Exploring Hume’s Distinction between Relations of Ideas and Matters of Fact: The Devil Is in the Premises
Background
For centuries, philosophers have debated the criteria for knowledge: When are our beliefs justified? David Hume (1711–1776) turned science upside down by questioning justification for cause and effect in nature. His argument was so effective that Immanuel Kant (1724–1804) felt compelled to respond: “I openly confess my recollection of David Hume was the very thing which many years ago interrupted my dogmatic slumber . . . “ (260). According to Hume, there are two sources of knowledge: relations of ideas and matters of fact. Relations of ideas refers to analytic claims[1] which can be justified a priori, that is to say, independent of experience and with necessity. To deny the truth of an a priori claim founded in relations of ideas would imply a contradiction. These include claims about geometry and algebra (70), and definitional statements. Matters of fact are a posteriori claims grounded in experience in the world, such as claims about substance and causal relations. But unlike as with a priori claims, to deny a posteriori claims implies no contradiction (Hume 4.2). We can also characterize Hume’s distinction between relations of ideas and matters of fact as the distinction between analytic and synthetic knowledge, respectively[2].
My Thesis
Hume’s project was to elucidate a common misconception regarding matters of fact, viz., that it is rationally justifiable to infer from experience the existence of substance, the necessity of cause and effect, and the Principle of the Uniformity of Nature (“PUN”). However, Hume left relations of ideas intact. Thus, Hume leaves us with a priori claims which are rationally grounded in relations of ideas on one hand, and a posteriori claims which are not rationally justifiable — but mere products of human imagination and custom — on the other. In this paper, I shall argue that Hume’s critique of a posteriori claims is correct, notwithstanding formidable challenges from Kant and others. I will further claim that Hume did not go far enough in questioning relations of ideas. I shall show that what appear to be relations of ideas are often subject to contingencies and indeterminacies which effectively cast doubt on their analyticity. Moreover, I shall show that claimed a priori beliefs are often contingent upon experience, thus negating their a priori status. Meaningful claims, therefore, whether they rely upon relations of ideas or matters of fact, are often not deductively justifiable — that is to say, they are contingent rather than necessary.
Various philosophers have cast doubt onto analyticity and the distinction between a priori and a posteriori claims. Often, these doubts arise because of the ambiguity and indeterminacy in language. In addition to providing an overview of these critiques of a priori knowledge, I shall develop an additional argument (which I have not found in my research) which casts doubt on many prima facie relations of ideas, viz., that “deductive” inferences are often subject to similar limitations and contingencies that Hume elucidates in inductive inferences.
Hume’s Critique of Matters of Fact
According to Hume, knowledge of matters of fact begins with impressions, which have several possible sources: sense perceptions, emotions, desires, or acts of will (2.3). Here I am concerned with sense perceptions. Copies of these impressions are stored in memory, and anticipated in the imagination (2.1). These copies of impressions Hume called thoughts or ideas (2.3). People associate these ideas in the imagination, based upon three principles: resemblance, contiguity in time and place, and cause and effect (3.2). But these associations are in the imagination; there are no impressions of these associations. One way of expressing Hume’s critique of causal claims is that people make unjustifiable inferences from their impressions to the existence of substrata, substance, and necessary connections which somehow bind discreet impressions together. The misconception lies in that people have impressions at moments in time, but no impressions of underlying substrata or substance which bind the impressions together — nor do people have impressions of causation (5.3). Bundles of impressions merely show resemblances and constant conjunctions. But people form complex ideas, such as those of substance and causation, from copies of bundled impressions. These complex ideas are situated in the imagination, and are not rationally justifiable. Complex ideas about substance and necessary connection are then merely situated in the imagination. Indeed, said Hume, “Sometimes, he [an historian seeking to explain cause and effect] supplies by conjecture what is wanting in knowledge . . . “ (3.9).Only by custom and habit do people associate effects with causes, not by rational inference (5.5).
Another way of expressing Hume’s critique of synthetic claims is articulated by Elliott Sober. Inferences from the particular to the general, and predictions, cannot be made deductively from mere relations of ideas because experience is required (this is apparent in the arguments given below). Such inferences from experience are inductive, in that the opposite of their conclusion would not imply contradiction. For example, any conclusion other than the one given in this deductively valid argument from relations would imply a contradiction:
P1. A or B
P2. Not A
C: B
Sober (Justified Belief 174) offers the following examples of inferences to elucidate how scientific induction is not rationally justifiable, given the contingency, rather than necessity, of the laws of nature:
P1. I’ve observed numerous emeralds, and each has been green.
C. Hence, all emeralds are green.
Or, as a prediction:
P1. I’ve observed numerous emeralds, and each has been green.
C. Hence, the next emerald I observe will be green.
According to Sober, Hume’s view is that there is “absolutely no rational justification for the beliefs we have that are predictions or generalizations.” Further, says Sober, it is Hume’s view that “it is merely a habit we have that we regard such premises as providing good reason to believe such conclusions” (Justified Belief 174). The problem is that all indictive arguments such as these requires an implied premise, PUN:
P1. The sun has risen each day that I have made an observation.
P2. The future will resemble the past (PUN).
