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Truth as the Relation between Logic and Metaphysics in Frege and Heidegger[DRAFT]Joshua Harris

Gottlob Frege and Martin Heidegger are very different

philosophers. Whereas the former’s project can be understood as a

“logicism” which reduces many classic philosophical questions to the

law-governed machinery of formal logic, the latter philosopher seems

to have dedicated his career to revitalizing what he takes to be the

perennial core of such questions. So although it might seem like a

hopelessly uphill struggle to find meaningful points of comparison

between Frege and Heidegger, recent literature (though sparse,

admittedly) has made some unlikely progress in doing so.1 Perhaps

ironically, it is not despite these fundamental differences but rather

because of them that instructive comparisons of their work can be drawn.

This study is an attempt to draw one such instructive point of

comparison between Frege and Heidegger on the question of the meaning

of truth. Drawing primarily from Frege’s Grundlagen der Arithmetik and Der

Gedanke, as well as Heidegger’s oft-neglected Metaphysische Anfangsgründe der

1 See, for example, Greg Shirley, Heidegger and Logic: The Place of Logos in Being and Time (New York: Continuum, 2010); Barbara Fultner, “Referentiality in Frege and Heidegger,” Philosophy and Social Criticism 31.1 (2005), 37-52; Wayne M. Martin, Theories of Judgment: Psychology, Logic, Phenomenology (Cambridge: Cambridge University Press, 2006); Edward Witherspoon, “Logic and the Inexpressible in Heidegger and Frege,” Journal of the History of Philosophy 40.1 (2002), 89-113.

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Logik,2 I aim to show that their differences on the meaning of truth can

be boiled down to their respective positions on the relationship

between logic and metaphysics. For Frege, logic is an unfounded

foundation for any and all objective science—metaphysics included.

Heidegger, on the other hand, argues that the science of logic as the

laws of thinking is intelligible only in light of a metaphysics of

being qua being. If successful, this thesis could prove to be important

for understanding the fundamental trajectories of these two thinkers

and their influence in the twentieth and twenty-first centuries.

The argument proceeds in three major sections: first, with a

reading of Frege’s Grundlagen and Der Gedanke; second, with a reading of

Heidegger’s Anfangsgründe; finally, with an assessment of an aporia that

results from two philosophers’ positions on the question of truth

construed as the relationship of logic with respect to metaphysics.

Frege: Logic as the “laws of truth”

It is well-known that Frege’s Grundlagen der Arithmetik takes its cue

from Kant. More specifically, it is concerned first and foremost with

Kant’s distinction between “analytic” and “synthetic” a priori judgments

2 Edward Witherspoon has dealt with this text briefly in an article comparing Frege and Heidegger on the nature of logic, but in my view he mistakenly argues that Heidegger concedes several Fregean points about logic without dispute. I submit that Heidegger does no such thing. One implication of the following study, then, is that Witherspoon’s “concessive” reading of Heidegger’s Anfangsgründe is mistaken. See Edward Witherspoon, “Logic and the Inexpressible in Frege and Heidegger,” 101-11.

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in his Kritik der Reinen Vernunft—especially in the science of mathematics.3

This distinction between analytic and synthetic a priori judgments is

described by Kant in the following manner: “Analytical judgments

(affirmative) are therefore those in which the connection of the

predicate with the subject is conceived through identity.” Synthetic

judgments, conversely, are judgments in which “that connection

[between subject and predicate] is conceived without identity.”4 The

point here is simple enough: The predicates of analytic a priori judgments

are “pure” deductions from the subject considered in itself, whereas

the predicates of synthetic a priori judgments are not deducible from the

subject considered in itself. “A bachelor is unmarried” is a classic

example of an analytic a priori judgment, since the predicate “is

unmarried” is nothing more than an analysis of the subject “bachelor.”

An example of a synthetic a priori judgment can be adduced from the

natural sciences: (to use Kant’s own example) “In all changes of the

material world the quantity of matter always remains unchanged.”5 In

this judgment, the predicate “always remains unchanged” requires more

than just an analysis of the subject “quantity of matter in the

material world,” since it seems to be accidental rather than essential to the

quantity of matter that it always remain unchanged. To put it another 3 See Immanuel Kant, Critique of Pure Reason, tr. Max Müller (New York: Anchor Books, 1966), 8-17. 4 Ibid., 7. 5 Ibid., 12.

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way, nothing prevents us from understanding the meaning of the

“quantity of matter in the material world” even if we fail to know

that it “always remains unchanged.”

The question that arises in Frege’s Grundlagen is whether or not

arithmetical truths (e.g. “7 + 5 = 12”) are synthetic a priori judgments.

For Kant, “7 + 5 = 12” is indeed an example of such a synthetic a priori

judgment:

[W]e find that the concept of the sum of 7 and 5 contains nothing

more than the union [Vereinigung] of the two numbers into one; but

in thinking that union we are not thinking in any way at all what

that single number is that unites the two. In thinking merely

that union of seven and five, I have by no means already thought

the concept of twelve.6

Kant’s point here is that the judgment “7 + 5 = 12” contains the

concept of a sum—that is, “the union of two numbers into one” (in this

case, the numbers 7 and 5) that cannot simply be “analyzed” into the

predicate. The predicate “= 12” involves the concept of a single

number—one that cannot be analytically deduced from the concept of a

sum of two numbers, 7 and 5. Kant maintains that the judgment is still

a priori, of course, but in order to arrive upon it, he says, “We must go

beyond these concepts and avail ourselves of the intuitions

6 Ibid., 11.

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corresponding to one of the two: e.g., our five fingers, . . . [i]n

this way we must gradually add, to the concept of seven, the units

[Einheiten] of the five given in intuition.”7 The intuition (Anschauung)

of which Kant speaks here seems to imply a modified version of the

Aristotelian position that numerical terms require the concept of the

“unit,” which serves as a common measure of any two [or more] numbers8—

a unity that is not itself subject to the category of quantity.

