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On modern logic

In this essay, I will make a comment on the way logic is studied currently.

In the first section, "Modern logic is Formalized," the notion of a formal system is characterized or

described in terms of an epistemological dualism I advocated in my previous essay, "Two ways of

identification." This characterization is included only for readers who have read the essay and

understood the notions, to indicate the relevance of the epistemological basics laid down there to

the kind of critical reflection on our contemporary practice of logic that I advocate in the present

essay. As a reminder, these terms are typographically marked by small caps, at their first few

occurrences in this essay. But, they are used without explanation.

I understand that this idiosyncratic characterization of a formal system would make the first

section inaccessible for those who have not read the previous essay. But, please do not quit reading

this essay for that reason, or think that this essay cannot be read without first reading the previous

essay. Having no familiarity with my previous essay should not affect the readability of the rest of

the present essay, which is the main contents of it, if readers know modern logic just enough to

understand what I mean by saying that modern logic is formalized (without the peculiarly

epistemological-dualistic understanding of what "formalizing logic" amounts to). 1

Modern logic is Formalized.

Currently, in the so-called analytic tradition, the study of logic --- or more precisely (for what is

really being done), metalogic --- is carried out formally. That is, it is practiced on the basis of a

technical, or more precisely, a methodological notion of a formal language or a syntactical system,

which is a formal system in the sense that it is a finitist-mathematical "object" consisting in (i) the

specification of symbols to be used in it and (ii) the finitist-mathematically exact definition

(recursive definition) of a class (or more than one class) of syntactically countenanced sequences of

symbols (up to the definition of the most important class, typically called a sentence or a well-

formed formula, wff).2

1 Just in case there are readers who have not studied the kind of formal logic I refer to here, and, only for that

reason, do not understand what I mean by "formalization of logic" at this point: For such people, good part of the points to be made in this essay may be unfortunately inaccessible. However, I entreat those people to plow through technicalities, at least to get the big idea behind the points I will try to make. I especially ask them to do this favor for me if they are young, promising graduate students of philosophy who think that logic, especially so-called mathematical logic, has been "finished" by now, with not much room to make novel contributions for new comers. Nothing is farther from truth than this, I think. I hope that this essay can help them to start re-thinking about "logic." 2 Of course, one can consider the notion of a formal language in such a way that the upper most syntactic class up

to which it syntactically defines is a (formal) proof (or a formal theorem). I'm simply adopting a different conception which limits the syntactic classes to be included in the notion of a formal language to that of wff, in order to use, for the purpose of characterizing modern formal logic, the concept of a formal language as the common basis for two kinds of formalization of logic: syntactic formalization (proof theory) and semantic formalization (model theory).

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The essence of this type of syntactical system is that it uses symbols as the SIMPLE PARTICULARS and

relies on "our" (pragmatically inevitably enabled) DIRECT ACQUAINTANCE with some sort of ORIENTED

CONCEPTUAL BACKGROUND to allow for some sort of "recursive definitions" of classes of syntactically

recognized COMPLEX PARTICULARS.3 On this ACQUAINTANCE-based syntactical system, modern

metalogic employs two distinct means of objectification of logical inference, juxtaposed under

various labels, e.g., (formal) semantic metalogic and (formal) syntactic metalogic, or model theory

and proof theory, and so on. I assume that my intended readers know enough about them, and omit

their explanations.

Better or worse, the modern logic is by now entirely based on this methodological infrastructure. It

is as if this methodological infrastructure, by its practical dominance by way of being the de facto

industry standard, declares that those who are not versed in it do not count as really knowing what

logic is.

Let us denote this sense of methodological formalness of the modern formal logic by the

capitalization of the word-stem, as in "Formal."

The invention/discovery of modern logic as a whole included other important breakthroughs, such

as the quantification theory and the algebraic or truth-functional treatment of propositional logic

(through the invention/discovery of propositional connective, a.k.a. Boolean operators). These

often overshadow the significance of the development of the Formal methodological infrastructure

in popular accounts of the history of modern logic (if the Formalization of logic is mentioned at all).

But, the explosive development of logic in the last century owes no less to the development of this

Formal infrastructure. There is no doubt of this.

Modern Formal logic is artificial; we know modern logic more intimately.

With all due respects to the progresses made possible by the Formal infrastructure, the

infrastructure is clearly artificial. One has to bite a bullet, in a sense, to swallow it at first.

