Logic and Buck-Passing

Henry Curtis

  1. Introduction

In his (2008), Robert Hanna identifies Husserl’s final obstacle in defeating the position of the logical psychologist as the “logocentric predicament,” which puts into question how exactly the pure logic advocated by Husserl can be justified without circular reasoning. The situation leading up to this predicament is as follows: Husserl, using an argument similar to one found in Frege (1897, 144), claims that the logical psychologist’s position is circular because the science of psychology itself relies on logic to maintain its status as a rational science, and therefore giving logic a “first foundation” internal to psychology would be explaining something prior to psychology by using psychology. The logocentric predicament appears when this sort of criticism is turned towards the practice of justifying logic. The charge is that any justification or explanation of logic will have to implicitly use or employ logic, and so any attempt to justify logic will in fact presuppose logic. For the purposes of this paper, we will take the logocentric predicament:

Logocentric Predicament (LP): Logic cannot be justified without presupposing logic.

to be a question about how to properly ground logic in something that is not itself logic, or in a way that does not presuppose logic. In this paper I will recap both Frege’s and Husserl’s responses to the predicament, with an eye towards what their responses say about their general views on grounding logic. Then I will try to make two positive points: 1) To assume that the logocentric predicament is in fact a predicament is already to have a certain conception of logic, and 2) there is a way to ground logic such that it can be positively justified without recourse to logic. In sum, my goal is to demonstrate that the logocentric predicament need not constitute a deep threat to logic, both because of the predicament’s own hidden commitments and our ability to justify logic without falling back onto logic.

 

  1.      Frege and Husserl on the Logocentric Predicament  

Frege phrases his own version of the logocentric predicament in his preface to The Basic Laws of Arithmetic (1893) by first conceding that logic can only justify it’s own laws by “reducing [each logical law] to another logical law. Where that is not possible, logic can give no answer. (Frege 1893, 204)” This reasoning limits what can be used to ultimately explain logical laws- namely, that whatever is used in the ultimate explanation of logical laws cannot itself be logic, or a restatement of logical laws. Recognizing the inability logic has to justify its own truthfulness, Frege cites the view that human judgment would be thrown into confusion and made impossible if logical laws were different. He refuses to explicitly endorse or reject this view, but states that the view itself is certainly not a statement of logic. It is rather a claim about the nature of human cognition and rational judgment. Lockhart (2016) takes Frege’s reluctance to commit to this view as a consequence of Frege’s belief that the most fundamental logic laws do not stand in need of any justification, and that to justify them in virtue of experience would be to offer a sort of “transcendental” explanation for why they are as they are. The explanation that is being avoided here would be that a logical law is ultimately true just in case it is a necessary condition for all thought, a statement Lockhart views Frege as unable to explicitly endorse, yet one he believes Frege holds to be true. Whether or not this is a correct assessment of the motivation behind Frege’s failure to explicitly justify logic, what is important for our purposes is that Frege would view judgment as a more rational site upon which to ground logic than upon logic itself. Frege goes on to write that his whole dispute with the poser of the logocentric predicament is motivated by a sort of deep ontological disagreement. For those who question the justificatory status of a non-relativized logic by posing the logocentric predicament, the laws of logic are statement about non-actual things, and therefore (in their mind) constitute non-objective truths. Frege, on the other hand, firmly believes that there can be objective truths about the non-actual (such as “Sinn” or number), and that logical laws are truths of this sort. So Frege does not only gesture towards grounding logic in the preconditions for judgment, but also in an ontological conception of what sort of true statements the laws of logic are.

 

