Category: Philosophy


The original paper: download

Summary for each part:

I: The mathematical solution to constructing a rational economic order is to achieve the same marginal rates of substitution between any two goods. This is not realistic, because it relies on the assumption of complete command of knowledge in a central single mind, while in the real society the knowledge is dispersed among separate individuals. This causes misconception about the nature of economic problem, which is essentially how to efficiently allocate resources by utilizing individual knowledge, rather than utilizing it in its integrated form.

 

II: Utilizing knowledge, which involves communicating it to the planner and among different individuals, is important in designing an efficient economic system, which can be in the form of central planning, completion and monopoly. Which kind of the economic systems is more efficient depends on whether the existing knowledge can be fuller used.

 

III: Different kinds of knowledge define different positions of the economic systems. The prominent position of central planning in public imagination is due to the exaggeration of the importance of scientific knowledge. Selecting a group of experts to command such knowledge is actually only a fraction of the wider problem. The knowledge of the particular circumstances, which is not always available, is equivalently socially useful, although it is sometimes regarded as disreputable if one gains advantage by using this knowledge.

 

IV: Economic problems arise as a result of change of circumstances, making the knowledge of the particular place and time important in making economic decisions. This sort of knowledge, however, cannot be statistically calculated therefore cannot be conveyed to the central authority who make plans based on statistical information.

 

V: Decentralization is necessary in solving economic problems, because adaptions to changes in economic systems require the knowledge of the particular circumstances to be promptly used. A price system helps coordinate separate actions for individuals whose visions in their own fields sufficiently overlap through intermediaries, thus brings about the outcome that might have been achieved by central planning with complete information.

 

VI: The price system acts as a mechanism that communicates only the most essential information for individuals to take the right action, and it extends the span of resources utilization beyond the control of any single mind. Like language, this is one of the formations upon which the foundation of civilization is built.

 

VII: The dispute about the indispensability of price system is not purely a political dissent, but also intellectual and methodological differences. Schumpeter’s argument that valuation of factors of production is implied in the valuation of consumers’ goods is untrue, because it also depends on the supply of the factors. His argument disregards the essential fact of imperfection of knowledge in the real world. Thus the solution to the economic problem has to be processed by interactions of people who possess their partial knowledge.

 

In sum, the key take-away ideas are:

 

In the real world, knowledge is spread throughout the society. The knowledge of particular circumstances of place and time is not always public available, but it is useful in making economic decisions. This is an essential feature of the real world’s economic problem, which makes central planning inefficient and infeasible. That’s because central planning requires a single mind processing all the knowledge. Decentralization overcomes this problem via a price system in which individuals with their own partial knowledge coordinate with each other and utilize resources that are beyond the control of any one person.

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In this paper, I will describe the psychological continuity theory of personal identity and I will show how it is assumed in the film Being John Malkovich. Then I will explain the problems of the theory.

The problem for personal identity is about what makes a personal numerically identical from one time to the next. Before going into further discussion, I will first clarify the definition of “numerical identity”, which is useful in describing the theory of personal identity. The sufficient and necessary condition for numerical identity is the sharing of all the properties including the spatial-temporal ones. Therefore, if a is numerically identical to b, then there is only one thing which it can be called either “a” or “b”. For example, Clark Kent is numerically identical with Superman in the sense that there is only one person. Alternatively, a and b are qualitatively identical if and only if a and b have all the properties in common except the spatial-temporal ones. For example, two qualitatively identical chairs are made in the same furniture factory on the same production line such that they look exactly the same, but they are two distinct chairs which occupy different spaces at the same time.

The psychological continuity theory of personal identity is that a person at one time is the same the person at another time if and only if the person has continuous psychological states including memory, consciousness and personality. In other words, self is numerically identical to the psychological states. Therefore, by definition of numerical identity, when we are referring to the self of a person, we are actually referring to his or her psychological states. Since psychological states persist through time and have a casual influence on future psychological states, one’s psychological continuity is essential in identifying a person over different periods of time. One representative feature of psychological states is memory. If person A can remember the earlier thoughts and perceptions of person B, then person A is identical to person B. My following discussions are mainly focused on this memory aspect of psychological states.

The film Being John Malkovich implies psychological continuity theory of personal identity. For example, as Craig Schwartz enters the portal, he experiences the sensory stream of John Malkovich and later gradually learns how to puppeteer John Malkovich’s body, but several scenes of the film suggest Craig remains to exist as Craig after he enters the portal, and never succeeds in being John Malkovich, even when he can completely control John’s body. For example, after Craig enters the portal, he has prior memories of being Craig, but not memories of being John Malkovich. Furthermore, the film shows clear discontinuities in the psychological characteristics that separate the John Malkovich prior to Craig’s entry from the John Malkovich after Craig’s entry. In addition, after Craig goes out of the portal, he is the same person as before because he remembers being Craig. The film also shows Dr. Lester and his friends can prolong their lives by staying in John Malkovich’s body, so Dr. Lester continues to exist because he consciously remembers being Dr. Lester. This is consistent with the psychological continuity theory as the change or cease of body is assumed to be independent from personal identity.