C. The sun will rise tomorrow.
But as Sober points out, PUN is not a rationally justifiable, because it cannot be demonstrated deductively, and any inductive argument is circular (Justified Belief 175). This seems to be true: There is no way for a human to take a God’s eye view of the world. There is nothing within the laws of nature that preclude them from changing at any time.
But is Hume (and Sober) correct? An objection to Hume is that there is good reason believe in the greenness of emeralds and that the sun will rise tomorrow. It is not merely willy-nilly that one assumes that the next emerald will be green. It’s not merely that all the previous emeralds were green. Geologists have discovered the structure of emeralds. Light interacts with the particular structure of emeralds such that it is reflected and refracted in a way that a disproportionate amount of green light intercepts the eye, causing the sensory experience of green. Because of this scientific knowledge, there is legitimate basis for predicting that the next emerald will be green. Similarly, physicists understand the nature of planetary orbits, which are determined by laws of motion. Such laws of motion provide justification for predicting the future position of planets. So, as an example, let’s update the emerald argument to reflect scientific justification for our prediction:
P2. Emeralds, by definition, have a crystalline structure c.
P3. Science tells us that objects with crystalline structure c appear green because of the way that light interacts with c.
This objection to Hume suggests that we indeed have better reason to believe that Emeralds are green than mere “habit.” But in defense of Hume: Despite scientific understanding of what makes emerald green, he was correct that the greenness of emeralds is not necessary. This is because of an additional implied premise — PUN — which Hume correctly would say is not justified:
P4. The laws of nature (which govern the interaction of light with crystalline structures) are uniform in that they will be the same in the future as they were in the past. (PUN)
Thus, Hume’s claim that we cannot make a sound argument from a posteriori claims is correct, because P4 is questionable. If one appeals to the laws of physics to justify causal claims, Hume could respond that the laws of physics themselves rely upon PUN, which is not necessary. Causal relations, therefore, are not necessary but rather contingent upon PUN, which is not certain. It seems we have not successfully refuted Hume by appealing to our scientific understanding of why emeralds are green or why the sun will rise tomorrow.
Is Hume a Foundationalist?
However, by understanding nature, we have accomplished something. We can legitimately say that one overstates Hume’s claim if one characterizes Hume as having claimed that we have no good reason to believe scientific claims. Hume merely situates our expectation in the realm of a contingent idea (PUN) rather than necessity. Hume cites custom as our reason for our expectation. Although custom is contingent, it is stronger than no reason.
This debate over whether Hume would accept scientific understanding as justification — albeit not rational justification, for causal relations, can also be expressed by the question, “Is Hume a foundationalist?” According to Sober, Hume is a foundationalist (Beyond 186): A “level 3” prediction (e.g., “The sun will rise tomorrow”) must be justifiable solely by level 2 beliefs (e.g., “The sun has risen each day that I have made an observation”). If it cannot, then the prediction is not justifiable. Hume points out that such a bridge between levels two and three does not exist, therefore the prediction is not justifiable. But Sober suggests there is an alternative — a nonfoundationalist approach to justification whereby other level 3 beliefs could be used to justify the prediction that the sun will rise tomorrow (Beyond 189). Sober implies that Hume would not accept such a nonfoundationalist approach. But is Sober correct? I suggest he is not, for the reasons I gave above. And Kant seems to agree: Kant said, “The question was not whether the concept of cause was right, useful, and even indispensable for our knowledge of nature, for this Hume had never doubted [emphasis added]; but whether that concept could be thought by reason a priori . . . “ (259). [3]
Feser’s Critique of Hume’s Position on Matters of Fact
Edward Feser (1968-) asserts that “. . . modern philosophers, at least since David Hume (1711–1776), tended to think it ‘conceivable’ that any cause might produce any effect or none. For example, when a brick is thrown towards a window, we naturally expect that the window will shatter, but (so it is said) it is at least in theory possible that the brick might turn into a bouquet of flowers, or disappear altogether.” (20). But Feser notwithstanding, Hume did not make quite this claim (I believe Feser is making a straw man argument against Hume). Feser uses flowery language in an apparent attempt to make Hume seem ridiculous; yet my research has found no claim by Hume that a flying brick might turn into a bouquet of flowers. Rather, Hume’s theory suggests that if we did an experiment and repeatedly threw a brick into a window and every time the window broke (and the brick never turned into flowers) then we might form a complex idea of causation, which would be situated in imagination and thus not be rationally justifiable. Custom and habit would predict the result of the flying brick, rather than an argument of necessity. Indeed, Hume stated that observation and experience may assist us in predicting effects (74). The point is that Hume situates our expectations of causal relations in matters of fact rather that relations of ideas, but doesn’t deny that our expectations don’t have some degree of legitimacy. Thus, Hume’s claim falls short of Feser’s silly suggestion that under Hume’s theory, anything could happen. Hume’s point was that induction can never be one hundred percent certain, in a logical sense, as can the conclusion of a valid deductive argument, and thus causal relations cannot be proven as certain by logic; rather, we rely upon habit of the mind “to anticipate the consequence, or effect, upon witnessing the premise, or cause” (Stanford Encyclopedia of Philosophy). Relying upon habit is not logically justifiable, yet is short of suggesting that bricks might turn into flowers, even though Feser qualifies this critique of Hume with “at least in theory.”