As we saw in the first paragraph, the logocentric predicament also comes up in Husserl’s anti-psychologistic writings, and he responds to it first by claiming the LP commits an equivocation error with regard to the term “presupposition”. In his Logical Investigations (1970) Husserl draws a distinction between two ways in which an argument can have a presupposition. The first way is for the argument to contain that presupposition as a premise, like the premise “Socrates is a man” in the argument “Socrates is a man, If Socrates is a man then Socrates is mortal ⊨ Socrates is mortal.” However, another way an argument can have a presupposition is to presuppose the validity of a certain logical structure, just as the previous argument presupposed the validity of modus ponens. Husserl claims that the first sort of presupposition can in fact lead to circularity, but that the second does not. Hanna writes that under Husserl’s conception of pure logic he holds the laws of logic to be “supreme constructive categorically normative logical meta-principles (Hanna 2008, 40)” which are themselves held to be the most general laws regulating human rationality. These meta-principles would themselves never serve as the premises of an argument justifying logic, but simply dictate the necessary form all rational argumentation would take. Here Husserl avoids the logocentric predicament by claiming that it would only be a problem if an argument justifying logic took logical laws as premises, and not as principles governing validity. However, since this is not the case, the LP fails to pose the threat of circularity upon the justification of logic, which Husserl believes is grounded in the ideal and normative status of logic with regards to human rationality (Husserl 1970, 209). Husserl also argues that the justification of logic comes from the epistemic route we make use of to know logical laws. In his view the laws of logic are established via insight- he writes that a logical law: “… is the single, sole truth which excludes all others and which, being established by insight, is kept pure from fact in its content and mode of proof. (Husserl 1900, 53).” Frege avoided the need to ground logic in logic by grounding it (on Lockhart’s view at least) in human judgment and the ontology of logical laws. Husserl avoids the need to ground logic in logic by invoking the normative status of logic for human rationality and logic’s availability to insight. These strategies run parallel, and they both give us the key to defusing the logocentric predicament- grounding logic in something that is not itself logic.

 

  III.     Buck-Passing and the Logocentric Predicament

So far, we have seen that the logocentric predicament requires us to take a certain strategy for justifying logic. Both Frege and Husserl assert that the laws of logic are not grounded in contingent facts about human psychology, but rather reflect deeper truths about the nature of rationality, truth, and perhaps even the structure of the world itself. However, they do not want to take what Hanna (2008, 39) refers to as a “fideist” justification of logic, claiming that the laws of logic are somehow “out there” independently of our minds, but that they can only be justified as a matter of faith. This would be, as I think Hanna correctly suggests, irrational and philosophically dubious. Just as a fideist justification of logic would be unacceptable in virtue of violating norms of explanatory rationality, so too would justifying logic by presupposing logic violate norms of argumentative rationality- namely, that we should avoid strictly circular arguments. So, both Frege and Husserl are in a bind with regards to how they are able to justify logic- they cannot presuppose logic in their justifications of logic and they cannot presuppose logic simpliciter. So the strategy they have to take is one I call buck-passing- they have to take the burden of justifying logic and pass it off to something that is not itself logic, and that does not itself presuppose a logico-inferential structure. In Lockhart’s view, Frege passes the buck to human judgment, and in my view also to the ontology of truth. Husserl passes the buck to the necessary conditions of human rationality and the epistemic status of logic. The strategy of buck-passing will be integral to my second argument against the logocentric predicament. I will now turn to my two positive points. In this section of the paper, I will outline my first argument, which is that the logocentric predicament, if it is to be read as a predicament, must make a presupposition about the nature of logic. Following that, I will propose a way to conceive of logic that allows logic to be justified without relying on logic itself, because I will pass the buck to the metaphysical status of logical laws.

 

The logocentric predicament is formulated as a problem that one encounters in seeking to justify logic- namely that one cannot do so without employing logic. The predicament itself may seem philosophically innocent, insofar as its an extension of a rather intuitive request made of the philosophical logicians. They assert that something, a non-relativized logic, exists, and as a consequence of that they can be asked to justify the existence of what it is they assert exists. However, it is not clear that logic, or the laws of logic, are the sort of thing that require a justification. In order to flesh out this point, I must say something about the structure of the explanans/explanandum relationship.

 

When we take a statement as something in need of an explanation or justification (call this statement the explanandum) we are saying that either it is truth-evaluable or that its placement in a certain theoretical schema requires motivation. In the first case the statement just is true or is not true, and the explanans must take the form of a set of statements which in some way reinforce the truth of the explanandum. In the second case the statement is not necessarily truth-evaluable, but will either be accepted or rejected on the basis of its coherence with certain theoretical desiderata, i.e. explanatory power, simplicity, ontological commitment, etc. In this scenario the explanans will take the form of a set of statements which reinforce the theoretical desirability of the explanandum, which in certain cases could even be taken as the truth of the explanandum itself. Where I claim the logocentric predicament smuggles in unmentioned premises is precisely in its presupposition of the explanans/explanandum relationship. We rephrase the logocentric predicament with this new apparatus in mind:

        Logocentric Predicament* (LP*): Logic as an explanandum must have logic as its explanans.

and recall what I stated earlier about explanandum in general, that they must either be truth evaluable or in need of theoretical motivation. However, whether or not logic fits neatly into either of these categories is a non-trivial issue.

