of a history text in which such a sentence like this would occur would recognize it immediately and in passing.  The sentence does make a truth claim, but it is structured rhetorically.  Because of his refusal to treat the sentence structure as such, Frege’s discussion of it is hopelessly misguided.  The principle structure of historical texts is narrational and cannot be reduced to the sentences used to construct such narratives.    “Napoleon, who recognized the danger to his right flank, himself led his guards against the enemy position,” taken in and of itself, without the contextual narrative and without a proper accounting of its enthymemic structure, communicates little useful information.

Frege’s other major strategic error was to insist that propositions had a double referentiality: the “proper name” elements referring to entities and the proposition as a whole referring to a truth value.  If correct, this would mean that every true propositions refers to “the True.” Rereading “On Sense and Reference” specifically to discover Frege’s working definition of truth or “the True,” I find direct reference to either, so all we’re left with is the sense.  Given his discussion of the conditions determining the truth of the conditional “If the sun has risen, the sky is cloudy,” it seems clear he’s operating with the assumption of a correspondence theory of truth.  What “the True” might be can only be surmised as a world described entirely with true propositions.  Despite the very different logical approach, this would appear to be yet another attempt to achieve what Hegel termed Absolute Knowledge.  But whereas for Hegel this would require an elaborate encyclopedia in order to account for the historical development of this knowledge, for Frege the final achievement would be a precise and logically ordered dictionary, and a thin manual on the logically proper grammar with which to use it.


I’m not going into an elaborate discussion of the technical arguments that have buzzed for years around the topics raised so far. [4]  After all, I’m not a professional epistemologist, and I don’t come to these problems to try to make right of either Gettier or Frege or the justified true belief principle.  I really want to say that they are all wrongheaded, and even if they aren’t, I don’t see what use they can be to anyone without an interest in professional epistemology.  First, they are moot as far as our daily experience is concerned.  No one goes around popping out propositions in order to test their truth value!  No one cares if a sentence in a biography of Napoleon is logically well-ordered, merely that it is well written and persuasive, with enough documentation cited to be considered a feasible interpretation of events.  Second, as far as their implied usage is concerned – purified deductive processes for mathematics, logically precise language for use in scientific inquiry – I have already remarked that this implication is also mooted, by the evident fact that most mathematicians and scientists have achieved success in their inquiries without recourse to such devices. [5]

But what if we were to develop understandings of logic, of language; of inquiry and invention; even of mathematics, that were not intended to provide foundation to the sciences, but instead derived from the logic, methodologies and languages that the sciences have already themselves developed, in order to explain how they developed, and what their commonalities are; and how they might intersect with common languages so that they could be better expounded to the non-specialist?

[A]ll the followers of science are fully persuaded that the processes of investigation, if only pushed far enough, will give one certain solution to every question to which they can be applied. They may at first obtain different results, but, as each perfects his method and his processes, the results will move steadily together toward a destined center. So with all scientific research. Different minds may set out with the most antagonistic views, but the progress of investigation carries them by a force outside of themselves to one and the same conclusion. This activity of thought by which we are carried, not where we wish, but to a foreordained goal, is like the operation of destiny. No modification of the point of view taken, no selection of other facts for study, no natural bent of mind even, can enable a man to escape the predestinate opinion. This great law is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real.[6]

We shouldn’t get hung up on the “predestinate” character of the truth. Peirce only means that reality is waiting to be discovered, given the proper investigation.  Or rather, given the convergence of investigations within the community of investigators.

For Peirce, knowledge comes as the result of inquiry.  Truth is a product of the exhaustion of lines of inquiry that converge to the satisfaction of all those engaged in it.  These inquiries themselves effectively establish the logics of their methodologies, which can then be summarized through logical statements.  However, for the classically trained Peirce, these statements, as propositions and premises, are not the most basic material requiring analysis.  Rather, the argument is.  How sentences weave together convincingly was more important to him than their ability to stand up to logical parsing.  A good methodology, well explained, effectively constitutes a good argument.

