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The meaning of "existence": Lessons from infinity
[Crossposted; Based on Can infinite quantities exist? A philosophical approach (downvoted)
The topic is the concept of existence, not why there's something rather than nothing—not the fact of existence—but the bare concept brings its own austere delights. Philosophical problems arise from our conflicting intuitions, but “existence” is a primitive element of thought because our intuitions of it are so robust and reliable. Of course, we disagree about whether certain particulars (such as Moses) have existed and even about whether some general kinds (such as the real numbers) exist, but disputes don’t concern the concept of existence itself. If Moses’s existence poses any conceptual problem, it concerns what counts as being him, not what counts as existence. Adult readers never seriously maintain that fictitious characters exist; they disagree about whether a given character is fictitious; even the question of the existential status of numbers is a question about numbers rather than about existence. As will be seen, sometimes philosophers wrongly construe these disputes as being about existence.
When essay 19.0 asked “Can infinite quantities exist?” existence’s meaning wasn't in play—infinity’s was. Existence is well-suited for the role as a primitive concept in philosophy because it is so unproblematic, but it’s unproblematic nature can be thought of as a kind of problem, in that we want to know why this concept is uniquely unproblematic. We would at least like to be able to say something more about it than merely that it’s primitive, but in philosophy, we acquire knowledge by solving problems and existence fails to provide any but the unhelpful problem of its being unproblematic. The problem of infinity provides, in the end, some purchase on the concept of existence, which concept I assumed in dealing with infinity.
In one argument against actual infinity, I proposed as conceptually possible that separate things might be distinguishable only concerning their being separate things. Then, if we assume that infinite sets can exist, the implication is the contradiction that an infinite set and its successor—when still another point pops into existence—are the same set because you can’t distinguish them. (In technical terms, the only information that could distinguish the set and its successor, given that their members are brutely distinguishable, is their cardinality, which is the same—countably infinite—for each set.)
What’s interesting here is the role of existence, which imposes an additional constraint on concepts besides the internal consistency imposed by the mathematics of sets. Whereas we are unable to distinguish existing points, we are able—in a manner of speaking—to distinguish points that exist from those that don’t exist. While no proper subsets are possible for existing brutely distinguishable points, the distinction within the abstract set of points between “those” that exist and “those” that don’t exist allows us to extend the successor set by moving the boundary, resulting in contradiction.
If finitude is a condition for existence, we’ve learned something new about the concept of existence. Its meaning is imbued with finitude, with definite quantity. Everything that exists does so in some definite quantity. Existence is that property of conceptual referents such that they necessarily exist in some definite quantity.
Existence is primitive because almost everyone knows the term and can apply it to the extent they understand what they’re applying it to. The alternative to primitive existence is primitive sensation, as when Descartes derived his existence from his “thinking.” But sensationalism is incoherent; “experiences” inherently lacking in properties (“ineffable”) are conceived as having properties (“qualia”). So, the heirs of extreme logical empiricism, from Rudolf Carnap to David Lewis, have challenged existence’s primitiveness. Carnap defined existence by the place of concepts in a fruitful theory. Lewis applies this positivist maxim to find that all possible worlds exist. Lewis isn’t impelled by an independent theory of logical existence, such as a Platonic theory that posits actually realized idealizations. Rather, the usefulness of possible worlds in logic requires their acceptance, according to Lewis, because that’s all that we mean by “exists.” Lewis is driven by this theory of existence to require infinitely many existing possible worlds, which disqualifies it on other grounds. But the grounds aren’t separate. When you don’t apply the constraints of existence because you deny their intuitive force, you lose just that constraint imposing finitude. The incoherence of sensationalism and of actual infinities argues for a metaphysics upholding the primacy of common-sense existence.