Epistemological Support for Hume’s Position
The traditional analysis of propositional knowledge holds that knowledge is justified true belief (“JTB”) (Crumley II 36). JTB is necessary and may be sufficient for knowledge[4]. Thus, first one must have a propositional belief, e.g., “A billiard ball rolling into the second billiard caused the second billiard ball to move.” Second, the belief must be adequately justified, e.g., by sensory observations. Third, the belief must be true, i.e., the actual world (independent of human perception) must be such that the proposition corresponds to reality[5]. But according to Hume’s theory, both the justification and truth requirements of this proposition are problematic, and rightly so. There is no way for a human to bypass human perception to ascertain the truth value of a causal claim. All one can do is claim reasonable justification for believing the causal claim is true. But because an observer has no impression of causation, he would need to rely upon inference. But Hume’s point exactly is that the inferential argument upon which the observer relies contains an implied and unjustifiable premise, viz., PUN. As Hume said, it might be customary to claim a causal connection between the rolling billiard balls, and repeated experimentation might reveal constant conjunction of events, but that the relationship is causal is an idea of the imagination.
Wittgenstein’s Picture Theory Supports Hume
Ludwig Wittgenstein (1889–1951) asserted that only objects that can fit together as part of a picture constitute possible states of affairs which can be experienced — and possible experience is identical to world. Therefore, round squares, metaphysical claims about morality, good, bad, God — and importantly, cause and effect — are not part of the world, but are rather nonsensical propositions, because such things cannot be pictured. As Hume asserted, billiard balls can be observed touching and not touching, but each observation is an independent state of affairs (TLP 5.135). There is no picture of causation! “Superstition is nothing but belief in the causal nexus” (TLP 5.1361).
Kant’s Response to Hume
Kant argued that in the necessary way that human beings experience the world in which they live (within the manifold of space and time) substance, the laws of nature, and causal relations are indeed necessary (contra Hume) — that is to say, synthetic claims which rely upon the persistence of substance and PUN may be justifiable a priori[6]. This seems to rectify a problem elucidated by Hume, viz., we have no a priori knowledge of causation. But Kant admits that we have no access to the world in itself (the noumenal world), though the source of phenomenal world is the noumenal world. (This is one way to distinguish Kant from an idealist: The phenomenal world is not made up in people’s minds, but rather it is driven by the noumena.) But because Kant recognizes that we have no access to the noumena, it follows that we cannot know that the laws of nature in the phenomenal world, which are synthetic a priori knowledge, may not change due to changes in the noumenal world which drives them. Thus, I do not see that Kant has sufficiently addressed the unjustifiability of PUN by merely relocating laws of nature to a phenomenal world — he still has not proven that the laws are necessary. He rather asks us to stipulate that nature is uniform, and will not change, because that’s how the phenomenal world works. But as Hume said all along, such a stipulation is merely custom and not rationally justifiable. Kant is begging the question, which is: “Might the laws of nature change?” Hume says it would not be a contradiction for them to do so. Kant merely begs the question by positing that a world where the laws of nature are uniform (the phenomenal world) then claiming the problem is solved. We have no reason to believe that is so.
To reiterate my position on Hume’s critique of matters of fact: Hume was correct. We have no possible method by which to be certain of PUN. Kant’s response is that we should stipulate that our ideas about PUN are justified, but this begs the question of whether they are. Attacks such as those from Feser are straw man fallacies: Hume does not claim that there is no basis upon which to expect that events will lead to particular effects: Hume does not deny constant conjunction. Rather, he correctly situates ideas of necessary connection in our imagination.
Challenges to Relations of Ideas
Now I turn to a priori claims, those Hume characterized as relations of ideas. Such claims are, by definition, necessary, universal, and independent of experience. I will present counter examples raised by other philosophers, and some of my own — which together cast doubt on whether prima facie a priori claims meet the definition of a priori.
Language Indeterminacy
The first category of counter examples to relations of ideas elucidate the difficulty in determining the meaning of words.
References to nonexistent objects
A famous problem in philosophy of language is that of references to nonexistents. “The present King of France is bald” is a claim that elucidates this problem. While philosophers such as Alexius Meinong (1853–1920) and Wittgenstein had no objection to attributing properties (e.g., baldness) to nonexistents (e.g., the present King of France), Bertrand Russell (1872–1970) was not satisfied[7]. Among other objections, Russell found that such a statement, in its grammatical form, violates the law of excluded middle (Swanson 166). Either an object has a property, or it does not. But a nonexistent King of France cannot have, and it cannot not have, the property of baldness[8].
For any proposition, either that proposition is true, or its negation is true.
Now let’s examine an example of how LEM is challenged by nonexistent objects such that an “analytic” argument makes no sense.
P1. Either the present King of France is bald or the Present King of France is not bald. (LEM).
P2. The present King of France does not exist.
P3. Nonexistent entities cannot have the property of being bald or not being bald.