Peirce was a quirky character.  He was very much an intellect of the 19th century.  He was known and respected by professional logicians (much more so than his contemporary, Frege), and he hoped to produce a “systematic philosophy,” much like that of Hegel’s Encyclopedia. But his commitment to a socially contextualized theory of truth (which, as social, inevitably instigates further inquiry) and to the Pragmatic Maxim (which defines a concept by the consequences and actions that it would impel or necessitate) and finally his development of semiotics (dependent on the contingency of context) as the ground of logic, left him spending much of his later writing working and reworking his ideas and their terminology.  Ultimately the implications of his Pragmatic theory of truth – and the logic and theory of knowledge it implied – had to be picked up by William James [7], and finally taken to the goal by John Dewey:

The present-day mathematical logician may present the structure of mathematics as if it had sprung all at once from the brain of a Zeus whose anatomy is that of pure logic. But, nevertheless, this very structure is a product of long historic growth, in which all kinds of experiments have been tried, in which some men have struck out in this direction and some in that, and in which some exercises and operations have resulted in confusion and others in triumphant clarifications and fruitful growths; a history in which matter and methods have been constantly selected and worked over on the basis of empirical success and failure.

The structure of alleged normative a priori mathematics is in truth the crowned result of ages of toilsome experience. The metallurgist who should write on the most highly developed method of dealing with ores would not, in truth, proceed any differently. He too selects, refines, and organizes the methods which in the past have been found to yield the maximum of achievement. Logic is a matter of profound human importance precisely because it is empirically founded and experimentally applied.” [8]

There is certainly a meaningful expression, ‘the truth’, but its meaning is probably found in the common language with all its rich history, rather than in epistemology.  That we ask witnesses in law courts to swear or affirm to tell the truth (as they best understand it) in the recollection of their memories (with real world legal consequences), tells us more about the meaning of truth than any mathematical, logical, or epistemological insistence that there is something that we can call “the True,” which our mathematics or sciences should ultimately refer to or produce.  [9]


[1] ‘Immigrants cross the border illegally and immigrants are employed instead of citizens’ is a truth-table verified true sentence; it just doesn’t remark immigrants who arrived legally, better qualified for the given jobs than citizens.



[3] See, for instance:

[4] For a brief survey, I suggest the article “The Analysis of Knowledge:” Ichikawa, Jonathan Jenkins and Steup, Matthias; Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.),

[5] I’m aware of the deep relationship between formal logic and mathematics developed over the past century. But once formal systems achieve studies of inquiry in their own right, they no longer require the kind of epistemological justification for them Logical Positivism promised.

[6] Charles S. Peirce, “How to Make Our Ideas Clear” (1878)

[7] “Any idea that helps us to deal, whether practically or intellectually, with either the reality or its belongings, that doesn’t entangle our progress in frustrations, that FITS, in fact, and adapts our life to the reality’s whole setting, will agree sufficiently to meet the requirement. It will be true of that reality” James, The Meaning of Truth, 1909:

[8] John Dewey, Reconstruction in Philosophy (1920; revised 1948), pages 137-138

[9] Worth listening to here are discussions between Richard Rorty and Hilary Putnam. Rorty would rather that philosophers stop using the word ‘true’ all together, while Putnam replies (correctly, I think) that it is too meaningful to be abandoned, but admits that “theories of truth,” even the Pragmatists’, are largely unsatisfactory.


  1. Hi EJ. An excellent read. I think if one is a naturalist about human rationality, there is a plausible hypothesis that that faculty is realised by manipulation and composition of simpler pieces, ie logical atoms. Artificial intelligence is one branch of engineering based on this approach (any neural network can be shown as equivalent to a “symbolic system” operating under a nonmonotonic logic). Those guys are interested in all kinds of logics (modal, adaptive, causal…).


  2. It would be nice if people would notice the reification of “truthfully” to “The Truth”. In ordinary conversation everybody relies on the correspondence theory of truth: ie that the map is not the territory so the question always arises whether the map truthfully depicts the territory. When a carpenter who has set up some forms for pouring concrete sends out the apprentice to “true” the forms he means for the apprentice to ensure that the corners are as close to 90 degrees (or otherwise as the blueprints prescribe) as can be contrived. To use the word “truth” to denote “The Truth” is to confuse the map with the territory. The territory is whatever it is, the map is whatever we say about the territory, and it is what we say about the territory which is capable of being true, or not, and in whatever degree, by virtue of how well what we say communicates a comprehension of what is. We may say as much as we know, or believe, and what we say may be more or less true, without it ever being The Truth, simply because what we say about what is is not in itself what is: the map is not the territory.


  3. EJ, obviously I don’t agree with you re: the merits of theories — and theorizing about — truth. Many matters of academic and intellectual import have little direct practical effect.