Without this intuition (captured nicely by Kant’s appeal to “fingers,”

i.e. something to count), we could not arrive at the predicate, which is

the single number 12.

Frege’s project of philosophical logicism might be said to have

begun with a rejection of this Kantian position. For Frege, the idea

that arithmetical propositions rely upon some sort of transcendental

or metaphysical “intuition” for their truth is simply untenable. He

laments the tendency of mathematicians and philosophers alike to

“lapse into psychology” when attempting to answer similar questions

about the nature of number.9 This is simply an intolerably vague and

shaky conclusion for Frege, especially given the otherwise exceptional

clarity and objective rigor that is characteristic of mathematics. His

7 Ibid. 8 On this point, see Aristotle, Metaphysics in: The Basic Works of Aristotle, tr. Richard McKeon (New York: Random House, 1941), 1021a. 9 Gottlob Frege, The Foundations of Arithmetic, tr. J.L. Austin (New York: Harper & Brothers, 1953), xx.

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alternative to the Kantian idea of arithmetical truths as synthetic a

priori judgments can be understood as a philosophical explanation of

arithmetical truths—one that matches the clarity and objective rigor

that is characteristic of mathematics as a science. It is the task of

his logicism, then, to provide a suitable philosophical foundation for

arithmetical truths by deriving them from primitive logical laws.

Frege proceeds to derive three fundamental principles of arithmetic

in §§70–83 of Grundlagen: namely, a logical formulation of the concept

of zero, natural number and perhaps most importantly, the “successor

relation” (Beziehung φ) that characterizes the infinite series proper to

arithmetic.10 It is beyond the scope of this paper to reproduce Frege’s

formalizations of these principles, but for our purposes it is

important to recognize two fundamental moves that Frege makes with

respect to Kant and Aristotle:

1. Contra Kant, Frege’s logicism about arithmetic conceives of the

analytic/synthetic distinction as pertaining only to the ground of the

judgment—not to the content of the judgment itself.

Whereas Kant’s distinction between analytic and synthetic hinges upon

the additional intuition (or lack thereof) that constitute certain

judgments qua judgments, Frege’s distinction “concerns not the content

of the judgment [der Inhalt des Urtheils] but the justification [Berechtigung]

10 Ibid., 84-95.

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for making the judgment. . . . [i.e.] the ultimate ground on which the

justification for holding it to be true rests.”11 This removal of the

analytic/synthetic distinction from the structural features of

judgment qua judgment allows Frege’s logicism to maintain a strictly

objective account of judgment—one that can successfully cut off any and

all psychologistic murkiness from the start.

2. Contra Aristotle, Frege’s logicism recasts the structure of

judgment in terms of function and argument rather than subject and

predicate. Whereas the fundamental structure of Aristotelian judgment

is marked by the “division and composition” of subject and predicate

terms (e.g. “Snow” [subject] is white [predicate]”),12 Frege’s

structure of judgment is marked by the “input” of arguments into

functions (e.g. “If x is snow, then x is white” [“snow” and “white” as

arguments; “If x is _, then x is _” as function]). There is much to be

said about the explanatory strengths of Fregean “predicate calculus”

over against Aristotelian “subject-predicate” logic,13 but for our

purposes it is important to note that all the possible formulations of

the structure of the “function” represent the objective, precise laws of

truth. Whereas the Aristotelian subject-predicate form is built to

11 Ibid., 3.12 On this point, see Aristotle, On Interpretation in: The Basic Works of Aristotle, tr. Richard McKeon (New York: Random House, 1941), 17a. 13 This includes, perhaps most notably, the ability to represent judgments involving multiple generalities.

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accommodate concepts such as “exists” and “true” as non-univocal,14

Frege’s logicism reduces them to the absolute univocity of the

functional calculus.

With these two points from the Grundlagen, we are now in a better

position to understand some of the key motivations behind Frege’s

project. It is clear that such a logicism has its central motivation

in the prospect of providing clear, objective rules for thought—that

is, rules that can provide ready answers to questions about the

foundations of the clearest and most pristine of sciences,

mathematics.15 These two points, then, are best understood as necessary

consequences that follow from carrying out such a project. (1)

undercuts what Frege considers to be a shaky Kantian transcendental

philosophy—which is, ironically, conceived by Kant as a relatively

sturdy foundation for the even shakier science of metaphysics—by

showing that the way in which a judgment is arrived upon has nothing at all to

do with the content of the judgment as such. (2) assigns clear and distinct

14 For reasons that are not unrelated to the difference between Frege and Heidegger on the meaning of truth and its relationship to logic, the Thomist philosopher Jacques Maritain famously argues in Formal Logic that the Fregean calculus attempts to replace intelligence with “logistics,” as it implies an exile of analogical reasoning from its natural home, i.e. the land of logical inference. See Jacques Maritain, Formal Logic (New York: Sheed and Ward, 1941), 221-4. 15 Or arithmetic, at least. There is disagreement about whether Frege agrees with Kant that geometrical truths are synthetic, though it appears that he does in the Grundlagen, at least.

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rules for thought which, together, form the absolutely objective,

univocal laws of truth.

Yet if we are interested in Frege’s understanding of truth and

its relationship to logic as he conceives it, it is necessary to move

beyond the Grundlagen to some later works. Before doing so, however, it

is worth visiting a final passage from the Grundlagen—one that sets the

trajectory of Frege’s logicist reduction of truth. In a discussion

reinforcing Frege’s steadfast criticism of any and all forms of

psychologism, he remarks,

I understand objectivity [Objectivität] to mean what is independent

of our sensations, intuitions, and imagination, and of all

construction of mental pictures out of memories of earlier

sensations, but not what is independent of reason [Vernunft]. For

what are things independent of reason? To answer that would be as

much as to judge without judging, or to wash the fur without

wetting it.16

Now the first part of this quotation should be uncontroversial,

assuming our discussion up until this point has faithfully represented

Frege’s views. Indeed, precisely to the extent that Kant and Aristotle

understand the faculty of intuition to be at least partially constitutive

of (certain kinds of) judgments, they fail to offer a sure foundation

16 Frege, Foundations, 36.

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for arithmetical truths—one that can only be derived from the

absolutely objective content of logical laws.