Can infinite quantities exist? A philosophical approach
Initially attracted to Less Wrong by Eliezer Yudkowsky's intellectual boldness in his "infinite-sets atheism," I've waited patiently to discover its rationale. Sometimes it's said that our "intuitions" speak for infinity or against, but how could one, in a Kahneman-appropriate manner, arrive at intuitions about whether the cosmos is infinite? Intuitions about infinite sets might arise from an analysis of the concept of actually realized infinities. This is a distinctively philosophical form of analysis and one somewhat alien to Less Wrong, but it may be the only way to gain purchase on this neglected question. I'm by no means certain of my reasoning; I certainly don't think I've settled the issue. But for reasons I discuss in this skeletal argument, the conceptual—as opposed to the scientific or mathematical—analysis of "actually realized infinities" has been largely avoided, and I hope to help begin a necessary discussion.
1. The actuality of infinity is a paramount metaphysical issue.
Some major issues in science and philosophy demand taking a position on whether there can be an infinite number of things or an infinite amount of something. Infinity’s most obvious scientific relevance is to cosmology, where the question of whether the universe is finite or infinite looms large. But infinities are invoked in various physical theories, and they seem often to occur in dubious theories. In quantum mechanics, an (uncountable) infinity of worlds is invoked by the “many worlds interpretation,” and anthropic explanations often invoke an actual infinity of universes, which may themselves be infinite. These applications make real infinite sets a paramount metaphysical problem—if it indeed is metaphysical—but the orthodox view is that, being empirical, it isn’t metaphysical at all. To view infinity as a purely empirical matter is the modern view; we’ve learned not to place excessive weight on purely conceptual reasoning, but whether conceptual reasoning can definitively settle the matter differs from whether the matter is fundamentally conceptual.
Two developments have discouraged the metaphysical exploration of actually existing infinities: the mathematical analysis of infinity and the proffer of crank arguments against infinity in the service of retrograde causes. Although some marginal schools of mathematics reject Cantor’s investigation of transfinite numbers, I will assume the concept of infinity itself is consistent. My analysis pertains not to the concept of infinity as such but to the actual realization of infinity. Actual infinity’s main detractor is a Christian fundamentalist crank named William Lane Craig, whose critique of infinity, serving theist first-cause arguments, has made infinity eliminativism intellectually disreputable. Craig’s arguments merely appeal to the strangeness of infinity’s manifestations, not to the incoherence of its realization. The standard arguments against infinity, which predate Cantor, have been well-refuted, and I leave the mathematical critique of infinity to the mathematicians, who are mostly satisfied. (See Graham Oppy, Philosophical perspectives on infinity (2006).)
2. The principle of the identity of indistinguishables applies to physics and to sets, not to everything conceivable.
My novel arguments are based on a revision of a metaphysical principle called the identity of indistinguishables, which holds that two separate things can’t have exactly the same properties. Things are constituted by their properties; if two things have exactly the same properties, nothing remains to make them different from one another. Physical objects do seem to conform to the identity of indistinguishables because physical objects are individuated by their positions in space and time, which are properties, but this is a physical rather than a metaphysical principle. Conceptually, brute distinguishability, that is differing from all other things simply in being different, is a property, although it provides us with no basis for identifying one thing and not another. There may be no way to use such a property in any physical theory, we may never learn of such a property and thus never have reason to believe it instantiated, but the property seems conceptually possible.
But the identity of indistinguishables does apply to sets: indistinguishable sets are identical. Properties determine sets, so you can’t define a proper subset of brutely distinguishable things.
3. Arguments against actually existing infinite sets.
A. Argument based on brute distinguishability.
To show that the existence of an actually existing infinite set leads to contradiction, assume the existence of an infinite set of brutely distinguishable points. Now another point pops into existence. The former and latter sets are indistinguishable, yet they aren’t identical. The proviso that the points themselves are indistinguishable allows the sets to be different yet indistinguishable when they’re infinite, proving they can’t be infinite.
B. Argument based on probability as limiting relative frequency.
The previous argument depends on the coherence of brute distinguishability. The following probability argument depends on different intuitions. Probabilities can be treated as idealizations at infinite limits. If you toss a coin, it will land heads roughly 50% of the time, and it gets closer to exactly 50% as the number of tosses “approaches infinity.” But if there can actually be an infinite number of tosses, contradiction arises. Consider the possibility that in an infinite universe or an infinite number of universes, infinitely many coin tosses actually occur. The frequency of heads and of tails is then infinite, so the relative frequency is undefined. Furthermore, the frequency of rolling a 1 on a die also equals the frequency of rolling 2 – 6: both are (countably) infinite. But if infinite quantities exist, then relative frequency should equal probability. Therefore, infinite quantities don’t exist.