    Towards the end you say this:

    “For Peirce, knowledge comes as the result of inquiry. Truth is a product of the exhaustion of lines of inquiry that converge to the satisfaction of all those engaged in it.”

    This conflates matters of semantics with matters of epistemology. Everyone may have “converged” to their satisfaction, and their conclusion might nonetheless be false. This is why the pragmatist theory of truth is, if not a non-starter, hopeless.

    Liked by 2 people

    1. I agree with Dan here.

      I took a course on symbolic too, and there was not one single reference to epistemological matters in it, none at all. Given that all those p’s and q’s and r’s were true (or not) certain logical expressions containing p, q and r were true (or not).

      But that was it. The reasons why should be believed or assumed that p, q and r were true (or not) are totally unimportant for symbolic logic. Indeed, the meaning of the expressions “true” and “false” wasn’t even discussed, and not one single time the course tried to define what truth and falsehood “are”. True and false were just symbols.

      The resulting framework is useful in some contexts, like mathematics, if “true” and “false” are given their proper meaning within that framework. But in other contexts, other frameworks are needed. That’s a common situation: Euclidean geometry works fine if you’re building a bridge, but if you’re doing general relativity you need something else.

      As you notice, symbolic logic is a difficult framework to apply when you’re describing natural language. Seen from the point of view of symbolic logic, the reason is simple: natural language is full of ambiguities. The same sentence can often be translated into several different logical expressions. The correct translation usually isn’t given by the argument itself. A compelling argument in natural language, may therefore be slightly less compelling if you examine “the logic behind it”. But that’s not really new, I think. Compelling arguments in natural language tend to become less compelling too when you examine other aspects of it, like the empirical justification of the claims in the argument.

      One last remark. You write

      “In short, the standard symbolic logic course of the 1970’s was an indoctrination in epistemic relativism, and in a certain kind of rhetoric. A simple course in truth tables can contribute to public skepticism, which can then be manipulated rhetorically.”

      But you also seem to agree with

      “… knowledge comes as the result of inquiry. Truth is a product of the exhaustion of lines of inquiry that converge to the satisfaction of all those engaged in it.”

      Isn’t that also a recipe for epistemic relativism?

      I’ve read a bit of Peirce for a course on semiotics I once took and the above quote reminds me why I found him frequently maddening. It’s that little expression “the exhaustion of lines of inquiry”. It renders the idea behind the quote pretty useless. I’m interested in truth and knowledge when the lines of inquiry are NOT exhausted, because they never are.

      If all, really all the lines of inquiry indeed are exhausted, then it follows logically that truth is obtained – because if it’s not the truth, at least one line of inquiry would have shown it to be false, logically speaking. In a certain sense, Peirce seems to do here what you don’t like. He gives a logically unassailable definition of truth and knowledge – but one that is useless in real life circumstances.


      1. couvent2104
        Some of what you respond has been replied by the long reply I make to Dan. However:
        “Isn’t that also a recipe for epistemic relativism?” No,, as my reply to Dan hopefully makes clear, it’s a recipe for historical relativism (and possibly cultural relativism). There are certainly problems with historical relativism (and much more with cultural relativism. But epistemic relativism, as I understand it, is really just the beginning of an unyielding skepticism, possibly even cynicism.

        I am not speaking to symbolic logic as a field of research, merely remarking it as it was taught to me (and I suspect to many other undergraduates) back in the ’70s. Of course the teachers thought they needed to apply it to the common language, how else could they have made it seem ‘relevant’? But this may have been a serious mistake.


    2. Dan,
      Ok, If I understand your point here, what appears to be the Pragmatist conflation (at least as I present it) merges (in error) the question “what is the meaning of truth?” with the question “how can we know what is true?” Thus the convergence of inquiry that satisfactorily answers the first question can in no way satisfactorily answer the second question, since the achievement of such meaning doesn’t certify that the reference of the convergence isn’t actually false.

      Let’s see if I can’t talk around that, because confronting it directly would actually get a little complicated. (To understand why, let me say I am somewhat reminded of Russell’s criticisms of Dewey’s logic, which began in the ‘teens and recurred through to the ’40s. There has been some recent discussion of this; see Burke’s Dewey’s New Logic: Reply to Russell, for instance.)