The second part of this passage, however, contains a concept that

we have not yet explored: namely, the concept of “reason” as a

governing institution of any and all legitimate thought.17 Indeed, it

is even more than that; for Frege’s use of reason goes beyond a merely

“epistemic” conception. On the contrary, for Frege, it seems that

things themselves are if and only if they are reasonable. To the extent

that we grasp what Frege means by the nonsensical notion of “wash[ing]

the fur without wetting it,” I suggest, we also grasp the essence of

Frege’s reductionistic project with respect to truth. As we move on to

some of the later writings, it is important to understand what

“reason” could mean if it is entirely independent of “sensations,

intuitions, and imagination.” This becomes clear as we turn our

attention to Frege’s later essay, Der Gedanke.

Frege calls a thought “something for which the question of truth

arises. . . . [it is] in itself immaterial, clothes itself in the

material garment of a sentence and thereby becomes comprehensible to

us. We say a sentence expresses a thought.”18 This point is also clear

in “On Sense and Reference.” What he calls a thought here is a species 17 I am following Erich H. Reck in my understanding of this passage. See ErichH. Reck, “Frege on Truth, Judgment and Objectivity,” in: Essays on Frege’s Conception of Truth, ed. Dirk Greimann (Amsterdam: Rodopoi, 2007), 160-1. 18 Gottlob Frege, “The Thought: A Logical Inquiry,” Mind 65.259 (1956), 292.

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of “sense” in a sentence. It is the objective or propositional content

of a sentence—one which can be expressed and repeated regardless of

its “material garment” of natural languages such as English or

German.19 It is important that thought is a species of sense—not a synonym

for sense altogether. Whereas every thought is a sense of a sentence,

not every sense of a sentence is a thought.20 The question of truth

arises only in thoughts, which is to say that the question of truth

only arises in [indicative] sentences “in which we communicate or

state something.”21 Thus, three qualities of the thought are

immediately relevant for our discussion:

1. A thought is objective—not a psychological or physical

phenomenon.

2. A thought is expressed in an indicative sentence in ordinary

language, but in no way dependent upon ordinary language. It is

the “sense” of an indicative sentence in ordinary language.

3. A thought is the kind of thing that can be “true” or “false.”

I have already remarked that, in the Grundlagen, Frege is

interested in objective laws of thought. With this more precise

account of what “thought” actually means, however, we are in a better

position to avoid some potential misunderstandings. As Frege remarks 19 Ibid. 20 Imperative or interrogative sentences have sense but are not thoughts, for example. 21 Ibid., 293.

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early on in Der Gedanke, perhaps the most woeful of such potential

misunderstandings is the idea that objective laws of thought might be

a way of talking about empirically or phenomenologically verifiable

regularities in “mental occurrence[s].”22 If this were what Frege meant

by objective laws of thought, of course, than his aversion to

psychologism would be hopelessly undermined; for what could be more

psychologistic than mental occurences?

Since we now know that thoughts are marked by the differentiae

mentioned above, though, it is clear that objective laws of thought

could never take mental occurrences as their objects. Indeed, it may

even be a pleonasm to say objective laws of thought, since thoughts

themselves are already objective in the sense described above. So, if

this is Frege’s understanding of what is meant by logic as “laws of

thought,” we are in a better position to understand what will be a

more controversial claim in the context of the present discussion:

namely, Frege’s claim that “it falls to logic to discern the laws of

truth” [die Gesetze des Wahrseins].23 This is what will become an issue for

Heidegger in his Anfangsgründe, so it is worth exploring in some detail

here.

22 See Ibid., 289. 23 Ibid. A more literal translation might render die Gesetze des Wahrseins as “the laws of being-true.”

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Frege says early on in Der Gedanke that “[t]he meaning of the word

‘true’ is explained by the laws of truth.”24 Like the laws of thought

we have just mentioned, these laws are also objective in the sense

that they are not constituted in any way by physical or mental

occurrences. In order to understand what Frege means by truth, then,

it is instructive to take note of his critique of the more

“conventional” theory of truth as some sort of successful

“correspondence” between some mental picture and the mind-independent,

non-linguistic reality it depicts. He offers two major objections to

this idea.

First, according to Frege, “A correspondence [Übereinstimmung], . .

. can only be perfect if the corresponding things coincide and are,

therefore, not distinct things at all.”25 This point is

straightforward. To the extent that a two objects are similar, they can

be said to “correspond” to one another in a relevant way. Yet insofar

as the mental picture and the reality it depicts are different—and

indeed they must be different at least for the reason that one has the

property of being “in the mind” and one does not—a “perfect”

correspondence between the two is impossible, by definition. The

crucial point is this: namely, that if “there can be no complete

24 Ibid. 25 Ibid., 291.

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correspondence, no complete truth [vollkommene Wahrheit]. . . [then]

nothing at all would be true: for what is only half true is untrue.”26

What we have, then, is another example of Frege’s relentless demand

for clarity and precision—even and especially with regards to the

question of the meaning of truth. Among the rather unwelcome

consequences of the so-called “correspondence theory” is the abolition

of truth altogether!

Second, perhaps more famously, Frege raises a circularity

objection against the correspondence theory. Since a theory of truth

must involve a definition within which “certain characteristics would

have to be stated . . . the question would always arise whether it

were true [emphasis mine] that the characteristics were present. So one

goes round in a circle.”27 In other words, in any and all cases of

trying to offer a definition of truth—as correspondence or something

else—it turns out that we need a concept of truth before we can define

truth. A vicious circle indeed.