However, there are several problems in the psychological continuity theory. One of the philosophical problems is the paradox when dealing with breaks in the psychological states, which can be escalated into more serious moral issues. For example, suppose at time period t person A commits a crime, and at time t’ he gets amnesia such that he cannot remember anything he did before and his personality is totally changed. Because there exists obvious discontinuity in his memory, the theory implies the A in t’ and the A in t are not identical, which may contradicts with someone’s intuition. Furthermore, suppose later he is accused and has to go to court, it is unclear whether he should be responsible and get punishment for the crime he commits at time t, because it is controversial whether we still have the same person, as A now behaves completely differently as he is in t, and he could not remember the crime he committed.

The second problem is that memory is not perfectly reliable as it can be altered over time, and we cannot distinguish between the genuine and non-genuine memories. In order to correctly identify a person by his continuity of memory, that person’s memory should be genuine, reflecting his true psychological states. The genuineness of memory requires a casual mechanism such that previous perception must have occurred and is causally responsible for the current memory, and the current memory must also accurately represent the previous perception. However, the criterion is sometimes hard to achieve as the perception and memory can be easily swayed by suggestions or other interventions. Moreover, since one has privileged access to his mind, we cannot reliably tell whether someone’s memory is genuine. In this sense, memory based psychology continuity cannot server as a perfect link for personal identity. One possible solution to this might be to identify the casual link between the different pieces of memory across time, but it is still difficult to implement as it requires dividing the time periods into very small pieces in order to closely track the casual events that cause memory change alone the time period.

Furthermore, the fading memory can cause paradox of the identities for different periods of time. That is, we cannot remember everything we have done, and what we can remember also changes over time, so using the time-varying memory to identify a person would contradict with the transitivity of identity. For example, suppose an old man has forgotten the time when he was a child when he was spanked for knocking over the milk, but he can remember when he was a college student and awarded a scholarship for academic excellence, so by the psychological continuity theory the old man is the same person as the college student. But now suppose that when the man received the scholarship, he could remember being spanked for knocking over the milk as a boy. This means that the person who received the scholarship is the same person who was spanked. Transitivity of identity tells us if A is identical to B, B is identical to C, then A is identical to C. Therefore, by transitivity, the old man is the same person who was spanked, contradicting to the theory due to fact that the old man does not remember being the boy who was spanked.

To conclude, the film Being John Malkovich assumes the psychological continuity theory of personal identity, which uses long-standing psychological characteristics to identify person. However, this theory has several problems, and they mainly result from the time-varying property of psychological states and their presence of discontinuities, as well as the lack of effective method to detect the genuineness of memory.

 

In this paper, I will explain why Turing proposes an “imitation game” as a reformulation of the question of “Can computers think”. However, I will argue that passing the “Turing test” neither constitutes a sufficient nor a necessary condition for answering this question. Based on Searle’s argument, I will explain that judging whether a computer has an original intentional mental status is a better test. Finally, I will show although Searle does not provide a “test” to measure intentionality, he in fact answers the question that computers cannot think.

By asking “Can computers pass the Turing test”, Turing innovatively converts a difficult theoretical question to an operational question that is open to experimental research. Directly answering “Can computers think?” is hard, given the ambiguous definition of “thinking” and “computer”. A clear definition of “thinking” and “computer” is the premise of judging whether computers can think. According to Turing, the definitions might be framed to reflect the common understanding among people and the normal use of the words. Therefore, a statistical survey is necessary to be conducted in seeking the meaning and answer to the question, but it is absurd since it draws answers from imprecise public opinions rather than scientific studies. Instead of attempting a definition that satisfies everyone, Turing replaces the question by another, which is unambiguous, and operationalizable.

Turing proposes an “imitation game”, which we call “Turing test” today. According to Turing, passing the test can be equivalently considered as having the capacity of thinking. The test involves a human interrogator and two respondents. One respondent is a computer and the other is human. The interrogator could use a keyboard and screen to engage in a natural language conversation with the unseen respondents. After many trials, if the interrogator cannot reliably tell the computer from the human, the computer is said to have passed the Turing test.

However, I will argue that even if a computer passes the Turing test, it does not indicate the computer can think. The Chinese room experiment proposed by John Searle forms a counterexample. The person in the experiment mimics a computer program, and the whole system with Chinese symbols both as input and output mimic a human being that engages in a Chinese conversation with a real human. In the experiment, a monolingual English speaker isolated in a room is given English instructions for manipulating Chinese symbols, while he does not understand or even cannot recognize Chinese. Someone outside the room hands in a set of Chinese symbols. The person applies the rules, writes down a different set of Chinese symbols as specified by the rules, and hands the result to a person outside the room. It is logically possible that the person outside the room is convinced that he/she is interacting with a real Chinese speaker. Therefore, if we let a computer that can execute the same rules replace the person, it also can logically pass the Turing test. However, Searle argues that thinking requires understanding. Since manipulating Chinese symbols following formal rules is not sufficient for the person to understand Chinese, it is not sufficient for a computer to understand Chinese, either. Therefore, a computer passing the Turing test does not sufficiently implies it can think.