C. The present King of France is neither bald nor not bald. (Violates LEM)
This argument is inconsistent. It is impossible for the premises to be true and the conclusion true. How could we make the argument valid? We could alter P1, but then we would violate LEM:
P1. The present King of France is bald, or the Present King of France is not bald, or the present King of France is neither bald nor not bald. (Violation of LEM).
We could alter P2, but then we would be making a false claim:
P2. The present King of France exists.
We could alter P3. But the conclusion is counter-intuitive:
P3. Nonexistent entities can have properties.
C. The present King of France is not bald. (Or, the present King of France is bald)
In a further rebuke to Russell, widely accepted laws of logic such as LEM are false according to Jacques Derrida’s (1930–2004) concept of differance[9]: Logocentrism[10] failed to recognize dynamic flow based on relationships of opposites. Indeed, A implies not A. Love and hate, far from being mutually exclusive opposites, have something important in common: They are both strong emotions. Logical-centric philosophy, forever seeking primacies of meaning, has failed to recognize the symbiotic relationship of opposites.
Science gives us several examples which challenge LEM. The laws of physics reveal potential energy, which is energy that resides somewhere between existence and non-existence — again, challenging LEM[11].
Quine’s Two Dogmas of Empiricism
Willard Van Orman Quine (1908–2000) attacked the empirical philosophers’ sharp distinction between analytic and synthetic claims as dogmatic. He stated that the proposition “No bachelor is married,” presumed to be analytically true by definition, is not so — because definition “hinges on prior relations of synonymy” (261). But Quine points out that for words to be synonymous they must be interchangeable salva veritate[12]. If a statement such as “All bachelors are unmarried men” to be analytic, the words “bachelor” and “unmarried man” would have to be interchangeable. But said Quine, “Truths which become false under substitution of ‘unmarried man’ for ‘bachelor’ are easily constructed with the help of ‘bachelor of arts’ or ‘bachelor’s buttons . . .” But even if we ruled out alternate definitions of “bachelor,” interchangeability salva veritate would not be an assurance of cognitive synonymy, which Quine said would be necessary for analyticity. The general terms, “creature with a heart” and “creature with kidneys” are alike in extension, i.e., they point to an identical creature — because hearts and kidneys can only exist together. Thus, they are interchangeable salva veritate. But they are not cognitively synonymous. Therefore, in an extensional language, cognitive synonymy and interchangeability are distinct matters. That bachelor and married man point to the same thing does not mean that they are cognitively synonymous. If they are not assured to be cognitively synonymous, we can question whether “All bachelors are unmarried men” is analytic. Quine also attacked the second “dogma of empiricism”, viz., the verification theory of meaning, which states that the meaning of statement is its empirical verification condition. (267) The dogma here is that according to itself, the verification theory is meaningless, because as a theory it has no empirical verification condition.
Kripke claims that language has no meaning
Saul Kripke argues that one cannot reliably reverse-engineer a statement to ascertain what was in the speakers or writer’s mind. According to Alexander Miller:
The conclusion of KW’s [Kripke Wittgenstein’s] sceptic’s argument is that there is no fact of the matter in virtue of which sentence such as “Jones means addition by ‘+’” or “Smith means green by ‘green’ . . . (166)
Regarding the addition question: There would be no truth condition nor meaning-fact which would justify a belief that addition (rather than “quaddition”) were the rule used in the scenario provided. If you have experience of Jones adding together numbers less than 57 according to the standard rules of addition, you do not have sufficient data to with which to conclude which rule Jones is using. The reason is that there is (at least one) other possible meaning of “+” to Jones, which would fit with your previous observations. For example, the rule that Jones is following could be that if x and y are both less than 57, then “+” means perform standard addition to perform the calculation, but if either x or y is 57 or greater, then the result is always 5 (this rule is what is being called quaddition). Since you have never seen Jones work with a number 57 or greater, either addition or quaddition would be consistent with Jones’s previous behaviour — but you are looking for the one rule Jones is using. Therefore, a belief that he is using one or the other rule cannot be justified. You have not discovered the rule.
Quine claimed that language has no meaning
Another counter example to meaning in grammatical statements came from Quine[13]. For Quine, the problem starts with indeterminacy of translation (Miller 141). In a thought experiment described by Miller (141–148), a radical translator has no prior information or understandings which would assist him in creating a translation manual between English and a native language. He relies completely upon that what he can infer from the relationship between the spoken words and behaviour of the natives. The problem is that a second radical translator can produce her own translation manual which is an equally good match to the native language as the first translator’s manual — yet the two manuals are not in agreement with each other. This suggests that neither manual can be assumed to reflect an actual meaning of the native language, because it cannot be determined which manual (if either) is “correct.”
To summarize the issue of language: Making meaningful claims, whether deductive or inductive, normally requires the use of language. But I have shown various reasons recognized by philosophers why language is often not sufficient to make claims independent of experience — it seems we often need context from the experiential world to understand the meaning of the words. Even after examining context, we may still fail to determine meaning, according to some philosophers. This is in part because of the ambiguity of words themselves (Quine and Kripke), but more importantly, the difficulty of applying the logical laws required for analyticity to the real world, wherein we can speak of nonexistent things and opposites are not always mutually exclusive (Russell and Derrida). I believe I have now begun to cast some doubt on the plausibility of Hume’s claim that there are relations of ideas which are distinct from matters of fact. But there is more reason to doubt relations of ideas, as we shall now see.