There is an argument that logic is not truth-evaluable, since logic is not a set of true statements, but rather a set of guidelines for preserving truth in arguments. One could claim that it is a categorical error to claim that modus ponens is true in the same way that one could claim it is a categorical error to say that not leaving the stove on is true. The first is a guideline for preserving truth among statements, the latter a guideline for not burning a house down- neither are objectively true, just normative for those engaging in certain tasks. Furthermore, there is an argument that one can understand truth-evaluable claims without knowing whether or not they are true. For instance, I can imagine Moscow having a larger population than Beijing whether or not it is actually the case. But for the laws of logic, I might not be able to understand them without also simultaneously coming to understand that they do regulate all thinking. So they would not be truth-evaluable in the usual sense of that term. If logic is taken as an explanandum that must be motivated with regards to its acceptance in a theoretical schema, we have already adopted a conception of logic similar to that presented by Quine in his (1953), where the statements of logic are revisable if their revision is necessary to maintain a positive assessment of all our scientific beliefs taken as an aggregate. In Quine’s view, logic is not “safe” from revision, the way it is safe in the minds of the logical positivists or philosophical logicians. However, this constitutes another deeply non-trivial assumption about logic. There is a potential circularity argument that can be used against this conception of logic (“From what vantage point would you judge theoretical desirability? Wouldn’t this have to be objective in and of itself to serve as an adequate place from which to judge desirability?”) and whatever one thinks of it, it is certainly not the only available conception of logic. Judging that logic is revisable in the Quinean sense, or independently truth-evaluable, is a deep presupposition about the nature of logic. If the logocentric predicament is in fact a predicament, we have to assume that it is not an error to ask that logic itself be justified. However, as we have seen, this is a non-trivial assumption. This means that the logocentric predicament is not quite as innocent as it might purport itself to be, and that it subsequently loses some of its philosophical force in virtue of losing generality.

 

My final positive claim is the more contentious of the two. It is that there is a way to ground logic that does not itself presuppose logic. My strategy for defending this claim is twofold. First, I will give what my grounding of logic is, and motivate a brief defense of it. Then I will show how this grounding of logic avoids presupposing logic, in both senses of the term “presupposition” that Husserl discusses. My conception of logic is simply this- logic is a set of statements asserting all the essential properties of abstract objects called valid arguments. Each law of logic is the statement of an essential property of valid arguments. Arguments are simply sets of propositions, where one is given as the conclusion and all others are given as premises. If they stand together in a certain way, we call the argument valid, and each valid argument must take a certain form- having this form is an essential property of being a valid argument. To draw an analogy, the statements of logic are similar to the statements of which animals are dogs. Dogs are just collections of parts (noses, tails, organs, genes, etc.) that must be arranged in a certain way to be classified as forming dogs. Statements of what these forms are constitute statements of the essential properties of dogs. Valid arguments are just collections of propositions that stand to one another in a certain relation, and bearing these relations are essential properties of valid arguments. This conception of the laws of logic preserves the philosophical logicians view that the laws of logic are not dependent on contingent facts about human psychology, since they are statements about abstract objects. It would also mean that the structure of logic could be divorced from general concerns about the normativity of thought or rationality. The laws of logic would, strictly speaking, have no need to bear on human affairs- they would simply be truths about abstract objects. Any normative force they would be conceived of as having would be over and above their basic meaning. Under my view, saying the laws of logic would be normative for human thought would be like saying it is beautiful that the word “grandiose” has nine letters. The fact that “grandiose” has nine letters is simply an essential property of the abstract object which is the word “grandiose,” and saying it is beautiful has absolutely no bearing on whether or not it is true. In this way, saying that the fact that it is an essential property of all valid arguments that the conclusion cannot be false when there is a contradiction in the premises(whatever these terms “true” and “false”  and “contradiction” are taken to mean) has normative force for our belief is strictly speaking independent of the truth of the essential property. So two great points of contention are resolved upon my view. The first is that logic is grounded in human psychology; we have seen that this is false because logic is grounded in essential properties of abstract objects, and not in human psychology, which is concrete. The second is that logic must be in some way defined via recourse to the norms for human rationality; we have seen that this is also false in virtue of the formal separation between our logical laws being true and having normative import- that is, our drawing of the is/ought distinction between the laws of logic and the way humans should think.

