The Philosophical Methodology: Answering the original question
This will be probably the last brief essay which I post in the blog. I do not know why the fate has driven to me to devote this (dubious) privilege to analytic philosophy, but, anyway, this is what I post now. The essay is mainly a commentary on one particular chapter of The Philosophy of Philosophy, by T. Williamson. It is one of the main recent contributions about meta-philosophy in the analytic philosophy. But, besides that, I have tried to reelaborate Williamson’s account, in a way that I have been able to develop a critic account and to give a (in some way) renewed vision to grasp the question.
1. Introduction
In a whole attempt to discuss about the methodology of philosophy, the treatment by these means of a particular philosophical question should be faced. In the second chapter, Taking Philosophical Questions at face value, of his Philosophy of Philosophy, Timothy Williamson develops this aim.
It is not clear how philosophy should grasp its questions, and there is a tendency to prioritize formal accounts to grasp them. Particularly in the tradition of the analytic philosophy, one thinks that to achieve a philosophical question properly, it is necessary to either take it as a linguistic or conceptual question, or to grasp it in formal terms. Williamson reflects that mentality and, in fact, develops the chapter in its terms.
This essay wants to discuss the grounds that develop such a philosophical methodology. Therefore, once the particular question that Williamson raises has been expounded, Williamson’s exposition will be observed in order to extract from it a controversial account of this methodology. A first section will be devoted, so, to view what is the nature of a paradigm of philosophical question, and how should be faced the problem of how such a question is about. A second section will concern the formal debate that Williamson raises in order to obtain reasons to answer the observed question in a way or another. This debate can be reconstrued in a way that exploits the discussion and not the answer; and that will be interesting in relation of Williamson conception of what is the relevance of this formal discussion. A last section will summarize all the discussion of the essay and will point general remarks concerning the whole chapter.
2. The original question
2.1. Initial reflections: the original question as a philosophical question
The aim of chapter 2 is to show how philosophical questions should be considered in philosophical inquiry, and how this investigation, even if questions are not explicitly concerned with thought or language, might consider these issues in order to give a sustainable answer. Williamson pretends to reflect how a philosophical question is answered.
In the concerning case, the author gives an example, called «the original question». In a context where Mars changes its state from clearly not dry to clearly dry, one can ask: Was Mars always either dry or not dry? As a matter of fact, the property of dryness cannot be clearly decided in many cases; when Mars comes to be dry, it is not clear how one should evaluate its state of dryness. So, the original question has not, at once, a direct and no problematic answer. For transparency, Williamson says: “The question queries just the supposition that Mars was always dry or not dry, which we can formalize as a theorem of classical logic, 
2.2. To answer what is the original question about
Once the problematic character of the original question is recognized, the first issue that has to be accounted in order to develop a philosophical reflection about it is the nature of the contents of that question. In other words, what the original question is about must be decided. But some remarks should be done at this point, as Williamson does:
“What is the original question about? “About” is not a precise term. On the most straightforward interpretation, a sentence in a context is about whatever its constituents refer to in that context. Thus, taken at face value, the original question is about the planet Mars, the referent of “Mars” in this context; perhaps it is also about dryness, the referent of “dry”, and the references of other circumstances too. Since the original question contains no metalinguistic expressions, it is not about the name “Mars” or the adjective “dry”. Evidently, the original question is not explicitly about words” [2]
So, however that the original question is not explicitly about words seems clear, and the fact that it does not contain metalinguistic expressions seems a good reason for supporting that, the possibility that it is about concepts or words, even implicitly, has to be discussed.
Williamson rises a parallel argument [3] in order to show either the original question is not implicitly about words or it is not about concepts. The argument consists firstly in giving disquotational biconditionals that are clearly about, respectively, words and concepts; those biconditionals can be considered equivalent to the content of the original question. Nevertheless, his move is to point that, in this case, other non-philosophical and uncontroversial question, such as “Was Mars always either inhabited or not dry?” will be considered about words or concepts too. This last stand seems strongly wrong.
Against the possibility of the original question to be about words, there is another argument, a translation test. This test goes to argue that the original question is not implicitly about words, since it can be formulated in other languages and conserve its problematic character; in that case, it cannot be about a particular word in english.