4. The nonexistence of actually realized infinite sets and the principle of the identity of indistinguishable sets together imply the Gold model of the cosmos.
Before applying the conclusion that actually realized infinities can’t exist together with the principle of the identity of indistinguishables to a fundamental problem of cosmology, caveats are in order. The argument uses only the most general and well-established physical conclusions and is oblivious to physical detail, and not being competent in physics, I must abstain even from assessing the weight the philosophical analysis that follows should carry; it may be very slight. While the cosmological model I propose isn’t original, the argument is original and as far as I can tell, novel. I am not proposing a physical theory as much as suggesting metaphysical considerations that might bear on physics, whereas it is for physicists to say how weighty these considerations are in light of actual physical data and theory.
The cosmological theory is the Gold model of the universe, once favored by Albert Einstein, according to which the universe undergoes a perpetual expansion, contraction, and re-expansion. I assume a deterministic universe, such that cycles are exactly identical: any contraction is thus indistinguishable from any other, and any expansion is indistinguishable from any other. Since there is no room in physics for brute distinguishability, they are identical because no common spatio-temporal framework allows their distinction. Thus, although the expansion and contraction process is perpetual and eternal, it is also finite; in fact, its number is unity.
The Gold universe—alone, with the possible exception of the Hawking universe—avoids the dilemma of the realization of infinite sets or origination ex nihilo.
The deeper solution to the mystery of moralism—Believing in morality and free will are hazardous to your mental health
[Crossposted.]
The complex relationship between Systems 1 and 2 and construal level
The distinction between pre-attentive and focal-attentive mental processes has dominated cognitive psychology for some 35 years. In the past decade has arisen another cognitive dichotomy specific to social psychology: processes of abstract construal (far cognition) versusconcrete construal (near cognition). This essay will theorize about the relationship between these dichotomies to clarify further how believing in the existence of free will and in the objective existence of morality can thwart reason by causing you to choose what you don’t want.
The state of the art on pre-attentive and focal-attentive processes is Daniel Kahneman’s bookThinking, Fast and Slow, where he calls pre-attentive processes System 1 and focal-attentive processes System 2. The reification of processes into fictional systems also resembles Freud’sSystem Csc (Conscious) and System Pcs (Preconscious). I’ll adopt the language System 1 andSystem 2, but readers can apply their understanding of conscious –preconscious, pre-attentive – focal-attentive, or automatic processes – controlled processes dichotomies. They name the same distinction, in which System 1 consists of processes occurring quickly and effortlessly in parallel outside awareness; System 2 consists of processes occurring slowly and effortfully in sequentialawareness, which in this context refers to the contents of working memory rather than raw experience and accompanies System 2 activity.
To integrate Systems 1 and 2 with construal-level theory, we note that System 2—the conscious part of our minds—can perform any of three routines in making a decision about taking some action, such as whether to vote in an election, a good example not just for timeliness but also for linkages to our main concern with morality: voting is a clear example of an action without tangible benefit. The potential voter might:
Case 1. Make a conscious decision to vote based on applying the principle that citizens owe a duty to vote in elections.
Case 2. Decide to be open to the candidates’ substantive positions and vote only if either candidate seems worthy of support.
Case 3. Experience a change of mind between 1 and 2.
The preceding were examples of the three routines System 2 can perform:
Case 1. Make the choice.
Case 2. “Program” System 1 to make the choice based on automatic criteria that don’t require sequential thinking.
Case 3. Interrupt System 1 in the face of anomalies.