But if correspondence jettisons the possibility of arriving at

truth, and other definitions of truth are hopeless circular, what can

be said about truth qua truth, according to Frege? In “On Sense and

Reference,” of course, we receive what might be some preliminary

26 Ibid. 27 Ibid.

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thoughts about an answer to such a question: namely, that truth values

(i.e. “the True” and “the False”) serve as the objective references of

thoughts.28 Just as ordinary “proper names” such as “Felix” refer to a

single feline object, so does the thought expressed by the declarative

sentence “Some cats are black” refer to the “object” of the True.

Thus, to return to Frege’s preferred language of function and

argument, we might say that the truth value of “Some cats are black”

is the output of a combination of a function (i.e. “there is at least

one x such that x is a _ and x is _”) and its arguments (i.e. “cat” and

“black”).

Yet while this Fregean schema is helpful for getting a sense of

what ordinary language seems to demand of certain kinds of declarative

sentences (i.e. their truth values), it still does not give us a

robust account of what sort of object a truth value is. Put simply, though

we might have an idea of why we need truth, we are still in the dark

about the nature or essence of truth. Yet this is precisely the question

that Frege cannot answer: “it is probable that the content of the word

‘true’ is unique and indefinable [undefinierbar].”29 Even with the

assistance of his sense-reference relationship—a relationship that is 28 As Frege remarks, “Every declarative sentence concerned with the reference of its words is therefore to be regarded as a proper name, and its reference, if it has one, is either the True or the False.” Gottlob Frege, “On Sense and Reference” in: Meaning and Reference, ed. A.W. Moore (Oxford: Oxford University Press, 1993), 28. 29 Frege, “The Thought,” 291.

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lost on his early Begriffschrift and Grundlagen—Frege is reduced to silence

when it comes to offering a definition of truth. This is the perhaps

anti-climactic end to Frege’s majestic project of unearthing the most

general “laws of truth.”

To come full circle, then, perhaps we are now in a position to

understand the meaning of Frege’s aforementioned curious passage from

his Grundlagen: “For what are things independent of reason? To answer

that would be as much as to judge without judging, or to wash the fur

without wetting it.”30 Frege’s anti-psychologism is consistent

throughout his career, from Grundlagen to Der Gedanke. By salvaging the

purely analyticity of arithmetical truths from the threatening

intuitive transcendentalism of Kant, he banishes the

analytic/synthetic distinction from the content of judgments

altogether. This leaves him with the task of coming up with a new

schema for judgments, which is accomplished in his function-argument

conception of logic. Ultimately, as we have seen, it is the logical

machinery of the function that serves as the laws of truth. To think

“reasonably,” then, for Frege, is to think in accordance with such

laws. The ever-looming specter of psychologism is warded off only by

the absolute objectivity of these laws.

30 See note 17 above.

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Yet, as we have also just seen, the absolute necessity of

thinking in accordance with these laws precludes any attempt to

“ground” or “define” them; for to embark on such a project would be to

arbitrarily exempt oneself from the laws for a moment, i.e. “to wash

the fur without wetting it.” This holds a fortiori for the concept of

truth, since the laws of the function are governed by truth values.

They are the laws of truth, after all. To “ground” or “define” truth

would be the ultimate exercise in washing the fur without wetting it.

Thus, Frege leaves the question of the meaning of truth

unanswered for reasons directly associated with his conception of

logic as nothing other than the objective laws of truth. If this is

the case, then we are now in a position to move to Heidegger’s

alternative in his Anfangsgründe—an alternative that deals with

precisely this sort of Fregean position on the meaning of truth.

Heidegger: Logic as λόγος

Heidegger’s Anfangsgründe is a series of lectures delivered at the

University of Marburg in 1928 which feature a close consideration,

appropriation and criticism of Gottfried Wilhelm Leibniz on the

relationship between metaphysics and logic. Although the particulars

of his interaction with Leibniz does not concern our discussion

directly, it is of interest here to the extent that it occasions an

explicit point of contact between Heidegger and Frege. The most

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important of these points of contact is a mutual disdain for

psychologism. Heidegger is clear: any psychologistic appeal to an

empirically available context as somehow explanatory for a genuine

philosophical question “circumvent[s] the real contents of the problem

itself (This is always the case when one believes he has solved a

problem by figuring with psychological probability what impulses might

have been involved in posing and solving the problem).”31 Later he

appeals to his teacher Edmund Husserl’s critique of psychologism as a

bastion against any such shallow attempts “to give empirical grounds

for an a priori statement.”32 Of course, as we will see, Heidegger’s

way out of psychologism is far different than Frege’s. Despite this

divergence, it is important for comparison’s sake that they share a

common opponent in the ever-lingering specter of psychologism with

regards to logic and truth, especially.

Heidegger’s task in the Anfangsgründe is to provide a genuinely

“philosophical” conception of logic: “logic is in fact a propaedeutic

[Vorschule] to academic studies in general and is, at the same time,

quite correctly valued as an essential entry into philosophy—assuming

that logic itself is philosophical. So this is the challenge: logic

should change; logic should become philosophical!”33 Heidegger seems to31 Martin Heidegger, The Metaphysical Foundations of Logic, tr. Michael Heim (Bloomington, IN: Indiana University Press, 1984), 115. 32 Ibid., 121. 33 Ibid., 5.

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share this starting point with Frege insofar as he understands

questions of logic to be part and parcel of “first philosophy.” Unlike

Frege, however, Heidegger is interested in unearthing the

“foundations” of logic as that which “asks about the properties in

general of λόγος, of statement, of that determining where the essence

of thinking as such resides.”34 Again, it is striking how similar this

sentence reads when compared to Frege’s own development of logic as

the laws of truth and the transcendental condition of “reason” for any

and all objective thought. Despite Heidegger’s project of “fundamental

ontology” that he had only recently published in Sein und Zeit (1927, just

one year before the Anfangsgründe), the importance of texts such as the

Anfangsgründe show that the issue is not so much about “going beyond” the

confines of logic in order to develop a phenomenology of being qua

being or Sein; rather, it is about uncovering the essence of logic

itself as the science of λόγος.