But, even if this last argument is stated, one should note that the lack of fruitfulness of disquotational biconditionals is not a conclusive argument to show definitely that the original question is not about words or concepts. It only establishes that, as other uncontroversial instances like “Was Mars always either inhabited or not dry?”, the original question does not seem to be about words or concepts. Even thought, Williamson points out his thesis: “Even if the equivalences did show that the original question was in some sense implicitly about thought, they can be read in both directions: they could also equally show that the explicitly metaconceptual questions were in an equally good sense implicitly not about thought” [4]. So, the conclusion can only be stated “in some sense”, and that leads to admit that it is a provisional conclusion, supported by its apparently fruitfulness and convincing character.
It is perfectly possible that the nature of the discussion goes not to develop that conclusion so forth. In fact, Williamson is only showing how an example of a philosophical statement actually is and ought to be considered. But that is exactly the point; if this methodological exposition is not perfectly convincing, the particular way in which Williamson tries to drive philosophical inquiry loses part of it strength. It is not the aim of this paper to develop a critical argument against Williamson in this matter, but it will be illustrative of what will be argued below.
3. The discussion about vagueness
Once the problem of what is the original question about has been considered, or almost once it has been treated in discussion, one can start the attempt to solve the original question in itself, in the sense of giving a concrete answer to it. At first sight, the original question is hard because it is settled in a context of vagueness. To decide when Mars starts to be dry or stops to be not dry is not, if possible, an easy question, just because the context of this discussion is vague. So, as Williamson says,
“It is useful to look at some proposals and arguments from the vagueness debate, for two reasons. First, they show why the original question is hard, when taken at face value. Second, they show how semantic considerations play a central role in the attempt to answer it, even though it is not itself a semantic question” [5]
If this attempt can help to clarify one possible answer to the original question, its treatment seems unproblematic. One can doubt its fruitfulness, but, at this initial level of discussion, Williamson’s aim and his reasons to elaborate it can be accepted without difficulties.
3.1. A pluralistic exposition
Even though Williamson does not show explicitly, his account of different proposals from the vagueness debate are pluralistic in form. It is necessary, firstly, to clarify what can be understood by «pluralism» or, better, by « logical pluralism». Logical pluralism is a philosophical proposal about the interrelations and the hierarchy between logics. Thus, as Field points,
“There are quite a few theses about logic that are in one way or another pluralist: they [pluralists] hold (i) that there is no uniquely correct logic, and that (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic” [6]
So, pluralism defends, as a general matter, that there is not one true logic. That implies the recognition of several logics as perfectly valid, but to reject some logics as incorrect and to accept others is consistent with pluralist theses. In this sense, pluralism, as an interesting and substantive proposal in philosophical logic, is not relativism; it does not accept each logic of the plurality as equally good or, better, there is no need to do that. The context for this pluralism is not the evaluation of logics in itself, that is, as pure mathematical structures [7]. Thus, the context is their evaluation as theories, as logics applied to one particular concern. So to speak, one can be a pluralist about logic, and accept classical logic and intuitionism as valid account for logical consequence, but reject paraconsistent logic and fuzzy logics to the same application.
Williamson’s exposition of several proposals from the vagueness debate can be reconstrued in this way. He exposes every account and evaluates its answer, but he does not go to give a unique solution to the problem of vagueness. In fact, even if he prefers one proposal, the aim of his exposition is not to argue in favor of it, but to see, as it has been showed previously, how to achieve semantic considerations is interesting and fruitful in order to analyze one philosophical question. Williamson states that “this is no place to resolve the debate between opposing theories of vagueness. The present point is just that different theories support contrary answers to the original question. All these theories have their believers. Any answer to the original question, positive, negative, or indefinite, is contentious” [8].
There is no need to develop each account from the vagueness debate that Williamson mentions. But to give some remarks about them can be interesting. The easier way to classify them is by their answer to the original question; positive, negative or indefinite (so to speak, neither positive nor negative) answer.
Classical logic is the proponent of the first choice; its answer to the original question is affirmative, as it is considered “a generalization over instances of the law of excluded middle (…) for various times” [9]. Thus, as a logical truth, the original question can be proved without premises, and it is always true.
As a significant proponent of the negative answer one can localize intuitionistic logic. This account rejects the law of excluded middle because it can be false that a prove to prove or refute an instance is unobtainable. So, by this requirement of obtaining constructions in order to affirm one instance, “(…) one might assert that Mars was not always either dry or not dry (…), on the general grounds that there is no adequate procedure for sorting all the times with two categories, without thereby committing oneself to the inconsistent existential question that it was once either dry or not dry” [10]. Williamson localizes two problems with this account, mainly concerned with the paradigmatic character of the original question and with the domain of quantification.