      In the late 19th century and early 20th, a handful of philosophers (including Marx, Nietzsche, the early Heidegger) began to grasp, and grapple with, what was Hegel’s single most profound insight – that knowledge is not only the product of history, but is thus necessarily entangled in history, since history doesn’t stop to wait for ‘what is true’ to be gathered in completion. But Hegel also believed that if we understood the process by which knowledge develops through history (the infamous Dialectic), we could at last reach such completion, a stopping place (the end of history), at least as far as what could be known of all that was essential of the world as it appears to us – hence Hegel’s main text on knowledge is not titled “Epistemology,” but “Phenomenology.” (Thus he gets to claim a view-from-nowhere without claiming actual divine insight or revelation.)

      The major Pragmatists, in different ways and for different reasons, recognized the validity of Hegel’s insight into the historical nature of knowledge, but ultimately rejected his Dialectic, and along with it any hope for the completion of knowledge. Inquiry is an ongoing process. In the statement giving you problem here, I say that truth is the product of the exhaustion of *lines* of inquiry, not inquiry itself. And it’s important to understand inquiry as necessarily social “which, as social, inevitably instigates further inquiry” – how so? because in any social setting there will be disagreements, outliers, innovators. The truth is always the truth *for now* and functions as knowledge as long as it can be relied on. (For Peirce it is usually understood as probabilistic and fallibilistic. For Dewey, it is a resting point in an ongoing narrative – which is why his major texts always include re-telling the histories of the ideas he discusses.)

      In the Middle ages, it was thought that maggots were spontaneously generated *by* rotting meat (or at least that’s what I’ve read). So in, say, 1300 CE it would have been true to say that, because that was what was known. How would one have known this truth? Because there were authorities telling one this is so; and also, visually, it certainly seems obvious…. Here is a convergence of certain lines of inquiry that, we know from our present condition of knowledge, referred to what was false…. But no one in 1300 would have been able to say that. Two hundred years later, a different kind of inquirer with different tools for inquiry begins seeing fly eggs under microscopes, or bottled flies mating and reproducing, etc., and thus new lines of inquiry open up requiring a new convergence…. And though the question, ‘where do maggots come from?’ has effectively been settled, biologists are still researching flies. (And it is still the case that if you don’t like maggots, don’t leave a piece of meat out to rot on a warm day)

      Now, *how* do we know this? Well, interestingly enough, we know this in pretty much the same fashion as our Medieval forebears: by reliance on our senses (or sense-prosthetics, like microscopes), by trusting select authorities who have done research we haven’t or can’t do ourselves, by engaging a process of reasoning that filters in the music while filtering out the noise. Epistemology, loosely put, attempts to discover the ‘proper’ relationship between our sense-reliance, our trust in authority, our process of reasoning, such that we have a dependable methodology for determining that what we claim to *know* is really a fact that we do know.

      I haven’t suggested that there is anything wrong with academic inquiry of this nature. Epistemology has had the beneficial side effect of throwing a lot of the hooey of traditional Ontology into question, for instance. I will admit I have a problem with it, one that goes back a long way for me. Since Kant’s response to Hume, it has been de rigueur to insist on the complete divorce or epistemology from psychology. I confess I have always thought this mistaken, and I sense something similar in James and Dewey (and Nietzsche, it must be said). It makes no sense to me to ask ‘how can a consciousness know this?’ when there can be no consciousness without a living human being.

      Finally, almost as side note, in strict epistemology terms, I have always claimed to be a Medieval Nominalist (think Occam); but Susan Haack has suggested persuasively that Pragmatism’s fall-back epistemological stance is really a Common-Sense Realism à la Thomas Reid (only more sophisticated), a position I found myself in when I wrote my essay on belief.


  4. So, my criticisms out of the way, now let me say that the piece is excellent and thought provoking and pairs beautifully with my dialogue with Crispin. Together they provide a great overview of the issues involved and what’s at stake. Thanks, EJ!


    1. And thank you; I don’t expect my earlier reply to be either particularly persuasive or convincing (though one can hope…); because the devil is in the details, there will always be disagreements.


  5. couvent2104, re logic and epistemology. yesterday I was going to mention

    Click to access MartinLofOnTheMeaning96.pdf

    where Martin-Lof is very big on propositions being Judgements (Urteil), so “A is true” is “I know A is a proposition” (that is, I can conceptualize it) followed by “I know A is provably correct” (an evident judgement).

    “…[N]o longer do we need to prove metamathematically that the proof figures, divested of sense, reduce to introductory form. Instead of proving it, we endow the proof figures with sense, and then we see it! Thus the definition of convertibility, or computability, and the proof of normalization have been transposed into genuine semantical explanations which allow you
    to see this, just as you can see consistency semantically.”