Heidegger embarks on this investigation into λόγος with

characteristic respect for the history of philosophy. Because his

“challenge” is to reveal the philosophical roots of logic, he must

first provide a working definition of what he means by

“philosophical.” Here he follows Aristotle in understanding the

subject matter of philosophy as being qua being. “The striving for the

34 Ibid., 2.

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possibility of a correct understanding of the essential, or this

understanding, has for its object being. . . . of what precedes

everything else.”35 There cannot be a more fundamental philosophical

subject matter than the meaning of being, for Heidegger, since anything

that might be posited as more fundamental would itself beg the

question of its own thing-hood or being. Thus, we have a clear

statement of what is the central question in his famous introduction

to Sein und Zeit: namely, the question of “the meaning of being” (der Sinn

von Sein).36

When Heidegger says that he means to inquire after the

“metaphysical foundations” (metaphysische Anfangsgründe) of logic, then,

what he means to inquire after is the special relation that λόγος

maintains with respect to being. On this question, he takes his cue

from Parmenides’ curious remark about the intimate relationship

between thinking and being in fragments from On Nature, “For to think

and to be are the same” (τὸ γὰρ αὐτὸ νοεῖν ἐστίν τε καὶ εἶναι).37 Now a

commonsense reading might lead one to conclude that this strange

Parmenidean claim is trivially false. Stones, for example, can be

without knowing; for they are not the kind of thing that has the

capacity for knowledge. But if something can be and not know, then it 35 Ibid., 13. 36 Martin Heidegger, Being and Time, tr. Joan Stambaugh (Albany, NY: SUNY Press, 2010), 6 [in the original German pagination]. 37 Heidegger, Metaphysical Foundations, 15

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seems to follow that being and knowing are distinct in at least this

respect. Therefore it seems that Parmenides’ “way of truth” is

actually quite false.

Yet this commonsense reading is superficial. Indeed, it is

Heidegger’s interpretation of Parmenides that turns out to be an

occasion for the former’s “existential analytic” of human Dasein as a

sort of transcendental condition of possibility for any science of

being. But what could this mean? Heidegger’s answer comes as an

analysis of “thinking.” He first warns against understanding thinking

as an “activity and comportment of humans. The investigation into

thinking as a form of human activity would then fall under the science

of man [sic], under anthropology. The latter is, of course, not

philosophically central, but only reports how things look when man

thinks.”38 Again, to mistake this sort of observable phenomenon for a

philosophical issue (i.e. an issue with implications for the essence

of logic or truth) would be to lapse into psychologism. Heidegger is

always clear about his stridently critical stance against any such

position.

The crucial difference between this psychologizing tendency to

understand thinking as one human “activity” or “comportment” among

others and Heidegger’s properly philosophical interpretation of

38 Ibid., 18-19.

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Parmenides is the ontological difference, i.e. the difference between

being qua being (Sein) and particular beings (Seienden). Whereas the

psychologist or the anthropologist is concerned with the observable

regularities of particular beings—human beings, specifically—the

philosopher is concerned with the fundamental unity that all beings

share insofar as they are beings in the first place. Heidegger’s

interpretation of Parmenides’ identification of νοεῖν and εἶναι, then,

has to do with the “understanding-of-being [that] belongs to Dasein’s

ontological constitution. . . . Its understanding of being is not one

capacity among others, but the basic condition of possibility of Dasein

as such.”39 In other words, for Heidegger (and for the medieval

philosophical tradition that produced him), because being qua being is

the proper object of intelligence,40 being qua being is always already

being-as-understanding. The elusive unity of being qua being is co-

extensive with the equally elusive unity of understanding. Thus, νοεῖν

and εἶναι are “equiprimordial,” meaning that both are equally

fundamental, and that neither are intelligible without the other.

With this clarification of the Parmenidean affirmation of the

equiprimordial status of νοεῖν and εἶναι, then, we have a context 39 Ibid., 16.40 Thomas Aquinas, for instance, consistently maintains, Primo autem in conceptione intellectus est ens . . . ens est proprium objectum intellectus. “That which is first conceptually in the intellect is being . . . being is the proper object of theintellect [translation mine].” Thomas Aquinas, Summa Theologiae, Ia, q. 5, a. 2.

23

within which to grasp the essence of λόγος. Thinking implies being—and

vice versa—and λόγος has to do with the laws of thought. Again, it

cannot be stressed enough that Frege and Heidegger share the conviction

that the essence of logic, i.e. what it is most fundamentally has to do

with the purely objective laws governing reasonable thinking. Where

Frege and Heidegger differ, however, is on the question of the

“ground” of these laws. As we have seen, for Frege, any attempt to

ground logical laws metaphysically is doomed from the outset, since

any science of metaphysics must presuppose the laws that it is trying

to ground. It is an exercise in “wash[ing] the fur without wetting

it.” For Heidegger, however, the laws of logic themselves do not make

sense without such a ground. He asks, “What are the fundamental laws

belonging to thinking as such? What is, in general, the character of

this lawfulness and regulation? We can obtain an answer only by way of

a concrete interpretation of the basic laws of thinking which belong

to its essence in general.”41 Crucially, for Heidegger, it is not

enough to take the lawful character of logic as some sort of self-

evident given; for even the meaning of lawfulness itself is a rich and

varied object of philosophical inquiry.