My Critique of Relations of Ideas: Unjustifiable Premises
Keeping in mind Hume’s claim that cause and effect is imaginative, and an appeal to inference ultimately fails because of inevitable dependence upon the unjustifiable PUN, let’s now explore so-called analytic claims in search of their necessity. This second category of counter examples to a priori claims as relations of ideas relate to the implied premises such claims seem to contain. My critique takes a different track than that of the aforementioned philosophers: Rather than merely showing the insufficiency of language in making analytic claims, I shall show that such claims often suffer from a similar flaw to that which limits inductive claims, viz., they include at least one premise (implicit or explicit) which is not justifiable. Similar to PUN, this premise is a claim about the future; In this case, it is a claim that there will be no new discoveries which are relevant to the argument and threaten the truth of the conclusion. I shall call this premise “NND.”
Geometry
Hume places “the sciences of Geometry, Algebra, and Arithmetic” into the realm of affirmations which are “either intuitively or demonstrably certain” (70). Let’s begin by examining a claim about geometry whose conclusion at first glance might seem to be certain buy the mere relations of ideas, but whose further exploration reveals ambiguity.
P1. T is a triangle.
P2. The three angles of every triangle add up to 180 degrees.
C. The angles of T add up to 180 degrees.
This is a valid argument. Further, if one accepts P2 as true by definition, then we seem to have a sound argument by “the mere operation of thought,” to borrow Hume’s term (70). We should not have to go out and observe a triangle to determine the soundness of the argument. But if we were to measure a triangle in the real world, we would find out that the angles may not add up to 180 degrees. This is because a problem arises with an understanding of scientific discoveries subsequent to Hume, viz., space is curved[14], and in curved space the angles of a triangle may not add up to 180 degrees. Therefore, P2 is a questionable premise. Therefore, to maintain the soundness of the argument, we must modify P2:
P2. In flat space, the three angles of every triangle add up to 180 degrees.
And add a new premise:
P3. Space is flat.
Or, we can modify the conclusion by limiting its scope:
C. In flat space, the angles of T add up to 180 degrees.
But where is our argument now? There remain several problems. One, if we chose to add P3, P3 is not true, at least vis-à-vis the actual world. Two, if we modified our conclusion, then we have limited the scope of the claim to theoretical flat space — which again does not describe the actual world. Three and most profoundly, we may be missing other as-yet unknown premises of which we have not yet conceived, just as neither non-Euclidean geometry nor the curved space of Einstein’s general relativity were known until after Hume’s time. Thus, we are now left with uncertainty as to the soundness of this argument. If we examine the original argument, it turns out that P2 is false.
We could attempt to rescue this argument by adding a new premise:
P4. There are no new possible discoveries about the world which would require us to add a new premise to this argument to retain its soundness (NND).
But as one might quickly realize, P4 is a questionable premise. It is at least as questionable as PUN, whose unjustifiability is the limitation of arguments from matters of fact. Thus, although at first NND seemed to have saved the soundness of our argument, we cannot say that the argument is sound, because the truth of NND is impossible to know.
Gender identity
Let’s examine this argument, which is also a language problem, but the language problem provides hints as to deeper conceptual problems:
P1. Mary is a mother.
P2. All mothers are women.
C. Mary is a woman.
This is a valid argument. If one accepts P2 as true by definition, then we seem also to have a sound argument by the mere relations of ideas. But a problem arises with ambiguity in the understanding of gender discovered subsequent to Hume, viz., people can have sex-change operations after which the binary male/female assessment becomes ambiguous.
Therefore, to maintain the soundness and a priori justification for the argument, we could add a new premise:
P3. The definition of a woman is a person who has female reproductive apparatus.
But, then we have continuing ambiguity. What are female reproductive apparatus? Can their definition change over time? What if such a “woman” had the sex-change operation subsequent to giving birth? Is this person still a “woman”? We can see that the validity and soundness of this argument runs into trouble with definitions that are difficult to determine without adding premises, but there may be an infinite regress of premises required. Again, as in the first example, what at first glance appears to be indubitable knowledge derived from relations of ideas is cast into uncertainty due to the discovery of hidden premises and a necessity for adding additional premises, some of which may be as-yet unknown. Therefore, to maintain the soundness of the argument, we could modify P3:
P3. The definition of a woman is a person who has female reproductive apparatus at the time of the utterance of the statement.
But some statements are not uttered, they are merely written — as in a philosophy textbook, for example. So, let’s try again.
P3. The definition of a woman is a person who has female reproductive at any time during the course of life.
We could further attempt to rescue this argument by adding a new premise:
P4. Such woman will never gain or lose reproductive organs in the future (NND).
But as one might quickly realize, P4 is a questionable premise. It is at least as questionable as PUN, whose unjustifiability is a limitation of arguments from matters of fact. Thus, although we tried to preserve the soundness of our argument, we cannot say that it is sound, because the truth of NND is impossible to know.