When System 2 initiates action, whether it retains the power to decide or passes to System 1 is the difference between concrete and abstract construal. The second routine is key to understanding how Systems 1 and 2 work to produce the effects construal-level theory predicts. Keep in mind that the unconscious, automatic System 1 includes not just hardwired patterns but also skilled habits. Meanwhile, System 2 is notoriously “lazy,” unwilling to interrupt System 1, as in Case 3, but despite the perennial biases that plague system 1, resulting from letting System 1 have its way, the highest levels of expertise also occur in System 1.
A delegate System 1 operates with potentially complex holistic patterns typifying far cognition. This pattern is far because we offload distant matter to System 1 but exercise sequential control under System 2 as immediacy looms—although there are many exceptions. It is critical to distinguish far cognition from the lazy failure of System 2 to perform properly in Case 3. Such failure isn’t specific to mode. Far cognition, System 1 acting as delegate for System 2, is a narrower concept than automatic cognition, but far cognition is automatic cognition. Nearcognition admits no easy cross-classification.
Belief in free will and moral realism undermine our “fast and frugal heuristics”
The two most important recent books on the cognitive psychology of decision and judgment areThinking, Fast and Slow by Daniel Kahneman and Gut Reactions: The Intelligence of the Unconscious by Gerd Gigerenzer, and both insist on the contrast between their positions, although conflicts aren’t obvious. Kahneman explains System 1 biases as due to the mechanisms employed outside the range of evolutionary usefulness; Gigerenzer describes “fast and frugal heuristics” that sometimes misfire to produce biases. Where these half-empty versus half-full positions on heuristics and biases really differ is their overall appraisal of near and far processes, as Gigerenzer is a far thinker and Kahneman a near thinker, and they are both naturally biased for their preferred modes. Far thought shows more confidence in fast-and-frugal heuristics, since it offloads to System 1, whose province is to employ them.
The fast-and-frugal-heuristics way of thinking is particularly useful in understanding the effect of moral realism and free will: they cause System 2 to supplant System 1 in decision-making. When we apply principles of integrity to regulate our conduct, sometimes we do better in far mode, where System 2 offloads the task of determining compliance to System 1. To the contrary, if you have a principle of integrity that includes an absolute obligation to vote, you act as in Case 1: on a conscious decision. But principles of integrity do not really take this absolute form, an illusion begotten by moral realism. A principle of integrity flexible enough for actual use might favor voting (based, say, on a general principle embracing an obligation to perform duties) but disfavor it for “lowering the bar” when there’s only a choice between the lesser of evils. To practice the art of objectively applying these principles depends on your honest appraisal of the strength of your commitment to each virtue. System 2 is incapable of this feat; when it can be accomplished, it’s due to System 1’s automatic skills, operating unconsciously.Principles of integrity are applied more accurately in far-mode than near-mode. [Hat Tip to Overcoming Bias for these convenient phrases.]
But belief in moral realism and free will impel moral actors to apply their principles in near-mode. Objective morality and moral realism imply that compliance with morality results from freely willed acts. I’m not going to defend this premise thoroughly here, but this thought experiment might carry some persuasive weight. Read the following in near mode, and introspect your emotions:
Sexual predator Jerry Sandusky will serve his time in a minimal security prison, where he’s allowed groups of visitors five days a week.
Some readers will experience a sense of outrage. Then remind yourself: There’s no free will.If you believe the reminder, your outrage will subside; if you’ve long been a convinced and consistent determinist, you might not need to remind yourself. Morality inculpates based on acts of free will: morality and free will are inseparable.
A point I must emphasize because of its novelty: it’s System 1 that ordinarily determines what you want. System 2 doesn’t ordinarily deliberate about the subject directly; it deliberates about relevant facts, but in the end, you can only intuit your volition. You can’t deduce it.
What a belief in moral realism and free will do is nothing less than change the architecture of decision-making. When we practice principles of integrity and internalize them, they and nonmoral considerations co-determine our System 1 judgments, whereas according to moral realism and free will, moral good is the product of conscious free choice, so System 2 contrastsits moral opinion to System 1’s intuition, for which System 2 compensates—and usually overcompensates. The voter had to weigh the imperatives of the duty to vote and the duty to avoid “lowering the bar” when both candidates are ideologically and programmatically distasteful. System 2 can prime and program System 1 by studying the issues, but the multifaceted decision is itself best made by System 1. What happens when System 2 tries to decide these propositions? System 2 makes the qualitative judgment that System 1 is biased one way or the other and corrects System 1. This will implicate the overcompensation bias, in which conscious attempts to counteract biases usually overcorrect. A voter who thinks correction is needed for a bias toward shirking duty will vote when not really wanting to, all things considered. A voter biased toward "lowering the bar" will be excessively purist. Whatever standard the voter uses will be taken too far.