41 Heidegger, Metaphysical Foundations, 19.

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Heidegger’s answer to his own question regarding the lawful

character of logic could be considered as the “thesis statement” of

the Anfangsgründe:

[O]bligation and being governed by law [Gesetzlichkeit], in

themselves, presuppose freedom as the basis for their own

possibility. Only what exists as a free being could be at all

bound by an obligatory lawfulness. Freedom alone can be the

source of obligation. A basic problem of logic, the law-governedness of

thinking, reveals itself to be a problem of human existence in its ground, the problem of

freedom [italics in the original].42

Here we have the essential trajectory of Heidegger’s project of

unearthing a properly “philosophical” logic.

1. Thinking and being are mutually constitutive or

“equiprimordial.”

2. The science of logic concerns the laws of thinking.

3. Lawfulness as such is unintelligible without a prior freedom

that is to be regulated.43

If these three claims form the original contribution of the text, then

Heidegger’s reading of Leibniz could be considered a “case study” that

42 Ibid., 19-20. 43 It is precisely this point that seems to be missing from the aforementionedthesis of Edward Witherspoon regarding the position of Heidegger’s Anfangsgründe with respect to his later work, especially Vom Wesen der Wahrheit. See note 2 above.

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either confirms or disconfirms the hypotheses. Although again it is

beyond the scope of the present work to offer a detailed account of

his rather original interpretation of Leibniz, it is worth offering a

brief outline for the sake of illuminating the three theses.

Heidegger sketches Leibniz’s logic as a science of judgments,

i.e. sentences that are either “true” or “false.” For Leibniz, the

affirmative quality of a true proposition, i.e. “All bachelors are

unmarried” is its inclusio of the predicate within the subject. Indeed,

“affirmation means simply inclusion”44—even to the counterintuitive

extent that all true propositions are ultimately instances of a priori

judgments (or “analytic,” in Kantian terms).45 This analyticity of all

true judgments is a necessary condition for Leibniz’s own rejection of

psychologism. Now this may appear farfetched in that some propositions

seem to situate some sort of relation between subject and predicate

that is not a purely analytic inclusio, e.g. “The cat is on the mat,”

Leibniz is not necessarily committed to the idea that human intellects

are capable of grasping the fullness of any one subject and all of its

possible predicates. Indeed, for Leibniz, so-called “contingent truths

[veritates contingentes] arise from the will of God, not simply, but from a

will directed by the intellect, through considerations of what is best

44 Ibid., 37. 45 See note 4 above.

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or most fitting [optimi seu convenientissimi].”46 Truths that appear to us as

a posteriori are of this “contingent” variety, which explains their (only)

apparent non-a priori character. Indeed, Leibniz takes this disparity

between human comprehension and the divine so far as to suggest that,

as inclusio, truth is ultimately identitas. This conclusion marks another

striking similarity to Frege’s own argument against correspondence

theory,47 since Leibniz is moved to this radical conclusion by way of

logic’s intolerance of any “more” or “less” with regards to truth and

falsehood. If truth is inclusio, and truth cannot tolerate a more or

less, then there must be some concept of “perfect” inclusio. This perfect

inclusio is exactly what is expressed by identitas.48 Indeed, if there is

anything like a divine perfection, it can be nothing other than the

perfection that is manifest in this relation of identitas between subject

and predicate.

The strategy behind this interpretation of Leibniz, for

Heidegger, is a setting up of a dialectical opposition. The point is

something like the following: if there were any paradigmatic case in

the history of philosophy of founding metaphysics in logic (i.e. the very

reversal of Heidegger’s own stated project), it would be here in

Leibniz’s grounding the truth of the divine intellect and will in the

46 Heidegger, Metaphysical Foundations, 49. 47 See note 26 above48 Heidegger, Metaphysical Foundations, 39.

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perfect inclusio of the predicate in the subject as identitas. The strength

of Heidegger’s argument against this apparent move in Leibniz (and

Frege, by implication), then, is his next interpretive step, which

demonstrates that even this attempt cannot ultimately resist doing

exactly the opposite of what Leibniz himself sets out to accomplish.

Heidegger demonstrates this reversal in Leibniz’s project by

exploring the question-begging nature of identitas. While we do seem

capable of comprehending the role of identitas as a logical operator

among others, identitas as a perfect inclusio of a predicate within a subject

seems to beg the question of the source of its own unity. In other

words, what are the more original conditions of possibility for a

perfect inclusio of a predicate within a subject? What is it that

“confers” the unity that is implied in such an inclusio?49 For Leibniz,

the meaning of identitas is conferred to the proposition by the unity that

is readily accessible for all as the unity of the self-sufficient ego

in the act of perception. Heidegger quotes Leibniz in the latter’s

correspondence with Queen Sophia Charlotte of Prussia,

This thought of myself, who perceive [sic] sensible objects, and

of my own action which results from it, adds something to the

objects of sense. . . . And since I conceive that there are other

beings who also have the right to say “I,” or for whom this can

49 Ibid., 77.

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be said, it is by this that I conceive what is called substance

in general.50

Remarkably, it seems that Heidegger has used Leibniz’s own words to

bring his study back to the Parmenidean identification of νοεῖν and

εἶναι.51 Because “substance” is the metaphysical correlate for the

logical principle of identitas, we now have a “metaphysical foundation”

for logic in the self-perception of ego. Quite literally, then, Leibniz

must agree with Parmenides: to think is, indeed, to be.

Far from some quirky speculation that can be extracted from a

more “levelheaded” logic, Leibniz’s counterintuitive metaphysical

doctrine of the single substance (or “monad”) as “containing” the

universe in itself turns out to be constitutive of his understanding of

logical identitas. Indeed, Leibniz is a far more radical metaphysician

than Aristotle; for the latter only says that “the soul is, in a

sense, all existing things,”52 whereas the former implies that every

substance is, in a sense, all existing things.