We remain determined to pin down an analytic definition of gender, so we discover that two X chromosomes make a woman, and an X and Y chromosome make a man. But further research reveals that some people have an additional X chromosome (“super females)” and some have two X chromosomes and a Y chromosome (“feminine” men) (Thomas). What was originally thought to be an analytic argument about women and mothers seems rather to be floundering in the indeterminacy of the experiential world.
LNC — The Law of Non-Contradiction
LNC is one of the fundamental laws of logic, and is important in constructing analytic claims from relations of ideas:
The two propositions “A is B “ and “A is not B “ are mutually exclusive
But let’s examine an example of how LNC is challenged by discoveries about the world.
P1. If it is the case that ladder L fits inside garage G, then it is not the case that L does not fit into G (LNC).
P2. By hypothesis, L fits into G.
C. By hypothesis then, it is not the case that L does not fit into G.
At first look, this seems like a sound argument, whose conclusion we can be sure of by relations of ideas (note that we are not making an empirical claim that the ladder fits into the garage, we have qualified the claim with “by hypothesis”). But when we apply our a priori argument to the real world, Einstein’s discovery of special relativity seems to open the possibility that both L fits into G and L does not fit into G are true. The famous ladder paradox thought experiment (UNSW) shows how a ladder could both fit and not fit into a garage relative to observers in different inertial frames. Now we see that P1 is questionable because of the questionability of the law of noncontradiction.
We could try to salvage the soundness of the argument by limiting the scope of the claim to observers in the same inertial frame:
P1. Relative to observers O in a single inertial frame, if it is the case that ladder L fits inside garage G, then it is not the case that L does not fit into garage C (LNC).
P2. Relative to O, L is fits into G.
C. Relative to O, it is not the case that L does not fit into G.
But where is our argument now? There remains at least one problem: Just as at one time no one thought about the ramifications of special relativity, we may now be missing other as-yet unknown conditions of which we have not yet conceived. Thus, we are now left with uncertainty as to the soundness of this argument. We are also now uncertain whether we can know the conclusion to be true by relations of ideas, because there may be further ideas of which we are not aware.
We could attempt to rescue the argument by adding a new condition:
P3. There are no new possible discoveries about the world which would require us to further limit the scope of this claim to retain its soundness (NND).
But as one might quickly realize, P3 is a questionable premise. It is at least as questionable as PUN, whose unjustifiability is a limitation of arguments from matters of fact. Thus, although at first glance we seem to have saved the soundness of our argument, we cannot say that it is sound, because now the truth of NND is impossible to know. It seems that the truth of the conclusion cannot be determined as necessary by relations of ideas.
Now, let’s examine another counter example which challenges LNC and our ability to create an argument from relations of ideas. First, here’s an argument I will not challenge:
P1. I have an idea of a small round thing R. R is either an apple, or an orange, or neither an apple nor orange (LNC-R can’t be both an apple and an orange, which are two distinct things).
P2. I have the idea that R is an apple.
C. Therefore, I am justified in claiming that R is not an orange.
This argument seems to valid by mere relations of ideas. For the moment, I will not challenge that idea. But now let’s construct a similar argument from another observation:
P1. I have the idea of blue light L. L is either wave, or a particle, or neither a wave nor particle (LNC- L can’t be both a wave and a particle, which are two distinct things).
P2. I have the idea that L is a wave.
C. Therefore, I am justified in claiming that L is not a particle.
This is a valid argument. If the premises are true, the conclusion must be true. We might want to say that the truth of the conclusion, therefore, can be determined by mere relations of ideas. However, the problem is that quantum mechanics tells us that the conclusion is false: Under some methods and contexts of observation, light behaves as a wave; under other methods and contexts of observation, light behaves as a particle. We can try to salvage the analyticity and thus a priori nature of the argument by limiting the scope:
P1. I have the idea of in context C, blue light L. L is either wave, or a particle, or neither a wave nor particle (LNC- L can’t be both a wave and a particle, which are two distinct things).
P2. I have the idea that in context C L is a wave.
C. Therefore, I am justified in believing that in context C L is not a particle.
But the problem is that it is possible there will be a new scientific discovery, heretofore unknown, which would require us to further limit the scope of the claim. Even though the discovery would be made in the future, the facts which it will discover are true today, but unknown to us. Therefore, it is possible that this argument is wrong. If that is possible we do not have a necessary and universal argument. We cannot say that the conclusion can be known a priori. Indeed, the conclusion is dependent on facts about the world which are likely discovered by experience, again refuting an a priori nature of this argument. We could try to salvage the necessity of this argument by adding a premise:
P3. There are no new possible discoveries about the world which would require us to further limit the scope of this claim to retain its soundness (NND).
But as in prior counter examples, P3 is a questionable premise. It is at least as questionable as PUN. Again, it seems that the truth of the conclusion cannot be determined as necessary by relations of ideas.
Are there any bona fide a priori claims?
I am not refuting the analyticity of all possible a priori claims. Indeed, one could argue that the analyticity of a logical statement without reference to the world, such as the following, cannot be challenged:
P1. A or B
P2. Not A
C: B
Similarly, Quine said that the following statement is logically true, and remains true under any interpretations of ‘man’ and ‘married’:
No unmarried man is married. (258)
But claims such as the two above convey little useful information about the world. The second class of analytic claims, according to Quine, are typified by statements such as:
No bachelor is married.