Belief in moral realism and free will biases practical reasoning
This essay presents the third of three ways that belief in objective morality and free will can cause people to do what they don’t want to do:
- It retards people in adaptively changing their principles of integrity.
- It prevents people from questioning their so-called foundations.
- It systematically exaggerates the compellingness of moral claims.
Some will be tempted to think that the third either is contrary to experience or is socially desirable. It’s neither. In moralism, an exaggerated subjective sense of duty and excessive sense of guilt co-exist with unresponsiveness to morality’s practical demands.
The raw-experience dogma: Dissolving the “qualia” problem
1. Defining the problem: The inverted spectrum
Philosophy has been called a preoccupation with the questions entertained by adolescents, and one adolescent favorite concerns our knowledge of other persons’ “private experience” (raw experience or qualia). A philosophers’ version is the “inverted spectrum”: how do I know you see “red” rather than “blue” when you see this red print? How could we tell when we each link the same terms to the same outward descriptions? We each will say “red” when we see the print, even if you really see “blue.”
The intuition that allows us to be different this way is the intuition of raw experience (or of qualia). Philosophers of mind have devoted considerable attention to reconciling the intuition that raw experience exists with the intuition that inverted-spectrum indeterminacy has unacceptable dualist implications making the mental realm publicly unobservable, but it’s time for nihilism about qualia, whose claim to exist rests solely on the strength of a prejudice.
A. Attempted solutions to the inverted spectrum.
One account would have us examine which parts of the brain are activated by each perception, but then we rely on an unverifiable correlation between brain structures and “private experience.” With only a single example of private experience—our own—we have no basis for knowing what makes private experience the same or different between persons.
A subtler response to the inverted spectrum is that red and blue as experiences are distinct because red looks “red” due to its being constituted by certain responses, such as affect. Red makes you alert and tense; blue, tranquil or maybe sad. What we call the experience of red, on this account, just is the sense of alertness, and other manifestations. The hope is that identical observable responses to appropriate wavelengths might explain qualitative redness. Then, we could discover we experience blue when others experience red by finding that we idiosyncratically become tranquil instead of alert when exposed to the long wavelengths constituting physical red. This complication doesn’t remove the radical uncertainty about experiential descriptions. Emotion only seems more capable than cognition of explaining raw experience because emotional events are memorable. The affect theory doesn't answer how an emotional reaction can constitute a raw subjective experience.
B. The “substitution bias” of solving the “easy problem of consciousness” instead of the “hard problem.”
As in those examples, attempts at analyzing raw experience commonly appeal to the substitution process that psychologist Daniel Kahneman discovered in many cognitive fallacies. Substitution is the unthoughtful replacement of an easy for a related hard question. In the philosophy of mind, the distinct questions are actually termed the “easy problem of consciousness” and the “hard problem of consciousness,” and errors regarding consciousness typically are due to substituting the “easy problem” for the “hard,” where the easy problem is to explain some function that typically accompanies “awareness.” The philosopher might substitute knowledge of one’s own brain processes for raw experience; or, as in the previous example, experience’s neural accompaniments or its affective accompaniments. Avoiding the “substitution bias” is particularly hard when dealing with raw awareness, an unarticulated intuition; articulating it is a present purpose.
2. The false intuition of direct awareness
A. Our sense that the existence of raw experience is self-evident doesn’t show that it is true.
The theory that direct awareness reveals raw experience has long been almost sacrosanct in philosophy. According to the British Empiricists, direct experience consists of sense data and forms the indubitable basis of all synthetic knowledge. For Continental Rationalist Descartes, too, my direct experience—“I think”—indubitably proves my existence.