    You’d know how this might relate to HoTT etc.


  6. EJ

    You present a critique of *the excesses* of logical positivism etc. but this leads you, I think, to mischaracterize what the logicists and logical positivists were doing.

    Frege and Russell and others made a bold attempt to reduce mathematics to logic and though it failed its failure revealed extremely important things about the nature of logic and mathematics. You write as if they were totally misguided and “wrongheaded”. They were not misguided.

    Did they and the logical positivists overreach? Yes. No logically perfect language is possible (or needed).

    I agree with you that formal logic has little *direct* application to our ordinary reasoning. Natural language works fine as it is for ordinary purposes and does not need to be revised or improved. Training in formal logic can, however, open up some new and valuable avenues of thought and understanding (as mathematics does).

    Let me make a point about sentences, and the distinction between syntax and pragmatics.

    You talk about meaning as being dependent on the context of sentences, in other words on what linguists call pragmatics (“… the branch of linguistics dealing with language in use and the contexts in which it is used, including such matters as deixis, the taking of turns in conversation, text organization, presupposition, and implicature.”).

    And, of course, ordinary real world communication (unlike formal logic and mathematics) is dependent on all these things.

    That said, the sentence (and its structure: syntax, in other words) is in a sense fundamental. It is the smallest unit in a language which expresses something.

    You write:

    “But this project, embedded implicitly in Frege’s text, is not its worst strategic error. That would be the decision to treat the sentential proposition as the principle bearer of truth, and the necessary object of logical analysis. In the development of logic after Frege, this decision has had beneficial consequences, including the development of symbolic logic and formal logic and computing languages.”

    Precisely. Given Frege’s interests and concerns (mathematics and logic), the focus on the sentence was by no means a strategic mistake. It was entirely appropriate, and the fact that some post-WW2 philosophical logicians went off in fruitless directions does not retrospectively condemn Frege’s or Russell’s work.

    Linguistically speaking, you are interested in pragmatics, not syntax. But syntax is also important (and fundamental in certain ways) in the study of natural language.

    I was also puzzled by your account of an introductory course…

    “In short, the standard symbolic logic course of the 1970’s was an indoctrination in epistemic relativism, and in a certain kind of rhetoric.”

    I would have thought it would have been about such matters as introducing the notion of a formal system and distinguishing validity from truth. Formal or symbolic logic is about as far from rhetoric as you can get.

    “A simple course in truth tables can contribute to public skepticism, which can then be manipulated rhetorically. So much for truth!”

    By way of explanation of these cryptic assertions, you have a footnote…

    ” “Immigrants cross the border illegally and immigrants are employed instead of citizens” is a truth-table verified true sentence; it just doesn’t remark immigrants who arrived legally, better qualified for the given jobs than citizens.”

    This is not formal logic. You are using natural language, with all its ambiguities and scope for deception, etc.. Propositional logic deals with propositional symbols: the propositions in question are quite opaque. We need predicate logic to flesh them out. And the predicates, individual variables and quantifiers of predicate logic work on two levels: purely as formal symbols, and also in terms of an interpretation (where meaning comes in).

    Truth tables give an interpretation of the formal system of propositional logic. Notions of “true” and “false” bring meaning in, bearing in mind that the various connectives are unambiguous and not exactly equivalent to “and”, “or” and “if… then…” in natural language. (Implication, for example, doesn’t work quite like the English “if… then…”.)


    1. Mark,
      Your points are well taken.

      Concerning: “‘In short, the standard symbolic logic course of the 1970’s was an indoctrination in epistemic relativism, and in a certain kind of rhetoric.’
      “I would have thought it would have been about such matters as introducing the notion of a formal system and distinguishing validity from truth. Formal or symbolic logic is about as far from rhetoric as you can get.”

      As noted to couvent 2104, this remark is not so much about symbolic logic (and it would be both weird and silly to carry a grudge against symbolic logic – to the formation of which Peirce also made significant contributions), but about how it was taught in at least some schools at a certain point of history. My understanding is, if I remember rightly, the school I took this course at had used it to replace a more traditional ‘intro to logic’ (syllogistic) course *, possibly to introduce students to the more technical language of academic philosophy per se. At any rate, as noted to couvent, there seemed to be some attempt at ‘relevancy;’ – much of the course involved translating common language sentences and arguments into propositional sentences, conditionals, and arguments, or translation of the symbolic into common language examples.