According to Quine, it’s in this second class of statements that we run into problems with the meaning of words (259), which as I have explained, is problematic. Thus, when we replace logical symbols and logical tautologies with real-world information, like claims about angles of triangles or gender identity, we risk our claim to analyticity. Implicit in such claims is the unjustifiable premise that we know all there is to know about the laws of nature and the world.
Conclusion
Hume said there are two types of claims: Those grounded in relations of ideas and those grounded in matters of fact. The former claims are analytic and a priori in that they are necessary and independent of experience. The latter claims are contingent and arise from experience. Hume suggested that there is a rift between the two sources of knowledge, and it cannot be bridged[15]. Relations of ideas tell us only how ideas relate to each other — not to the physical world of experience. Ideas about matters of fact begin with copies of impressions, and it is human nature to work up in the imagination complex ideas — derived from bundles of impressions — about substance and cause and effect. However, such complex ideas cannot be justified rationally, because we have impressions of neither substance nor causation, and because all a posteriori arguments are inductive and saddled with an implied premise asserting PUN. Therefore, claims as to matters of fact arise from custom and habit rather than necessity and cannot be rightly called a priori.
I have shown how Quine, Kripke and Derrida cast down on the analyticity of many claims grounded in apparent relations of ideas because of the difficulty in determining the meaning of language. I then showed how some prima facie necessary claims are rendered contingent because the words employed to make those claims cannot be understood outside the context of experience; and when we must look to the world for meaning in relations of ideas, they are no longer mere relations of ideas. Moreover, such prima facie a priori claims shown rather to be synthetic a posteriori suffer from unjustifiable premises similar to PUN, which I call NND. In the previous examples we saw how, paradoxically, one needs to observe and experience the world to determine the soundness of what are supposed to be a priori statements.
These doubts cause us to reexamine Hume’s claim that relations of ideas are known to be certain independent of experience: “Propositions of this kind [geometry, algebra, and arithmetic] are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe” (70). I pointed out that in the case of gender identity, it is only because of social and political changes, and breakthroughs in medicine (the ability to perform sex-change operations) that we have become aware of ambiguity. Similarly, physicists who developed theories that space is curved rather than flat conducted scientific experiments to confirm their theories. Scientists literally measured triangles a posteriori to determine if their claimed a priori theories of curved space are correct[16]; it is therefore most paradoxical that the comprehensibility of a claimed analytic, a priori statement about angles of a triangle is dependent upon observation — and then the observation suggests that the statement is indeterminate and contingent. Einstein developed the theory of special relativity, which was confirmed by conducting scientific experiments a posteriori. Similarly, quantum theory was confirmed by observational experiments. The data from such experiments throws many prima facie claims of analyticity into doubt, particularly because there may be future discoveries which require us to change our models of the world — thus casting into doubt the possibility that a premise such as NND will save the necessity of such arguments.
Unfortunately, Kant does not rescue us. Stipulating that the way we think about the world because of our human nature (e.g., our idea of cause and effect) is good enough — so let’s just agree that our (phenomenal) world is as we imagine it to be — seems to be a circular argument and does not answer as to what happens if the laws of nature change (and the laws of nature could conceivably change because of changes in the noumenal world posited by Kant). Thus, we should understand that all claims, including analytic and synthetic, are limited by the human inability to obtain a God’s eye view of the world.
Because I have suggested that Hume did not go far enough in questioning relations of ideas, and because I have argued that we cannot separate prima facie relations of ideas from matters of fact, the reader might think I am objecting to Hume’s critique of cause and effect. But this is not the case. Rather, I am propounding Hume’s theory, perhaps even louder than did he. Hume claimed that there is an unbridgeable gap between relations of ideas and matters of fact, and I agree. At first glance, it may seem that I argued the opposite, viz., that relations of ideas cannot be separated from matters of fact. But what I argue is that bona fide relations of ideas are indeed distinct from matters of fact. It’s just that bona fide a priori claims are a vanishingly narrow class consisting mainly of formal logic laws and statements which omit grammatical reference to the actual world and are non-interactive with the world beyond themselves. Once we replace logical notation with words, we lose analyticity and statements which we first thought were grounded in relations of ideas are revealed rather as matters of fact, subject to the same types of contingencies that Hume convincingly argued limit the latter. Just as Hume said, from necessary relations of ideas we can learn nothing about contingent matters of fact — indeed, relations of ideas don’t tell us much at all except how the ideas relate to each other. Manipulation of logical symbols a priori will get us nowhere in discovering facts about the world.
I have shown, by examples, how it is that when we replace logic symbols with words we show precisely what I believe Hume wanted to show, viz., the world of experience and logic are mutually exclusive. Relations of ideas employ logic, but the world is not a logical place. The world is imbued with ambiguity, shades of grey and our ideas of it are constantly evolving, as it itself may be. Thus, we cannot move from a priori logical statements to the actual world a posteriori, nor can we move from the actual world to logical statements. As Hume stated, because of human nature, sense perceptions lead to complex ideas of substance and causation which cannot be justified logically. The logic of anatomical statements, and logical laws such as LNC and LEM simply don’t fit the real world.