 

This is one possible way logic can stand, and it seems as if it would be nice if it were this way. However, it seems as if this conception might fall victim to the logocentric predicament. If logical laws are construed as statements of essential properties of abstract objects, can they be justified without presupposing logic? We will discuss this by using the two conceptions of presupposition discusses by Husserl. Recall that the first conception of presupposition is that an argument can presuppose something by having it as a premise in the argument. It should be clear that we don’t need to list out the logical laws as premises in an argument defending the logical laws. If someone asks us why exactly these, and not some other, list of essential properties define valid arguments, e.g. why the laws of logic are as they are, whatever response we created would not be a simple list of these logical laws. This could never constitute a non-circular justification,  and hence would never be our actual answer to the question behind the logocentric predicament. So we wouldn’t presuppose logic to ground logic in the first sense of presupposition. However, would we need to have a logical structure in our justification of why the essential properties are the way they are, and not some other way? I claim we would not. Recall that the question behind the logocentric predicament is why the laws of logic, or logic itself, are one way rather than another, or, more broadly speaking, what we would say to justify the laws of logic. If the laws of logic are taken as being essential properties of valid arguments, the question would be: “Why are these the essential properties of valid arguments?” To which our answer would be simply: “Because that’s what it is to be a valid argument.” If I were to claim that water is necessarily made of atoms, and someone asked me to justify that statement, I would respond by simply saying: “That is what it is to be water.” Does this explanans/explanandum relationship necessitate a logical structure? To believe this would be to believe that the relationship between the statement “X is the set of essential properties of valid arguments” and the statement “Because that’s what it is to be a valid argument” is one of logical inference. However, it is not a relationship of logical inference. Rather, the statement “Because that’s what it is to be a valid argument” is the statement of a modal intuition, one to the effect that, in knowing what valid arguments are, we intuit that they could never possibly lack certain properties. What is important here is that our justification directly references the fact that the essential properties constitute the metaphysical nature of the object we are seeking to define, whether it be water or valid arguments (“that’s what it is to be x”). In essence, we are simply restating the claim we are seeking to justify- the truth of which depends on the modal intuition we point to when we claim “that’s what it is to be a valid argument.” We have not justified the explanandum by citing some alternate fact(s) that, in virtue of the logical form for their relation to one another and the explanandum, necessarily entail the explanandum. Rather, we have simply restated the explanandum, in a way that suggests the modal intuition that justifies it. In effect, we have explained why the logical laws are what they are without invoking a logical structure- simply by emphasizing the modal intuition which is synonymous with our statement of what logical laws are. Perhaps the argument is metaphysically circular, in that there is just a restatement of the fact that the properties are in fact essential properties. But this circularity is not a circularity of logic justifying logic, and thus it avoids the logocentric predicament.

 

In this paper, I have argued that the logocentric predicament is not a deep threat to logic. This is because the logocentric predicament itself presupposes a certain form for logic, and whatever this form is, it will constitute a non-trivial assumption about the nature of logic. In addition, there is a way to conceive of logic such that the we do not need to presuppose logic in our justification of logic. This is when the laws of logic are taken to be essential properties of abstract objects.

 

References

 

  • Frege, Gottlob. (1893): “Preface” to The Basic Laws of Arithmetic in Michael Beaney (ed.) The Frege Reader (Blackwell, 1997), pp. 201-208.

 

  • Frege, Gottlob. (1897): “Logic” in Posthumous Writings, pp. 128-151.

 

  • Hanna, Robert. (2008): “Husserl’s Argument Against Logical Psychologism” in Verena E. Mayer & Christopher Erhard (eds.), Edmund Husserl: Logische Untersuchungen. Akademie Verlag Berlin. pp. 27-42.

 

  • Husserl, Edmund. (1900): Logical Investigations: Prolegomena, trans. J.N. Findlay, ed. D. Moran, ch. 4, pp. 46-55.

 

  • Husserl, Edmund. (1970): Logical Investigations, trans. J.N. Findlay, 2 vols., London.

 

  • Lockhart, Thomas. (2016): “Frege on Anti-Psychologism and the Role of Logic in Thinking” in Theoria 82:4 2016, pp. 302-328.

 

  • Quine, W.V.O.. (1953): “Two Dogmas of Empiricism” in From a Logical Point of View, pp. 20-46.

 

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