Unfortunately, such methodological artificiality by nature tends to become imperceptible as one

gets more accustomed to the methodology in question. I'm afraid that, just for this reason alone,

some readers might have hard time to understand, or rather, not to misunderstand, what I mean by

this artificiality, if they are too accustomed to the modern Formal logic. To overcome this obstacle,

let us remind ourselves of this: We all do have a more intimate knowledge of what logic, or logical

3 This is how I would specify the essence of the kind of formal system, or finitistic-mathematical complex object,

that we formal logicians know as a (formal) language. (Calling it a "finitistic mathematical object" is an allusion to one of its historical origins, so-called Hilbert's program, which was a finitist-mathematics-based metamathematical program aimed at the epistemological/ontological foundation of real number arithmetic.) I put it in this abstract way because I think that sequentiality might be just one of many principles that can serve as the principle of ORIENTED-NESS (or BREACH OF SYMMETRY) in the CONCEPTUAL BACKGROUND for the "construction" of "recursive" COMPLEX

PARTICULARS capable of being syntactical "materials" for a formal system. A key to this way of thinking is how to think about the ORIENTED-NESS of a conceptual background on which to conceptualize or to identify SIMPLE

PARTICULARS. My research on this oriented-ness is still in its infancy. But some results are given in the "Order without orientation."

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inference, is; and, because of this intimately known logic, we call those Formal systems "logics" (in

the sense of systems of logic). That is to say, (i) the two independent objectifications of logical

inference are both objectifications of this intimately known logic, and (ii) these objectifications (and

the underlying "Formalization of a language") have been accepted, more implicitly (i.e., by practice)

than explicitly (by words), as the appropriate infrastructure for the rigorous meta-logical study ---

study of or about "logics" (of various kinds, both classical and non-classical) --- primarily because of

their (independent)capacity for approximating or simulating this intimately known logic. The

technical demands of the completeness and consistency (or soundness) of the proof theory of a

"logic" (relative to its model theory) are only secondary requirements, which are naturally

demanded as a result once the primary requirement is assumed to have been met independently by

the proof theory and the model theory of a given "logic. At the very least, this is the most natural

picture to understand what we do, with respect to "classical logics."

Perhaps there is no more need of reminding, but let us remind us further of the following: when we

do such metalogical studies, for classical or non-classical systems alike, we do engage in this

intimately known "classical" logic at that metalogical level, which is in neither sense Formalized.

And this is the same sort of logic in which we engage (once we are trained to use it), whenever we

make and take rigorous deductive inferences in any sector of modern-rational human life, such as

doing mathematics. (As every modern Formal logician knows, this is one reason why mathematical

logic is so called. It studies (Formalized) "mathematical theories" and (Formalized) "logics"

mathematically in this sense, that is, in accordance with the same sort of discursive normativity

which dictates mathematical discourses.) So, we must say we know, at least by competence, if not

by cognizance, what logic is, epistemologically prior to our Formal-artificial re-definition of what a

"logic" is (which goes like: It is a Formal syntactical system equipped with two ways of

distinguishing an acceptable from a non-acceptable inference).4

Before moving on, a word of caution. Some readers might have felt something awkward at a

parenthesized qualification in the previous paragraph: I said to the effect that the intimately known

logic is the kind of logic we use once we are trained to use it. If it is something intimately known in

the sense of competence, why should we be trained to use it? The answer is that even this

intimately known logic is a skill in an artificial convention.5 I will explain what I mean, or mean to

4 (This footnote should be re-read after my distinction between non-Formal, intimately known modern logic and

what I late call "raw logic.") More exactly speaking, the intimate modern logic and logic we use in, say, mathematical discourses, are the "same" only in terms of which inferences to recognize as "correct." But, to use a cliché, just as planes fly by a different way from the way a bird flies, the intimate modern logic and raw logic make the same inferential behaviors by different rationales. 5 The convention in question is called "artificial" in the sense that it is not an integral part of any natural language.

That is, human beings do not grow up to develop or acquire the kind of competence I call intimately known logic just by virtue of acquiring a native language (although acquiring a native language comes with acquisition of what may be called rationality, something very akin to what we should call logical competence). However, drawing a line between a natural language and other (non-linguistic) conventions (in order to distinguish any competence belonging to the former as "natural," distinct from any competence belonging to the latter which is "artificial") is admittedly arbitrary, no matter where the line is drawn. One may say that I draw this line here to express my position on what "logic" is (ultimately), on top of describing it (as I will later in this essay).