The last possible answer to the original question is to consider it as indefinite, that is, to point that it has not a truth value. One option is to extend possible truth values, and to get three of them. This enlarges the values assigned to each connective by the value «indefinite». So, as there are moments of time where it is indefinite whether Mars is dry or not dry, a generalization of these moments of time will give a indefinite answer; either the positive answer or the negative answer to the original question have indefinite value for three valued logic.
The second option of answering the original question as indefinite is fuzzy logic. Its attempt is to replace the two truth values scheme by a continuum of degrees of truth values. Bu an analogous reasoning, fuzzy logics can consider the answer to the original question as three valued logic does, as indefinite.
Williamson notes that this last attempt has problems too, such as the indefinition of the definiteness or indefiniteness. But, anyway, he does not develop this criticism because it is not his aim. As it has been stated, the question is not to decide clearly whether which logical attempt for vagueness is the correct one, but to give grounds to the analysis of the original question. To explicit this in his words:
“Even when one has settled on an answer [to the original question], one can see how intelligent and reasonable people could answer differently while understanding the meaning of the question in the same way (…). [T]he original question, read literally, has no unproblematically obvious answer in any sense that would give us reason to suspect that someone who asked it had some other reading in mind” [11]
3.2. Pragmatic pluralism
Once these different logical accounts has been exposed in a pluralistic way, Williamson considers an alternative way of developing pluralism. There can be several meanings of the connectives, so, if two logics have a different meaning to one particular connective, their dispute acquires another nature.
But a connective can differ in meaning in two different ways. The first case occurs when no independent genuine meaning is recognized and logics establish that their meaning is genuine. In that case, pluralism disappears because logics are not treating the same issues. If there are two logics that give different genuine meanings for the connective «not», they are not considering, treating the original question, the same concern; so to speak, one logic is dealing with the original question* and the other is dealing with the original question**. As Williamson comments, “the dispute between different theories of vagueness is verbal in the sense that their rival semantics characterize different possible languages or conceptual schemes” [12]. So, the grounds to decide which theory is true are independent of the question considered, and in that sense they are verbal.
The second way by which a connective can differ in meaning occurs when a genuine sense is recognized an different theories have different accounts of it. So, in that sense, logics are dealing with the same, but considered with divergence. That will be the context of the pragmatic account; its goal is to hold a pluralistic picture given this particular divergence of meaning. In that case, then, in Field’s view “if the connectives differ in meaning between the theories in a more substantial sense (…) then that might suffice to remove disagreement” [13]. Thus, as it has been presented, this pluralism solves the difficulty of the previous case and can be developed as a substantive position. But on further reflection one can argue, as Williamson does, that pragmatic thesis is not sustainable.
Its main problem is that it constrains every logical account in order to dissolve its disagreement. As a matter of fact, there is disagreement when one theory answers the original question and another negatively. The result is that “this reconciliation of the contrasting theories does justice to neither side” [14]. To leave the decision of which theory use in every case to pragmatic grounds does not solve anything, for every proponent is clearly incompatible relative to each other. From a trivalent perspective, if classical logic is considered seriously, that will imply the recognition of the falsity of the own trivalent account. By the other hand, from classical logic point of view, trivalent logics does not fix a complete meaning for connectives because the indefinite truth value is not a statable value for a sentence. Thus, pragmatic account seems to have two choices: either accept a less significance difference of meaning and to turn the dispute between logics into a verbal rivalry, or to recognize its own falsity.
3.3. Williamson’s monism
Williamson’s exposition has been reconstrued as a pluralistic picture of a debate from vagueness about answering the original question. But further remarks should be done concerning his own position. The present development is reached from Williamson’s account of how a philosophical question have to be taken at face value. The original question is a difficult matter mainly because of its vagueness, and for that is relevant to consider the vagueness formal debate. But a picture of that debate suffices to illustrate how those semantics considerations are important to handle with the original question. There is no need to give a unique answer to it.
Even though, Williamson is not completely neutral with this debate. Even if his exposition can be seen as a pluralistic development, he tends to think that the original question has a direct answer: “In my view, that reasoning [to answer positively to the original question in virtue of the law of excluded middle] is sound” [15] and, later, “If it [the original question] has an obvious answer, is the answer “Yes” dictated by classical logic” [16].