Those who are uncomfortable with such contingency in the world might find their saviour in Immanuel Kant after all: Concerned with the threat that a contingent world — without the certainty of underlying substance and cause and effect — posed for science, Kant decreed that the truth of what Hume characterized as complex ideas of the imagination is hereby necessary! Thus, synthetic a priori claims were born, and many were reassured that necessity was restored and science rescued.
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[1] Analytic claims: “‘All bachelors are unmarried men’ is an analytic statement, since ‘unmarried men’ is already contained within the meaning of ‘bachelor’” (Baggini and Fosl 268).
[2] This distinction did not hold for Kant, who postulated the existence of synthetic, a priori knowledge. Hume did not recognize such knowledge.
[3] Kant proceeded to argue that cause and effect could be known a priori, but he recognized the scope of Hume’s claim, viz., that cause and effect cannot be shown to be necessary, not that there was no basis upon which to accept it.
[4]Some have suggested that additional criteria are necessary. Further, exactly what constitutes justification, and the definition of truth, are not universally recognized.
[5] Per Crumley, most believe that truth is a necessary condition for knowledge, even if they do not concur with the traditional analysis in its entirety (38). Further, Crumley adopts a non-epistemic, as well as a correspondence theory of truth, viz., the truth of a proposition depends on its correspondence to the state of the world, independently of human beliefs (40).
[6] Particular scientific claims of cause and effect, such as “The sun warms the rock,” are not a priori but rather a posteriori claims — they are believed to be true by experience. But that there can be causal relations without sense perception of “cause,” is known a priori. Kant claimed that Hume missed this point, viz. that there are justifiable synthetic a priori claims.
[7] Meinong was not so troubled by nonexistents: He protested the bias in favour of actual over nonexistent, and he pointed out that according to the Characterization Postulate, nonexistents can have properties, such as that of being nonexistent — and in the case of a round square, impossibility (Swanson 168–171). Wittgenstein likewise had no problem with nonexistents: If they can fit into a picture of a state of affairs, such as can the Present King of France, then they are part of the world. They may be “negative facts,” but they are facts in the world, nonetheless (TLP 2.06).
[8] Problems like this inspired Russel’s famous theory of descriptions (Lycan 12–19), wherein he sought to clean up sloppy language by translating it into logical form, a superior “language” which explicitly elucidates the intent of the deficient grammar, which is in this case, “There exists one and only one present King of France, and he is bald.” If we apply Russell’s logic, we have a conjunction, A + B. Unless both conjuncts are true, the statement is false. Since A is false, we now have successfully determined the falsity of the entire statement. Thus, by elucidating what he claimed to be the logic underlying the grammar, Russell “cleaned up language,” at least with respect to nonexistent definite descriptions.
[9] Derrida intentionally misspelled the word difference to illustrate that words are difficult to interpret without context. He gives us context for differance, otherwise we would not know its meaning (Signature 352,363).
[10] The term logocentrism is used by Derrida’s to describe naïve devotion to reason, logic, and clear definition (Signature 347–366).
[11] Arguing for idealism, W.T. Stace used the indeterminacy of potential energy as an argument against the objectivity of science (620).
[12] Two expressions are said to be interchangeable salva veritate if the substitution of one for the other does not change the truth value or meaning of any context in which either expression appears
[13] Miller says that even if a radical translator correctly determines the native’s method of indicating assent, Quine would claim that the radical translator is still prone to being mistaken about to what the native is assenting. For example, the translator, pointing to a rabbit and saying “yo gavagai” might hear an assent (“yevet”) from the native, and assume that gavagai was the native word for rabbit. The translator would even conduct experiments to confirm his hypothesis, such as pointing to a rabbit and making other sounds, to which she receives dissenting response (“nok”). But the other radical translator might conclude that “gavagai” translated to “undetachable rabbit part,” and could justify this translation by pointing to a rabbit, saying “yo gavagai,” and receiving an assenting response. Further, if the native word for same were determined, each translator would receive an affirmative response when pointing to a rabbit’s nose and asking if it were the same “gavagai” as when pointing to another rabbit’s nose. Each translator might believe that he has strong evidence that “gavagai” translates to rabbit in one case, or undetachable rabbit part in the other. Both translations are consistent with the observational evidence, yet each translation contradicts the other. Both translations could not correspond to the native language if the native language had meaning. There is no other way to determine which translation is correct.
If the radical translators can’t determine meaning, then the same would be true for infants attempting to learn a language, because they, like a radical translator, would have only observational evidence for the meaning of words. The implication is that there is no reason to believe that all speakers of a language have determined a single meaning of words. Therefore, the meaning of language is indeterminant, and if it is indeterminant, then there is no meaning.
[14] The first experiment to show that space is curved was conducted in 1919 by Arthur Eddington.
[15] This rift is often referred to as Hume’s fork (Baggini and Fosl 200–201).
[16] A triangle is formed by rays of light from two stars and earth. In 1919, Arthur Eddington showed that the path of light from stars was bent when passing by the sun.