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claim, in saying this, shortly. For now, let me just clarify this claim of mine , and call this intimately

known logic intimately known modern logic, to convey a sense that it is a convention (not known to

all times), according to my position.

What are "non-classical logics"?

Some people who know the modern Formalized logic in a sense too much (but in a sense too little)

might object to the above picture, thinking that this picture is not universally adequate because

there are no such a thing as "an intimately known logic" for a non-classical logic. Perhaps I should

say something on this objection before I move on. --- What I can (and, should, I think) say here is

not to or against this objection, but on or about this objection. That is to say, what follows is my

diagnosis of the current state of the industry of modern logic which seems to make some logicians

think that way.

To begin with, we should realize that the very notion, or the intelligibility of the notion, of "non-

classical logics" owes, for its "existence," that is, for the wide circulation of the recognition of such

Formal systems as (representing or being) variant kinds of "logic," to the Formal methodological

infrastructure which had been originally and previously developed for "a logic" that may be labeled

as "classical" (with some anachronism --- read on for what I mean by this). So, their status as

systems of "logic" is doubly derivative, in the following sense. First, the two ways of objectifying the

intimately known logic had been accepted as such (i.e., objectifications of logic), despite their

artificiality, due to their independent capacity for approximation of the intimately known modern

logic. The solid or tangible way in which these objectifications are defined or built, together with

the given acceptance of these objectifications as objectifications of logic, created a huge

conceptual/methodological room in which to try out various modifications in the way of "defining a

logic." No sooner had this room been created than people started to fill it by actually inventing

various modifications of the basic Formal leitmotiv, producing what were all along accepted as

"logics" (if not "classical") solely due to their being built on the same Formal infrastructure (in one

way or the other of the Formal objectifications).

Here, a brief review of the history of modal logic seems informative. As is well-known, when

various modal systems were invented by C.I. Lewis, they were built on this Formal infrastructure

only in the sense that they were based on a Formal language equipped with one way of objectifying

"inference," the proof theory. They lacked Formal semantics, and, therefore, were not subject to

such "meta-logical" questions as completeness and soundness, until young Kripke invented the

Kripke semantics that prove to be just the semantics needed for Lewis systems. It seems to me that

Kripke's invention was especially applauded because it finally brought the Lewisian modal logics to

the full modern status of "logics." That is, it seems to indicate the existence, in the industry of

modern Formal logic, of a tacit industrial standard that a system counts as "a logic" only if it is

equipped with both objectifications of "inference" (so that questions like completeness and

soundness can be asked of it). The existence of such a standard, if it really exists, hardly makes any

sense to me unless it is understood as a historical and sociological product. What makes no sense is

not why two are needed (why one is not enough --- which makes some sense, for one is not enough

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to do the cross-examinations), but why just having two (or, more than one) such artificial ways of

objectification, granted that it makes the cross-examination possible, should make a mere Formal

system "a logic." Recall that in the case of "non-classical logics," there is no counterpart of intimate

logic. So, whether they are Formal syntactical systems (proof-theoretic systems) or Formal

semantic systems (model-theoretic systems or systems of valuation) or systems with both, such

"non-classical logics" lack the independent claims for approximating the behavior of something

which we know as logic and call logic, prior to calling them "logics." Whatever the reason for the

existence of this standard may be, this piece of history of modal logic seems to indicate its existence,

and tempts me to diagnose some modern Formal logicians to be oblivious of the doubly derivative

origin of the modern-technical Formal notion of "a logic."

The aforementioned objection can make sense only if it is made by logicians with this sort of

oblivious attitude toward the Formal methodological infrastructure.

This historical development is even more ironical. The "classical" properties that various "non-

classical" logics lack (by design or by accident --- not the least of which is the so-called

extensionality or truth-functionality of propositional connectives) are precisely the properties

because of which the "classical" Formal logics were accepted as objectifications of the (modern)

logic we know intimately, and hence, precisely those which gave to the Formal infrastructure the

very status of the methodological infrastructure for metalogic. The properties that "non-classical"

logics inherited from the "classical" ones are essentially the very artificiality I'm trying to explain

here, by means of which the intimately known modern logic is supposed to be represented or

objectified, but which by itself has no power to baptize something "a logic," if not for this historical

accident of having been used for the objectification of (classical) logic. But, as observed above, what

happened in history is that it did acquire this power. The dazzling successes of this infrastructure

(in the "classical" investigations such as in the mathematical logic, i.e., the foundations of

mathematics), together with its methodological productivity (productivity in the sense of capacity

to create a huge professional industry), apparently had caused a shift of the very concept of "logic,"

as used in the expert community, so that the newly emerged notion, "to be a logic," came to mean to

be a system built on this Formal infrastructure.