So, in fact, Williamson holds a monist position [17], almost answering the original question. In other words, the pluralistic picture has its function in a methodological point of view, that is, to express how formal debates have not a clear answer and, relevantly, how they give resources to clarify philosophical problems, even if these problems are not directly concerned with formal or semantic issues. But, reflecting the vagueness debate as a formal debate, Williamson has his own point of view, and, for him, there is one truly account for vagueness of resolving the original question: the classical logic account.
As it has been seen, classical logic allows to answer positively the original question. Its strategy is to consider it as a logical truth, because it generalizes a concretion of the law of excluded middle. So to speak, for whatever predicate, it will be always true that every element of the domain (in this case, moments of time) either belongs to predicate interpretation in the model or not.
But an affirmative answer such as Williamson provides (instead of the fact that there can be alternatives to an affirmative answer) implies that Mars dryness can be decided at every time. Be that not the case, the answer will not be affirmative. At every time, one has to be able to decide whether Mars is dry or not. Thus, the extension of «dry» must be clear as well as its antiextension [18] and, moreover, it has to be statable in some way.
But, therefore, vagueness disappears as a difficulty that needs a formal treatment. Even if the original question has been taken as a problematic, and philosophically relevant, matter, this answer, which dissolves vagueness, leaves out the difficulty.
The answer context offers an explanation that, instead of considering the difficulty of the question, rules out it, and it does not seem Williamson’s will introducing it. The matter is not, just, to make the original question a trivial problem, but to treat it with full entity. The acceptance of classical logic account and the positive answer to the original question in the way reflected implies the lack of vagueness of a concept like «dryness». As Williamson’s exposition is developed, it seems surprising.
4. Concluding remarks
Once the complete treatment that the original question receives from Williamson has been reviewed, one can evaluate this account, and give to it general comments. The chapter which content has been commented is concerned with a practical reflection of proper philosophical methodology. So, a problematic question of philosophical character, the original question, is taken in order to show how philosophical inquiry has to face it.
But, this methodology manifests its first problems in the discussion of deciding what is the original question about. The solution of this discussion is only sketched, and in no way can be considered definitive or conclusive; it seems, and one can give some arguments, that the original question is not about language or thought. Even if that is the correct answer to the question what is the original question about, one should provide conclusive grounds for answering that. What Williamson gives is is a guide of how philosophy takes a problem such as the original question, but that guide has to prove why it gives fruitful grounds of a philosophical methodology.
At a second stage of his exposition, Williamson grounds the reference of the discussion between several metalinguistic or metaconceptual proposals on the necessity of giving a direct and simple, but completely reasoned, answer to the original question. This reference is seen almost as a duty, and for the author it supposes an argument against critics of the “”arid” technical minuteness of much philosophy in the analytic tradition” [19].
But these critics do not seem solved so easily. In fact, all this developed apparatus is only useful to give an answer equivalent to (in terms of simplicity and nature) that which comes from an attentive, although not so formal, reasoning. If the pluralistic picture is developed, one is not able to give a unique valid answer, and the discussion is therefore moved away of providing something more than formal discussion. If this discussion develops some useful content in order to achieve grounds to answer the original question, that content can be given simply by observing the question itself. It can be adduced that this question is only an example, and that the proper philosophical problems cannot be faced simply by an attentive reasoning. But, if that is the case, the original question is a bad example. If one faces the original question, a philosopher, not necessary a logician, is prepared to appreciate that the concept of dryness is related with vagueness, and that its answer depends on multiple issues, precisely because the nature of that concept.
Beyond practical motivations, to lower reduce Logic to these so particular applications (and, chiefly, to have to consider disputes between formal theories) can seem unnecessary, even more having in mind the given answer, either in a pluralistic account or in a monistic one. If vagueness is what is wanted to study, then the reflection offered in this chapter is insufficient, because this is a genuine philosophical problem, with a complete entity. However, if what is actually wanted is to give an answer to a problematic, though still paradigmatic, example, then the discussion between formal theories can seem excessive.
Nevertheless, it is clear that acquisition of arguments and the foundations in order to get a decision of an answer might be considered valuous. Anyway, what has to be kept in mind is if this answer is of an “”arid” technical minuteness”.
5. Notes