Thus, what Heidegger has shown is that even the most extreme

attempt to give absolute primacy to the logical principle of identitas

(i.e. Leibniz’s definition of truth) is ultimately intelligible only

by the light of a decidedly metaphysical “source.” In this case, the 50 Ibid., 87. 51 Note 38 above. 52 Aristotle, De Anima in: The Basic Works of Aristotle, tr. Richard McKeon (New York: Random House, 1941), 431b.

29

metaphysical source is the self-sufficiency of the perceiving ego as

the transcendental condition for the unity of anything at all. Even

for Leibniz, then, says Heidegger, “logic must be conceived as a

metaphysics of truth [Metaphysik der Wahrheit].”53 Parmenides remains

irresistible.

To recap, we have seen that Heidegger shares Frege’s disdain for

any and all psychologistic accounts of logic. However, unlike Frege,

Heidegger does not attempt to ground logic in some sort of absolute

objectivity considered as “independence” from human thinking. On the

contrary, perhaps counterintuitively, he follows Parmenides in

identifying νοεῖν and εἶναι in the ontological difference between

being qua being (Sein) and particular beings (Seienden). Whereas the

psychologistic mistake is to reduce the properly philosophical

question of being to anthropological questions about a particular

activity of particular beings, i.e. human beings, for Heidegger logic

as λόγος is the unity of νοεῖν—a unity that is co-extensive with εἶναι.

To the extent that λόγος concerns the ontological difference, then, it

is “objective” and decidedly not psychologistic.

Yet because λόγος concerns the laws of thought, there is after

all a sense in which it is a decidedly human concern—the crucial

qualification here being that this human concern is a concern which

53 Heidegger, Metaphysical Foundations, 102.

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saturates all beings insofar as they are beings.54 Heidegger’s concrete

“case study” of this properly philosophical hypothesis is Leibniz’s

apparent attempt to ground the meaning of identitas in the absolute unity

of the perceiving ego. At day’s end, Leibniz’s project is precisely the

opposite of what it initially appears to be. It is a grounding of

logic in metaphysics, not vice versa. This move is exactly what we

should suspect, on Heidegger’s line of reasoning, if metaphysics is in

fact the more fundamental science.

Frege and Heidegger: ἀπορία λόγου

I have attempted to demonstrate at least one striking similarity

and one fundamental difference between the respective philosophical

projects of Frege and Heidegger. The similarity, of course, is that a

resolute critique of psychologism forms a mutual point of departure

for each philosopher. The fundamental difference between them has to

do with their vastly different critical approaches with respect to the

problem of psychologism. Whereas Frege’s anti-psychologistic program

salvages the absolute independence of logic and mathematical judgments

from the relatively unreliable phenomena of human intuition or

activity, Heidegger’s anti-psychologism is merely an occasion to

remember the ontological difference between Sein and Seienden as it

appears in the Parmenidean identification of νοεῖν and εἶναι. The

54 For further elucidation of this point, see Heidegger, Being and Time, 191-6.

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result is two vastly different views about the essence of logic and

its relationship to metaphysics.

For Frege, logic as the laws of the functional calculus—which

amount to nothing less than the laws of truth—form the conditions of

possibility for any science at all. Any science which aims to

demonstrate a given truth or truths presupposes truth, which is, in

turn, exhausted by the laws of the functional calculus. Thus, insofar

as metaphysics is one such science, it too must presuppose logic as

the purely objective conditions of its own possibility. Any attempt to

do the reverse, i.e. to ground the laws of logic in metaphysics á la

Heidegger or Heidegger’s Leibniz, is doomed from the start. It is to

wash the fur without wetting it.

For Heidegger, metaphysics as the science of being qua being is,

by definition, the most fundamental of any and all inquiries—including

the science of logic considered as the laws of thought. A law is a

certain kind of being, and as such it begs the question of its being.

Logic as the science of λόγος does maintain a privileged position with

regards to other beings in that its essence arises directly out of the

Parmenidean νοεῖν, but this is only due to the fact that it is itself

co-extensive with Sein or εἶναι. Thus, for Heidegger, Frege’s insistence

upon a rather superficial notion of “independence” obscures the

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question of the essence of logic, and, by extension, the question of

the essence of truth.

Yet up until this point any specific philosophical engagement

between Heidegger and Frege has been left at a rather lofty level of

speculation, since Heidegger does not address Frege by name in the

Anfangsgründe.55 Nevertheless, we conclude the present discussion with

what seems to be a more immediate point of engagement on the part of

Heidegger. Although again it is not an explicit reference to Frege,

Heidegger concludes his reading of Leibniz with a treatment of what

amounts to the essential argumentative strategy of Frege regarding the

primacy of logic with respect to metaphysics. Although it would

certainly be irresponsible to say that Heidegger is engaging the

philosophical movement of Frege, Russell and the early Wittgenstein

directly here, it is difficult to imagine the German philosopher’s

words without this advent of the functional calculus as a “logically

perfect language.”56

55 The place of Fregean advances in logic in Heidegger’s work is a point of some contention in Heideggerian scholarship. It is clear, however, that Heidegger’s training would have equipped him with a ready familiarity with Frege, Russell and others. This is evident as early as Heidegger’s doctoral dissertation, The Theory of Judgement in Psychologism: A Critical-Positive Contribution to Logic. On this topic, see Shirley, Heidegger and Logic, 19. 56 It is notable, for example, that Heidegger criticizes “contemporary logic [as a] new distortion of the problem” of the relationship between logic and metaphysics, properly understood. Heidegger, Metaphysical Foundations, 106.

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Heidegger cites an argument that is “frequently enlisted” by

those who wish to demonstrate the “primacy of logic over metaphysics.”