I worry that this in effect has diverted attention of logicians/metalogicians from the investigation of

the intimate modern logic itself. This, in turn, probably caused the isolation of the professional

community of logicians from that of mathematicians, on the one hand, and that of

epistemologists/philosophers of language (except for those willing to apply the Formal engineering

to the so-called rational reconstructions of key notions in their areas), on the other, while causing

the (rather philosophically unhealthy) communication between logicians and metaphysicians. This

is, in my opinion, a very unfortunate circumstance for all parties involved. If a part of the reason for

these isolation and communication is the over-dominance of the technical Formal notion of "a

logic," the dominance should be loosened. That is, the notion of logic should regain its original

semantic core, roughly referring to the fundamental discursive normativity that is supposedly the

universally shared basis of human rationality. Or, at least, it should be freed from the current

Formal artificiality so that non-Formal study of the modern intimate logic gets a place in the

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modern logic industry. And, we should keep a critical and historical self-awareness of the doubly

derivative origin of the technical notion of Formal logic that has been prevalent in our tradition.

Modern intimate logic is artificial, too.

As some readers might have guessed, the other great developments of modern logic I mentioned

earlier are parts of the intimately known modern logic. (These include the quantification theory

and the algebraic/truth-functional treatment of propositional connectives.)

Now, logic we know and do intimately today is not without its own share of artificiality, or at least,

appearance of being artificial or counterintuitive to our untrained logical intuition that we possess

as competent native speakers of a natural language--- what we may call native rational intuition.

To take a glimpse of this artificiality, note that our competence in logical thinking usually gets

improved by receiving good training in the modern intimate logic. (By the way, when we receive

training in this non-Formal modern logic, such as from a chapter or an appendix of certain

mathematical textbooks, it is often symbolized to an extent, for the sake of facility. So, non-Formal,

intimate logic can be and often is symbolic logic, using the familiar symbols like ∀, ∃, ∧, ∨, →, but not

Formalized in the aforementioned sense.) This fact, that many of us benefit from this kind of non-

Formal logical training, seems to me to be explainable (in part) by the fact that there are certain

inference-related moves, in particular, so-called "translations" and operational rules of inference

(i.e., the non-Formal rules for using symbols like ∀, ∃, ∧, ∨, →, and variables, i.e., operational rules

for using the intimate-logical notions represented by those symbols), which are sanctioned and

incorporated in the modern intimate logic, which nonetheless usually are counterintuitive to our

native rational intuition, but which, despite their (initial) counterintuitiveness, do work as devices

for correct inference.6

Characteristically, the modern intimate logic not only accepts such "counterintuitive translations,"

but also accepts them without satisfactory explanation for why they work and why we find them

counterintuitive.7 And, its practitioners often force new comers to accept them similarly,

sometimes even with a tacit understanding that anyone who cannot accept them is not good

enough to study logic. (I personally think that such an attitude is not very philosophical.) The

initial discomfort notwithstanding, after getting this brute sort of "logic training," new comers are

6 The beneficiality of the training in the modern intimate logic can be explained by this fact in more than one way.

For instance, it may be that the brute mastering of these counterintuitive moves reduces the cognitive load of certain cognitive tasks, making extra cognitive resource available for further advanced tasks. Or, it may be that there are certain patterns in which we, untrained rational thinkers, tend to make fallacious inferences in a certain type of context, and these patterns of incorrect inference can be avoided by the brute mastering of these artificial (but combat-proven) moves. Most likely, it is both. But, for now, we only focus on the said fact of the existence of counterintuitive but working inferential moves. 7 I do not count as a satisfactory explanation a mere insistence, based on the past success of the intimate modern

logic (which is in no question), that they are correct and thus their counterintuitiveness must be only a revelation of irrational parts of our native rational intuition. I must admit that I am just as dogmatic as those I criticize here, in rejecting such an "account." Here, both their "account" and my rejection of it are "just because" insistences, revealing a difference in the kind of discursive norms which we respectively endorse and commit ourselves to.)

