The Last Word (Chapter Four)
This chapter serves to reiterate the sort of points Nagel has been making in previous chapters about the reality and extent of reason and to serve as a segue into further chapters, which explore what role, if any, reason has in science and ethics. The focus of this chapter is on defending the objectivity of logic and mathematics, which is a natural place to start, since they reveal the sort of principles for discovering what is part of reason (i.e., what is objective) that he will employ in other domains of thought (p. 55). Nagel is going to argue that the content of certain logical truths is such that to grasp them is to see that they must be necessarily true, and that this credibility cannot be overturned. Moreover, many of these principles or forms of thought have to be presupposed in any attempt to reject or relativize them or other ostensibly cases of objectively valid thought.
Section I & II
In this section, Nagel makes the point that total skepticism can only get off the ground if it adequately deals with the content of our logical or mathematical thoughts. But this it cannot do. "The simplest of such thoughts are immune to doubt," says Nagel (p. 55). For instance, to grasp what the claim that 2+2=4 amounts to, or what the form of modus tollens is, leads us to recognize that they are necessarily true and universally valid thoughts (pp. 55, 56).
In case of less fundamental mathematical or logical thoughts, Nagel readily acknowledges that these may be false (p. 57; cf. pp. 63, 64). However, this does nothing to support total skepticism. First, we must rely upon simpler logical and mathematical thoughts to ascertain that we are in error. Secon, when we ascertain that, we then have to form what we take to be a true description of what is actually going on. Part of that involves coming to understand how, given the content of the thought whose truth we are now skeptical of, we were or could be wrong. The lesson here is twofold. This whole process requires we take an internal view point: "Skepticism cannot be produced entirely from the 'outside'," Nagel says. Also, we can't automatically side with skeptical (and hence relativist) challenges (pp. 58, 59). Put another way, total skepticism is impossible and merely to offer an external viewpoint from which we can describe our, say, ethical thought doesn't give us reason to think that such thoughts are wrong or subjective.
In case of less fundamental mathematical or logical thoughts, Nagel readily acknowledges that these may be false (p. 57; cf. pp. 63, 64). However, this does nothing to support total skepticism. First, we must rely upon simpler logical and mathematical thoughts to ascertain that we are in error. Secon, when we ascertain that, we then have to form what we take to be a true description of what is actually going on. Part of that involves coming to understand how, given the content of the thought whose truth we are now skeptical of, we were or could be wrong. The lesson here is twofold. This whole process requires we take an internal view point: "Skepticism cannot be produced entirely from the 'outside'," Nagel says. Also, we can't automatically side with skeptical (and hence relativist) challenges (pp. 58, 59). Put another way, total skepticism is impossible and merely to offer an external viewpoint from which we can describe our, say, ethical thought doesn't give us reason to think that such thoughts are wrong or subjective.
Section II elaborates on this point - that the skeptic, insofar as his skepticism can get under way, reveals "his unshakeable attachment to first-order logical thought" (p. 60). He picks up a point he made in chapter two (p. 19).
Section III
So far, Nagel has been refuting total skepticism. Now, he explicitly applies the lessons learned to relativism. This move is justified because the relativist is a kind of skeptic about logic; the universal relativist parallels the total skeptic (who is skeptical of logic).
Traditional skepticism presupposes logic insofar as it makes it appeal by way of argument: all the evidence we have is as consistent with the notion that the universe came into being five minutes ago or billions of years ago, hence we can't believe one over the other (pp. 62, 63).
Total skepticism, since it is skeptical about logic, is not like this. Reason cannot be used to argue that 2+2 might equal 5, or that contraposition might not be a valid logical form, since these truths disclose themselves in such a way that makes it impossible to doubt them, and in any case we will often need them to formulate our skepticism of them, which defeats the attempt at skepticism (p. 63)
Given that these thoughts are indubitable - since their content reveals them to be objectively true and universally applicable - these thoughts resist not just skeptical assaults but "relativistic, anthropological, or 'pragmatic' interpretation" (p. 64). Note well how Nagel shows that these sorts of simple logical and mathematical thoughts have their power in virtue of their content (i.e., as known from an internal viewpoint) not in virtue of anything else (cf. p. 48). Hence, he writes, "Thought itself has priority over its descriptions, because it its description necessary involves thought." (p. 65) This extends to thoughts about the contingency of our make up as thinking beings: these must be based in experience and examined by first-order reasoning (pp. 65, 66); recall, too, that any serious attempt to describe thought from an external vantage point (from which one might try to relativize it) aims to be objective, which nullifies the total subjectivist agenda.