This argument, he goes on to say, is “capable of deciding the problem

of their relationship on the basis of quite general notions of logic

and metaphysics, without having to go into the specific problems

belonging to the content of either logic or metaphysics.”57 But what is

this argument? Although Heidegger himself does not represent it

formally in numbered premises, I do so here for clarity’s sake:

1. All kinds of knowing requires thinking.

2. Metaphysics is a kind of knowing [i.e. a science].

3. Therefore, metaphysics requires thinking.

4. All thinking presupposes the science of thinking.

5. Therefore, metaphysics presupposes the science of thinking

6. But logic is the science of thinking.

7. Therefore, metaphysics presupposes logic.58

At this point it should be clear that, although Frege is never named

as an advocate of the argument, it is quite a Fregean line of

reasoning. The conclusion, at the very least, supports Frege’s exact

point regarding the utter poverty of “washing the fur without wetting

it.”

57 Ibid., 103. 58 This is a formalized version of an informal argument. See Ibid., 103-4.

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Now there is a sense in which Heidegger has no qualms with one

interpretation of the argument; for he happily concedes that “[e]very

science, including metaphysics, . . . uses, as thinking, the formal

rules of thought.” The interesting question for Heidegger, however, is

not whether or not one or more premises of the argument is false, but

rather, “[W]hat is meant here by ‘presupposition’ [Voraussetzung]?”59 If

by “a presupposes b,” the argument simply means “a uses b,” Heidegger

is quite content with its conclusion. He believes it to be trivially

true that all metaphysical propositions use the laws of logic. However,

for Frege and for Heidegger’s imagined opponent, this interpretation

of “presupposes” does not go far enough. On the contrary, it seems

that the point of this argument is to demonstrate an asymmetrical

dependence in terms of conceptual priority. Metaphysics is grounded in

logic, so this argument seems to state, insofar as logic forms the

independent conditions of possibility for metaphysics as a science. In

other words, while it is possible to imagine logic without

metaphysics, it is impossible to imagine metaphysics without logic.

Again, this “independence” criterion is quite Fregean. It is this

stronger interpretation of “presupposes” that Heidegger cannot accept.

He remarks,

59 Ibid., 104.

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Thinking and rule usage may be inevitable for the operation of

all thinking, and thus also for establishing metaphysics as well,

but it does not follow from this that the foundation consists in

the use of rules. On the contrary, it merely follows that rule

usage itself is in need of justification. . . . [I]t is not even

in a position to make this fact, in its intrinsic possibility

[inneren Möglichkeit], into a problem, much less solve it.60

Heidegger’s response to the aforementioned argument is rather

straightforward here. Although the usage of logic is certainly

unavoidable for any genuine metaphysics, the question of “ground”

cannot arise from this fact alone. The language of “rule usage” seems

to demand further explanation, since any ordinary meaning of rule

usage seems to be derived from one observable activity among others.

This unavoidable regress of meaning can come to a halt only in

metaphysics, since the subject of metaphysics as Sein or being qua being

cannot beg a question of meaning beyond itself. As we have already

seen in Heidegger’s proposed solution to the problem of psychologism,

the only way to raise the problem of a properly philosophical account of

logic is by thinking through the implications of the ontological

difference between Sein and Seienden. Indeed, for Heidegger, the problem

of psychologism is properly understood as a mere species of the more

60 Ibid., 105.

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fundamental problem of a Vergessenheit des Seins, a forgetfulness of being

qua being.61

Heidegger concludes his rejoinder to the argument for the primacy

of logic over metaphysics with four points, which may be summarized as

follows:

1. Logic is not the operational condition for thinking, but a

science of rules.

2. As a science of rules, logic cannot raise the question of why

these rules obtain.

3. Logic is intelligible only via an analysis of thinking and its

conditions of possibility.

4. Unless conceived as a “metaphysics of truth,”62 then the question

of the primacy of logic over metaphysics (or vice versa) is not a question that is

answerable in terms of logic itself.63

Although Heidegger is quite clear about his position that logic is

founded in metaphysics and not vice versa, these four points are quite

humble in scope. They do not take shape as a demonstrative proof, and

they are compelling only to the extent that his readers recognize the

importance of the concept of “ground” or “foundation” for fundamental

sciences such as logic or metaphysics. If a philosopher such as Frege

61 See Heidegger, Being and Time, 2. 62 See note 53 above. 63 Heidegger, Metaphysical Foundations, 105.

37

is not interested in providing a philosophical explanation for logic

as a science, then meaningful debate on the topic is undermined. What

results is an ἀπορία λόγου, a fundamental, undecidable impasse with

regards to the essence of logic.

Ultimately, then, the difference between Frege and Heidegger on

the relationship between logic and metaphysics is most evident in

their respective accounts of truth, since the meaning of truth

evidences each philosopher’s conclusive position on this relationship.

Frege declares that truth is undefinable except in a qualified sense

as one of two output “values” arising from a well-formed proposition,

a “thought.” Heidegger understands truth to be a name for the

Parmenidean identity of νοεῖν and εἶναι and the existential “freedom”

precedes its own regulation by the laws of logic.64 For Frege, truth is

merely a name for the unity of the thought; for Heidegger, truth is

another name for the disclosure of Sein in the being for whom its own

being is an issue, Dasein. We might say that Frege’s “truth-bearer” is

the thought, whereas Heidegger’s “truth-bearer” is authentic Dasein.65

However we are inclined to describe this fundamental difference

between Frege and Heidegger on the relationship between logic and 64 Ibid., 185. 65 For an extended treatment of the relationship between existential authenticity and truth in Heidegger’s philosophy, i.e. Dasein as truth-bearer, see Lambert Zuidervaart, “Truth and Authentication: Heidegger and Adorno in Reverse” in: Adorno and Heidegger: Philosophical Questions, eds. Iain Macdonald and Krzystztof Ziarek (Stanford, CA: Stanford University Press, 2008), 22-46.

38

metaphysics, perhaps what is most important for our purposes is this

aporia’s potential for serving as a powerful early expression of at

least two divergent traditions of theorizing about the relationship

between logic, metaphysics and language itself in the twentieth

century and beyond.