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destined to accumulate experiences of confirming the correctness of these counterintuitive devices

or conventions. And, through such experiences, they usually train themselves out of some parts of

their native rational intuition that incorrectly veto against them. (These mentions of the

correctness/incorrectness are made only with regard to those of the final inferential judgment.)8 In

short, many of us simply get used to and grow tolerant about accepting the unexplained

counterintuitiveness of those "translations" and operational rules. (To repeat, I find this situation,

prevailing in the modern logic study and education, is unfortunate for philosophy.)

This kind of training is of course free from the artificiality of the modern Formal infrastructure. So,

the counterintuitiveness of those devices is distinct from the artificiality of modern Formal logic.

We should admit this gap between our native rational intuition and the modern convention we call

logic, without deceiving us by rendering the former simply as our native naiveté. And, we should

try to explain (i) why these counterintuitive "translations" (with intimate-logical operations with

notions of ∀, ∃, ∧, ∨, →) should work as parts of correct inferential strategies, and (ii) why our

native rational competence finds them counterintuitive.

The problematic "translation," at the level of propositional logic, is that of a natural language use of

a linguistic construction of the form "if p then q." Our modern intimate logic makes us "translate" it

into the assertion of a truth of a compound proposition known as material conditional (or material

implication) (as opposed to the assertion --- if it is an assertion at all9 --- of the validity of an

inference from p to q). The counterintuitiveness of this "translation" is tightly connected with the

counterintuitiveness of such operational rules as modus ponens (p, p→q, therefore, q) and ex falso

quodlibet (principle of explosion: from a contradiction, you can infer anything). I assume that most

of us remember when we first encountered these "translation" and operational rules and how we

were disturbed by them because they seemed just wrong, circular, and absurd. I mean, I assume

that most of us know firsthand in what sense they can sound counterintuitive. So, I omit detailed

explanations of their counterintuitiveness.10 Let me only repeat that we all know that these

counterintuitive devices of the modern intimate propositional logic have passed test of time, and, in

8 This may be a good time to re-read the footnote 4. But, it should be re-read again later.

9 It may be an expression of a norm-endorsement or a norm-commitment, as Robert Brandom claims. Indeed, to

assert the validity of a certain inference may be nothing but to express such a norm-endorsement/commitment. (We may have to fundamentally re-think about what it is to assert something.) 10

I actually wonder whether as many students of logic stumble upon the notion of MP, taught as if it were a non-circular inferential move, as they stumble upon the notion of material conditional ("if p then q" as a truth claim of a compound proposition). If what I mean by the circularity of MP sounds alien, Lewis Carroll's "What the Tortoise Said to Achilles" would be helpful. (Carroll's literally allusion to Zeno's paradox seems uncannily apt to me, not just because there seem to be many people who fail to find anything paradoxical or puzzling about their respective paradoxes, but because there seems to be a deeper connection between them, roughly in the sense that they are two examples of the same discursive phenomenon, "our" pragmatically inevitable "spatialization" or "synchronization" of what is really "diachronic." But, this is only a hunch at this point. I need to think more about this.) (I have no knowledge of why Carroll made this allusion. I know nothing about him as a logician or mathematician, except for having read this short piece. I thank Prof. James Garson for, among other things, having recommended this piece to me at a right context in our conversation.)

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that inductive sort of sense, have long proved themselves correct.11 Their correctness in that sense

is not in question. Our questions are the two (related) "why" questions above, and, ultimately, what

it means to say (or judge or assert) that "an inference is correct" (or "is incorrect"). I have an

account of my own for all these questions, at least in outline. However, it takes too much space to

explain it in this essay. I postpone its presentation until my fuller essay on an implication of the

epistemological dualism of the "Two ways of identification" on logic.

At the predicate level, the counterintuitive "translations" are the familiar ones of quantificational

expressions such as "all" and "some" (as well as those derived expressions such as "at most/least n"

and "exactly n"). I also assume that most of us remember how counterintuitive these "translations"

were when they were first taught. However, our understanding of this counterintuitiveness may be

quite inarticulate, compared to that we encounter at the propositional level. I try to articulate it

here, or at least to take an initial step for a full articulation of it.