So far, Nagel has been refuting total skepticism. Now, he explicitly applies the lessons learned to relativism. This move is justified because the relativist is a kind of skeptic about logic; the universal relativist parallels the total skeptic (who is skeptical of logic).
Traditional skepticism presupposes logic insofar as it makes it appeal by way of argument: all the evidence we have is as consistent with the notion that the universe came into being five minutes ago or billions of years ago, hence we can't believe one over the other (pp. 62, 63).
Total skepticism, since it is skeptical about logic, is not like this. Reason cannot be used to argue that 2+2 might equal 5, or that contraposition might not be a valid logical form, since these truths disclose themselves in such a way that makes it impossible to doubt them, and in any case we will often need them to formulate our skepticism of them, which defeats the attempt at skepticism (p. 63)
Given that these thoughts are indubitable - since their content reveals them to be objectively true and universally applicable - these thoughts resist not just skeptical assaults but "relativistic, anthropological, or 'pragmatic' interpretation" (p. 64). Note well how Nagel shows that these sorts of simple logical and mathematical thoughts have their power in virtue of their content (i.e., as known from an internal viewpoint) not in virtue of anything else (cf. p. 48). Hence, he writes, "Thought itself has priority over its descriptions, because it its description necessary involves thought." (p. 65) This extends to thoughts about the contingency of our make up as thinking beings: these must be based in experience and examined by first-order reasoning (pp. 65, 66); recall, too, that any serious attempt to describe thought from an external vantage point (from which one might try to relativize it) aims to be objective, which nullifies the total subjectivist agenda.
Section IV
In this section, Nagel advances his thesis, previously stated, that often enough relativistic interpretations of thought will be inconsistent with the content of the thought that one is trying to relativize (p. 29). The subjectivist might suggest that he is not saying that we should, say, speak of contraposition differently, but rather is giving us an account of what it means for us to speak of it as we do. He may say that our claim "it is a valid logical form even if we didn't say so" follows from our claim "it is valid" and that it is valid because "we are all prepared to say" that it is (p. 66). We've already seen Nagel speak on this point: if 'objectivity' depend on consensus it is contradictory to say that it extends to what would hold regardless of that consensus (p. 30). Here he also notes that there are "thoughts that are completely free of first-person content" and hence can't be interpreted "in a personal or communal form" (p. 67). Hence, this subjectivist interpretation of our thoughts contradicts itself and the content of (at least many of) the thoughts it aims to interpret.
Nagel also states something important about his conception of reason: reason operates in this region of impersonal thoughts. It's methods are impersonal or objective, and by means of these principles it can reason to further impersonal thoughts. Hence, reason is not limited merely to a set of first principles and forms of thought, but "in any forms of thought to which there is no alternative" (i.e., no way to regard as subjective) (pp. 68, 69). Whether ethics or science are forms of thought to which there are no alternatives is something we will consider in the next two chapters of this book.
In this section, Nagel advances his thesis, previously stated, that often enough relativistic interpretations of thought will be inconsistent with the content of the thought that one is trying to relativize (p. 29). The subjectivist might suggest that he is not saying that we should, say, speak of contraposition differently, but rather is giving us an account of what it means for us to speak of it as we do. He may say that our claim "it is a valid logical form even if we didn't say so" follows from our claim "it is valid" and that it is valid because "we are all prepared to say" that it is (p. 66). We've already seen Nagel speak on this point: if 'objectivity' depend on consensus it is contradictory to say that it extends to what would hold regardless of that consensus (p. 30). Here he also notes that there are "thoughts that are completely free of first-person content" and hence can't be interpreted "in a personal or communal form" (p. 67). Hence, this subjectivist interpretation of our thoughts contradicts itself and the content of (at least many of) the thoughts it aims to interpret.
Nagel also states something important about his conception of reason: reason operates in this region of impersonal thoughts. It's methods are impersonal or objective, and by means of these principles it can reason to further impersonal thoughts. Hence, reason is not limited merely to a set of first principles and forms of thought, but "in any forms of thought to which there is no alternative" (i.e., no way to regard as subjective) (pp. 68, 69). Whether ethics or science are forms of thought to which there are no alternatives is something we will consider in the next two chapters of this book.
Section V
Nagel finds the capacity of reason strange: particular individuals engage in it and it permits them access to what is universally or objectively the case. How is this possible? To see how this paradox can be solved, Nagel looks at our finite practice of counting, which he considers "a paradigm of the way reason allows us to reach vastly beyond ourselves" (p. 71).