      The lesson is not that symbolic logic should not be taught, but, as you suggest, taught as an introduction to formal systems. Confusing formal logic with the common language raises serious problems; and my main grudge with Frege is that he comes perilously close to that.

      * And what is the problem with a basic course in syllogistic? And why did I find myself, time and again, having to teach syllogistic in a basic Composition course, once it became obvious students didn’t know what an argument was or how it could be convincing?


      1. EJ: Your recollection is correct. We also spent a good amount of time in my introductory logic courses “translating” natural language sentences into forumlae and then purporting to “deduce” various things from them.

        If one hadn’t gone on and taken courses on Austin and Grice and learned about performative force and speech-act theory, one could very well have gotten a serious misimpression about what such “proofs” actually show (which is close to nothing.)

        Liked by 1 person

  7. Hi EJ: Yes, excellent and thought provoking. Three fairly simple comments from me.

    1. Formal logic, as I understand it, cannot give an account of truth because it concerns itself only with the truth-preserving validity of inferences. This means it has nothing to say about the acceptability of premises. And because it operates only with deductive inferences, it has nothing to say about non-deductive inferences. In general, formal logic is a very specialised instrument, excellent in its own way but not a multi-purpose tool. This is a point in addition to and in support of your contentions.

    2. Nevertheless, I think formal logic is not remote from ordinary reasoning. We all rely on modus ponens, modus tollens, transposition, and disjunctive syllogisms in everyday life. “If the light is green, you may go. The light is green, therefore you may go.” Etc. We usually do this sort of thing so efficiently that we hardly even notice that we have done it. But we can make logical errors, as formal logic shows.

    3. For me the most interesting point is your contention that “A sentence has little meaning outside the context of a paragraph, which may itself have meaning, but more often requires the even larger context of the whole text.” I fear that if we go down this track, there will be no stopping point. The whole text will get its sense only from the whole language. But meaning is less wholistic than this, surely. For (a) none of us knows the whole language. (b) You don’t need to read the whole of Shakespeare to understand each sentence of Shakespeare. And (c) small children can fully understand simple sentences put to them by their parents. It is only in special cases that the meaning of a sentence requires a special contextual search. Or am I missing something?

    (I have recently been grappling with the injunction “Forget this device”. What is that supposed to mean, I say to myself!?)



    1. alantapper 1950,
      “For me the most interesting point is your contention that “A sentence has little meaning outside the context of a paragraph, which may itself have meaning, but more often requires the even larger context of the whole text.” I fear that if we go down this track, there will be no stopping point.”

      There are always stopping points, and the exact nature of these, and how we reach them, is the subject of much research – and much debate – in various fields.Sometimes they are inevitable given the nature of learning – children can be fluid users of English, but it takes some further education before they can even recognize Chaucer’s English distinct from Shakespeare’s, distinct from Hemingway’s.

      I put it in those terms because I approach the question primarily from the perspective of a training in semiotics and literary theory – as a question of necessary limits to interpretation. As we all know certain soliloquys from Shakespeare have meaning in and of themselves – even powerful, moving meanings. But surely interpreting their meaning can only be enhanced and added to with comprehension of the plays in which they appear – and still further enhanced if we read other plays by Shakespeare, and learn something about Elizabethan England (etc.). The acquisition of meaning is not a one time affair, but changes – and with learning, expands – over time.

      As suggested in my reply to Dan, one of the reasons I remain committed to Pragmatist theories of truth and knowledge, – despite evident problems that Dan pointed out and that Hilary Putnam points out – is because they are the only viable theories that account for historical change, without having to lapse back into Hegelian Dialectics, with its pre-determined course to an ‘end of history.’ The main problem I have with certain other theories is that they seem to treat truth and knowledge as static, or as reaching some end point of certainty. That’s what I think is misguided.


    2. We also spent a good amount of time in my introductory logic courses “translating” natural language sentences into forumlae and then purporting to “deduce” various things from them.

      Back when I was a graduate student in mathematics, I decided it was time that I looked into philosophy. So I borrowed some entry level books from the library.

      I was appalled. The books contained many logic arguments. And what seemed obvious, was that the authors of the books had reached the conclusions of these arguments in some other way, and were just trying to make it look as if they had used the logical deductions presented.


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