When we use such a "quantificational" expression in natural language discourses, we use it as a

syntactic part of a noun phrase (or NP) --- in which the "quantifier" is to "modify," or "quantify" in

this case, the rest of the NP, which is the core of the NP, so to speak. With these "modified" or

"quantified" NPs, we make sentences of the syntactical form, after all, of the subject-predicate

structure. But, this original syntactic structure is distorted by the familiar "logical translation":

Quantifications are "translated" into a syntactical part of a proposition as a whole, not of a "term"

(the logical counterpart of a natural language NP). So, for the most important examples:

(i) a natural language assertion "some F's are G's" is "translated" into "there exists x such

that: Fx and Gx,"

and, similarly,

(ii) "all F's are G's" is "translated" into "for all x: if Fx, then Gx," where the "if – then"

expression is taken to be a material conditional and the whole expression is taken without

the so-called existential import.

A point I should stress here is that this existential import, or, as I prefer to call it, existential

presupposition, inevitably comes with every use of an NP in natural languages (as opposed to a

mention of an NP).12 It is a ubiquitous linguistic (pragmatic) phenomenon of any NP use (as

opposed to mention), not an exceptional phenomenon peculiar to NPs "modified" or "quantified" by

such expressions as, in English's case, "all" and "every." It comes with our use of NPs with "some,"

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Of course, by granting to them "inductive" proof, I do not mean to say that their correctness is an "empirical" matter --- unless we first go through preparatory re-thinking of "empirical." We will not do so in this essay. A full discussion of this point by me should wait until I write on implications on epistemology of the two ways of identification. 12

To be a bit more accurate, it comes even with a mention of an NP insofar as it is understood as a use of a meta-linguistic NP --- a "name" of the NP, to use Quine's terminology again. (In the case of a use of a meta-linguistic NP, what it presupposes is a former pragmatic occurrence (if not in the given stretch of discourse, then in the history of the language up to that point) of the "named" syntactical object, which is to say, the existence of its meta-linguistic referent.)

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or other related expressions such as "the," "at least/most n," etc. To use an NP is to make a

reference of some sort, and to make a reference presupposes the existence, of some sort, of the

referent.

So, the syntactic distortions forced on us by the "correct logical translations" of sentences with such

expressions generally come with systematic, yet ultimately artificial or ad hoc ways of canceling all

the existential presuppositions at the NP level first, and then restoring them, as needs arise, as the

semantic content (rather than pragmatic presupposition) of the proposition. So for instance, in the

case of (i) above, the existential presupposition that comes with our natural-language use of "some"

in "some F's" is first canceled at that NP level, and then is restored as a part of the sematic content

of the proposition which asserts (not presupposes) the existence. In the case of (ii), the existential

presupposition that comes with our use of "all" in "all F's" is canceled for good, and not restored

even at the propositional level. (These cancellations and restorations of existential presupposition

are incorporated and exhibited by the operational rules for using the quantifiers.)

In this way, the syntactical distortions forced upon us by these "translations" are made possible,

that is, made inferentially harmless (even made conducive to correct inference by checking our

native rational intuition from making certain errors), precisely by an artificial or ad hoc cancellation

and/or restoration of existential presupposition of this kind. However, because the modern

intimate predicate logic has taken this semantics-centric path in its effort to protect our inferential

judgments from making errors, it had to fail, and has failed, to do justice to the pragmatics of the

reference-predication pair of speech acts from which natural language discourses (including

inferential discourses, or rather, especially inferential discourses) are constituted.13 Frege's initial

motivation, behind his revolutionary Begriffsschrift, to develop a notation system that could protect

us from such inferential errors was honorable and ingenious. But, it seems that some influential

ancestors of us (probably including Frege himself)14 soon mistook what had been invented to the

extent of making such a confused diagnosis or rationalization of what was really its own

engineering defect (i.e., the neglect of the pragmatic aspect of human language, which was an

inevitable side-effect of tacitly adopting the semantics-centric strategy to simulate human

deductive inferential discourse) as the recovery or discovery of the lost logical (semantic) form that

had been lost from the surface syntactic form of natural language expressions. (From the point of

view of this semantics-centric stance, the "logical forms" are lost for the sake of some "mere

13

This pair of speech acts (reference and predication) is not to be confused with the Aristotelian "subject-predicate" analysis of a proposition (coupled with the Aristotelian syllogistic rules of inference). I'm inclined to think that this Aristotelian edifice too is a failed semantic-centric account. To defend this view, I must articulate the view and defend its plausibility, checking against the actual texts on the Aristotelian logic. I postpone this task until I finish writing on other more important topics. 14

I have read Begriffsschrift firsthand only the preface and the first chapter. From secondary literature (primarily Van Heijenoort's introductory comment on this work in the "From Frege to Gӧdel"), I believe that this work includes the essence of the aforementioned syntactic distortion and existential presupposition-management, and that Frege (at least as of writing this work) probably held this confused view of his invention.