Knowledge of the infinity of natural numbers doesn't arise simply out of the ability to use numbers in just any way: for example, if we all we did was designate a fixed number of stages. No, it is in counting that we recognize that the "numbers we use to count things in everyday life are merely the first part of a series that never ends". Once we can count, we see that this procedure has no limit (pp. 70, 71). It is within the practice that we see, in virtue of its incompleteness, that the natural numbers must be infinitely many. Looking at our practice of counting from the outside we can't see its incompleteness and so might be tempted to reduce "the apparently infinite to the finite" if we suppose that the external has priority over the internal. After all, we can only ever observe it in limited cases: we never count up to infinity. But clearly, we do know - from the internal point of view, as we count - that the natural numbers are infinitely many. And this infinitude can't be grounded in merely our contingent practice of counting: it is objectively the case that there are infinitely many natural numbers (pp. 71, 72).
Knowledge of the infinity of natural numbers doesn't arise simply out of the ability to use numbers in just any way: for example, if we all we did was designate a fixed number of stages. No, it is in counting that we recognize that the "numbers we use to count things in everyday life are merely the first part of a series that never ends". Once we can count, we see that this procedure has no limit (pp. 70, 71). It is within the practice that we see, in virtue of its incompleteness, that the natural numbers must be infinitely many. Looking at our practice of counting from the outside we can't see its incompleteness and so might be tempted to reduce "the apparently infinite to the finite" if we suppose that the external has priority over the internal. After all, we can only ever observe it in limited cases: we never count up to infinity. But clearly, we do know - from the internal point of view, as we count - that the natural numbers are infinitely many. And this infinitude can't be grounded in merely our contingent practice of counting: it is objectively the case that there are infinitely many natural numbers (pp. 71, 72).
Section VI
In this closing section, Nagel makes several important points. Any understanding of ourselves in the world cannot get rid of the fact that we form this understanding, so it cannot get rid of the internal point of view; so, to continue the case of counting, any adequate description of it must include what it is for us to count (i.e., from the inside), and hence it "must include the relation of that activity to the infinite series of natural numbers," a series that our particular exercise of arithmetical reasoning makes clear to us (p. 72).
A purely external view point will fail to capture these things, instantly falsifying it, even as behavioristic philosophies of mind (which offer a purely external view of the mind) fail because there are elements of mind that cannot be reduced to behavior (p. 73).
The sort of completely external vantage point that total subjectivism requires is impossible, because it "is inconsistent with what we know - for example that there are infinitely many natural numbers" (p. 74). Still, it would be good if we could form some kind of external view of ourselves which is at least consistent with us having the thoughts we have (p. 74). Such a view, says Nagel, must describe our capacity to think things like simple logical or mathematical truths "in a way that presupposes their independent validity". Nagel rejects an evolutionary naturalist answer to this question, though, he postpones discussion of it until chapter seven. He mentions and then briefly objects to the theistic answer: our finite minds and the cosmos were made for each other (p. 75). He suspects that this might be a God-of-the-gaps explanation; obviously, I disagree. He also suspects that, given the nature of our capacity for reason, we will not be able to explain them by employing them (p. 76). I want to note that we don't need to explain how reason works for Nagel's self-styled rationalist thesis to go through. That reason is objective is evident even if we can't see how it can be.
In this closing section, Nagel makes several important points. Any understanding of ourselves in the world cannot get rid of the fact that we form this understanding, so it cannot get rid of the internal point of view; so, to continue the case of counting, any adequate description of it must include what it is for us to count (i.e., from the inside), and hence it "must include the relation of that activity to the infinite series of natural numbers," a series that our particular exercise of arithmetical reasoning makes clear to us (p. 72).
A purely external view point will fail to capture these things, instantly falsifying it, even as behavioristic philosophies of mind (which offer a purely external view of the mind) fail because there are elements of mind that cannot be reduced to behavior (p. 73).
The sort of completely external vantage point that total subjectivism requires is impossible, because it "is inconsistent with what we know - for example that there are infinitely many natural numbers" (p. 74). Still, it would be good if we could form some kind of external view of ourselves which is at least consistent with us having the thoughts we have (p. 74). Such a view, says Nagel, must describe our capacity to think things like simple logical or mathematical truths "in a way that presupposes their independent validity". Nagel rejects an evolutionary naturalist answer to this question, though, he postpones discussion of it until chapter seven. He mentions and then briefly objects to the theistic answer: our finite minds and the cosmos were made for each other (p. 75). He suspects that this might be a God-of-the-gaps explanation; obviously, I disagree. He also suspects that, given the nature of our capacity for reason, we will not be able to explain them by employing them (p. 76). I want to note that we don't need to explain how reason works for Nagel's self-styled rationalist thesis to go through. That reason is objective is evident even if we can't see how it can be.
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