We do have a strong intuition that we have raw experience, the substance of direct awareness, but we have other strong intuitions, some turn out true and others false. We have an intuition that space is necessarily flat, an intuition proven false only with non-Euclidean geometries in the 19th century. We have an intuition that every event has a cause, which determinists believe but indeterminists deny. Sequestered intuitions aren’t knowledge.
B. Experience can’t reveal the error in the intuition that raw experience exists.
To correct wayward intuitions, we ordinarily test them against each other. A simple perceptual illusion illustrates: the popular Muller-Lyer illusion, where arrowheads on a line make it appear shorter than an identical line with the arrowheads reversed. Invoking the more credible intuition that measuring the lines finds their real length convinces us of the intuitive error that the lines are unequal. In contrast, we have no means to check the truth of the belief in raw experience; it simply seems self-evident, but it might seem equally self-evident if it were false.
C. We can’t capture the ineffable core of raw experience with language because there’s really nothing there.
One task in philosophy is articulating the intuitions implicit in our thinking, and sometimes rejecting the intuition should result from concluding it employs concepts illogically. What shows the intuition of raw experience is incoherent (self-contradictory or vacuous) is that the terms we use to describe raw experience are limited to the terms for its referents; we have no terms to describe the experience as such, but rather, we describe qualia by applying terms denoting the ordinary cause of the supposed raw experience. The simplest explanation for the absence of a vocabulary to describe the qualitative properties of raw experience is that they don’t exist: a process without properties is conceptually vacuous.
D. We believe raw experience exists without detecting it.
One error in thinking about the existence of raw experience comes from confusing perception with belief, which is conceptually distinct. When people universally report that qualia “seem” to exist, they are only reporting their beliefs—despite their sense of certainty. Where “perception” is defined as a nervous system’s extraction of a sensory-array’s features, people can’t report their perceptions except through beliefs the perceptions sometimes engender: I can’t tell you my perceptions except by relating my beliefs about them. This conceptual truth is illustrated by the phenomenon of blindsight, a condition in patients report complete blindness yet, by discriminating external objects, demonstrate that they can perceive them. Blindsighted patients can report only according to their beliefs, and they perceive more than they believe and report that they perceive. Qualia nihilism analyzes the intuition of raw experience as perceiving less than you believe and report you perceive, the reverse of blindsight.
3. The conceptual economy of qualia nihilism pays off in philosophical progress
Eliminating raw experience from ontology produces conceptual economy. A summary of its conceptual advantages:
A. Qualia nihilism resolves an intractable problem for materialism: physical concepts are dispositional, whereas raw experiences concern properties that seem, instead, to pertain to noncausal essences. If raw experience was coherent, we could hope for a scientific insight, although no one has been able to define the general character of such an explanation. Removing a fundamental scientific mystery is a conceptual gain.
B. Qualia nihilism resolves the private-language problem. There seems to be no possible language that uses nonpublic concepts. Eliminating raw experience allows explaining the absence of a private language by the nonexistence of any private referents.
C. Qualia nihilism offers a compelling diagnosis of where important skeptical arguments regarding the possibility of knowledge go wrong. The arguments—George Berkeley’s are their prototype—reason that sense data, being indubitable intuitions of direct experience, are the source of our knowledge, which must, in consequence, be about raw experience rather than the “external world.” If you accept the existence of raw experience, the argument is notoriously difficult to undermine logically because concepts of “raw experience” truly can’t be analogized to any concepts applying to the external world. Eliminating raw experience provides an effective demolition; rather than the other way around, our belief in raw experience depends on our knowledge of the external world, which is the source of the concepts we apply to fabricate qualia.
4. Relying on the brute force of an intuition is rationally specious.
Against these considerations, the only argument for retaining raw experience in our ontology is the sheer strength of everyone’s belief in its existence. How much weight should we attach to a strong belief whose validity we can't check? None. Beliefs ordinarily earn a presumption of truth from the absence of empirical challenge, but when empirical challenge is impossible in principle, the belief deserves no confidence.
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