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pragmatic" benefits that are immaterial for the semantics of the discourse, which is all we need to

be concerned with, free from "pragmatic distortions," in doing inference rigorously.)15

What had been invented, in the mighty single stroke of the Begriffsschrift, was nothing more than a

conspicuously artificial "machine" that was designed to simulate our native inferential judgments

and, in virtue of its "mechanical" rigidity, to protect us from our human errors. It was most

unfortunate that the invention of this "machine," which proved to be so influential to the following

generations of logicians, was achieved by such a mighty single stroke containing a number of

distinct innovations and insights, and with the entitlement to the somehow mystifying title of an

"axiomatization of logic." Together, all of these seem to have made it hard for its posterity to

separate apart the distinct parts involved in this invention and to be aware of the semantics-centric

nature of the tacit design strategy taken in this project of "mechanizing" human inferential

discourse.

As far as I'm concerned, logic is discursive normativity, and discursive normativity free of

pragmatics is oxymoron. Pragmatics is the heart of logic, not wild frontiers to be tamed by logic the

semantics. (Still, I agree that efforts by Formal logic (logic the semantico-syntax) to simulate logic

the pragmatics are not without their merits. I only claim that we should not confuse what we have

done with something else.)16

Some of typical, frequently raised objections to this mistaken confidence of modern intimate logic

did not seem to help the situation either. They considered that semantic-representational use was

just one of many ways we used our natural languages, and that, in reconstructing a language for its

single function, modern logic misrepresented what a language was, or that it fell short of being a full

reconstruction of all its main functions. (I'm not sure if people who made this line of objection

targeted their objection at the Formalized logic or non-Formal intimate modern logic, or if they

made this distinction at all, as of now. Whatever their original intentions may have been, the

objections are most appropriate for the non-Formal intimate logic.) In making this line of objection,

they left intact the modern intimate logical ways of "translating" the locutions mentioned above, or

put differently, they almost in effect endorsed those "translations" as correct reconstructions

insofar as the semantic-representational function of a language was concerned. The problem, as I

see it, is that we do various other things with language through language's representational

function. So, a reconstruction of a language that severely fails to do justice to its non-

15

I take this view (that I tentatively ascribed to Frege) as a sort of native rationalization, something analogous to what anthropologists call "native's theory." Of course, it goes without saying that, if my writings are read by my posterity, I do hope that some will take my views as native's theory and carry the torch of philosophy further ahead. 16

This insinuation against modern logic in general applies also against itself. I'm here doing the exactly same thing to "them" as "they" did to "their 'them'" before me. This self-recognition of repeating the same sin makes me no more excusable, but, if anything, less excusable, since I know what I am doing and choose to do it anyway. But I think this is my work.

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representational functions also severely fails to do justice to its representational function.

Semantics free of pragmatics is oxymoron just as logic free of pragmatics is.17

This reveals another, related problem: By endorsing, in effect, the intimate logical reconstruction of

natural language's semantic-representational function, this sort of objection helped to endorse its

semantics-centric marginalization of pragmatics and the idealized view of semantic representation

that was separated or independent or free from lowly pragmatics. I'm talking about the view of

representation that is free of perspectivality or free of any sort of (referential or representational)

indexicals. It was as if to say that there was the Platonic heaven, not just dwelt by Platonic Forms

(objects of representation in their pure Forms, to be represented free of pragmatics), but by

Platonic "Us" (subjects or agents of representation, who do the representation free of pragmatics).

Back to my diagnosis of what is happening with these "translations" (like (i) and (ii) above).

Crudely put, their effect of distorting the syntactic structures of sentences (and the correct

pragmatics of the original syntactic structure, the pragmatics of the reference-predication pair of

speech acts), is somehow rendered harmless, insofar as inferential judgments are concerned, by the

existential presupposition management maintained by these "translations" together with their

operational rules of inference. Notice that in making this diagnosis, we encounter yet another

image of "logic," on top of the Formal logic and non-Formal intimate logic. What my diagnosis says

is (i) that our original native rational intuition or competence contains in it sufficient inferential

competence,18 and (ii) that modern intimate logic is after all not "raw logic" but an artificial

simulation of this native inferential competence. Behind this diagnosis is my belief that all

linguistically capable human beings carry this native inferential competence because of certain

pragmatically inevitable pre-conditions for the existence of a language. I also think that natural

languages also contain discursive norms that are not due to such pragmatic inevitabilities, and that

their respective native rationalities vary in some ways and to some extents. What I take to be "raw

logic," something simulated by the modern intimate logic, is not just any native human rationality,

but this universally shared core of probably diverse native human rationalities. Moreover, I ascribe

the existence of mathematics, as universally shared or countenanced rational discursive practice, to

the existence of this hypothetical universal core.19 So, I think that we do not really need the

17

I realize that the point I am trying to get across here may be susceptible to a certain misreading, depending on how people understand what I mean by "we do various other things with language through language's representational function." Let me just warn here that for those people who haven't gone through the kind of normative-pragmatic re-thinking of what "representation" is (which I advocate in my re-thinking of "mind"), what I mean here is probably beyond their imagination or comprehension. 18

This native competence is of course fallible and is apparently particularly vulnerable to certain inferential errors, perhaps due to certain semantic or pragmatic interferences in cognition. But, we should note that we don't need, and ultimately cannot appeal to, such an artificial convention as modern intimate logic, for the final judgment of inferential correctness. It is we who adopted these counterintuitive "translations" (in the package deal with other operational rules) as correct tools for inference, and we must have used what may be called our "raw logical competence" in judging their correctness as tools of inference. 19

This means that I identify mathematical competence with logical competence. This may sound wrong, according to the modern standard of logic which makes us say that mathematics has been reduced to logic and set-theory, not logic alone. This standard seems to be held for a good reason, but not for an absolute reason. That is, I think

12

intimate modern logic to do mathematics at all, although getting its training helps most people to

get better in mathematical inference because it simulates this "raw logic."20

Hopefully, the above articulation gives some orientation, or hypothetical orientation, for why the

"translations" strike "us" (as untrained competent native users of, say, English) as counterintuitive.

Based on this hypothesis, I take a task of us as philosophers to be trying to explain why these

"translations" and the paired operational rules work. This task includes a sort of philosophical

investigation of what "logic" really is, which seems to have become rarer these days. And, if my

hypothesis is right, this philosophical investigation can expect help from a sort of empirical

investigation, study of the pragmatics of the reference-predication pair of speech acts realized in

various natural languages, for that is where our "raw logic" comes from. (I forgot to mention this

hypothesis: I believe that this pair is a part of pragmatically inevitable core of human languages,

and that here lies the universal core of our diverse native rationalities. So, the pragmatics of

reference-predication is subject both to empirical and a priori philosophical investigation,

according to my hypothesis.)21

Modern intimate logic may not be really modern.

A final short remark about calling the intimate logic in question "modern." This logic is modern in

the sense that it is usually associated with names like Boole, De Morgan, Frege, and Peirce, as if it

had not been known before them. Perhaps, the quantification theory had not been known before

Frege and Peirce. (I am not sufficiently familiar with the history.) But, good part of the modern

intimate propositional logic seems to have their origin in ancient Greek. In this sense, calling it

"modern" is not accurate. I only beg a pardon for using the term "modern" here in this inaccurate

way, mostly for the ease of reference to the topic of the present essay.

that the distinction Sellars and Brandom draw between "material" inference and "logical" (or "formal") inference should be taken as relative. 20

This may be another good place to re-read the footnote 4 (and perhaps the footnote 8, too). 21

The a priori investigation I refer to here is a priori only in the sense that it does not require observation of any discourse but one's own. To the extent that it requires observation of one's own discourse, it is still empirical. And, it's crucial to note that everyone's discourse is made possible, and hence, is restricted, by the "grammar" of one's language in which the discourse is held. The distinction between pragmatic limits peculiar to that language's "grammar" and the pragmatic inevitabilities of any human language is conceptually easy to draw, but they are hard to tell apart in concrete cases. I think we have two ways to check us from going astray in this research in this regard. One is mathematics. Assuming the hypothesis that basic mathematical competence and the universally shared core of human native rationality (i.e., the "raw logic") are one and the same, we may find, in or among our own "private" discourses (the most raw data of reference-predication acts we can ever get), a distinction between aspects that are pragmatically inevitable (needed for mathematics) and which are not (not so needed). The other is, after all, the empirical investigation of the reference-predication acts realized by various existing (and extinguished) languages.