According to Searle, understanding is a criterion for thinking, and “understanding” implies the possession of original intentional mental states and the truth of these states. Searle defines that “intentional mental states have propositional content that are directed at or about objects and states of affairs in the world.” In other words, it is about something. For example, the belief that dog is human’s friend is about dog, the desire to have a cat is about cat, so they are intentional states; while sensations like pains and itches are not about anything thus are not intentional states. Therefore, testing whether a computer has original intentional mental states is a better way to judge whether computers can think. However, how do we conduct such a test is an open question, given that intentionality is introspective, that is, one only privately knows he/she has intentionality, but cannot access others’ minds. If we evaluate others by interacting with them and observing their behaviors, then we again run into the Turing test.

Although Searle does not provide a test of whether computers can think, he indeed disposes of the question. He rejects that computers can think, as he disagrees that mind to brain can be duplicated by program/software to hardware. First, he argues that programs can have realizations but no understanding, because programs have no intentionality. In the Chinese room, the English speaker can memorize the rules and Chinese symbols, but memorizing won’t enhance his understanding of Chinese. Likewise, a computer can mimic human beings, but “mimicking” is not “duplicating”, as it only mechanically execute the programs that result in human-like behaviors or languages, but it does not involves any understanding of the corresponding meanings. Second, Searle shows that passing the Turing test is neither a sufficient nor a necessary condition for understanding/thinking. The Turing test requires using a computer program. As it is shown, programs do not have original intentionality, but understanding requires intentionality, so a program that lets the computer pass the Turing test does not indicate the computer can think. On the other hand, it is possible that original intentionality goes through other channels other than programs. Therefore, even if a computer can think, it is not necessary that it has to pass the Turing test.

To conclude, due to technology in-advance and ambiguous definition of the terms “thinking” and “computers”, Turing reformulates the question “Can computers think?” to “Can computers pass the Turing test?” However, this reformulation still does not answer whether computers can think, since passing the Turing test is not necessarily related to understanding, which requires intentional mental states. A test designed to detect original intentionality can essentially answer this question. However, this is empirically difficult as intentional mental states can only be privately experienced and one cannot have access to others’ mental states. Furthermore, although Searle does not provide such a test, he answers the question which denies that computers can think.

Outline:

  • The Paradox of Change
  • Chrysippus’ Paradox
  • The Paradox of 101 Dalmatians
  • The Paradox of Constitution
  • The Ship of Theseus Paradox

Summary:

  • Some Definitions
    • Paradoxes: arguments from apparently undeniable premises to obviously unacceptable conclusions.
    • LL: x=y=>[f(x)->f(y)].
    • NI: if a=b is true, then it is necessarily true.
    • ND: if a!=b is true, then it is necessarily true.
  • The Paradox of Change
    • What is the paradox?
      • Photo A: old dog with a gray muzzle
      • Photo B: young dog without a gray muzzle.
      • A and B are photographs of the same dog Oscar.
      • Dog in B has a property that the dog in A lacks => A and B are not photos of the same dog. Contradiction.
  • What are the solutions?
    • (1) Properties are relations to times: t, and t’.
    • (2) Extend the object in time as well as space: photos capture distinct temporal parts.
  • What are the objections?
    • To (1): Properties are complicated relations, not only relations to times.
    • To (2): Objects are not “wholly present” at any given time.
  • Chrysippus’ Paradox
    • What is the paradox?
      • In time t’, Oscar loses tail.
      • In time t<t’, Oscar-minus (the whole dog minus his tail) and Oscar are distinct.
      • In time t’, by ND, Oscar and Oscar-minus are distinct, since Oscar has a property at t’ that Oscar-minus lacks. Contradiction.
  • What are the 4 responses?
    • Deny there are such things as Oscar-minus.
    • The parts of an object are essential.
    • Objects of different kinds can occupy the same space at the same time, but objects of the same kind cannot.
    • Temporal parts of distinct objects can occupy the same space at the same time.
  • The Paradox of 101 Dalmatians
    • What is the paradox?
      • If Oscar-minus is a dog, then Oscar minus a hair is also a dog.
      • There are at least 101 dogs (actually many more).
  • What are the responses/solutions?
    • Maximality principle: no proper part of a dog is a dog.
    • Lewis: deny that the “many” are Dalmatians or deny that Dalmatians are many.
  • The Paradox of Constitution
    • What is the paradox?
      • Day 1: statue s1 is made from clay c, so c is identical to s1.
      • Day 2: statue s2 is made from clay c, so c is identical to s2.
      • Day 3: a part of s2 is replaced by a new piece of clay, c’.
      • s1 is identical to c on day 1, s2 is identical to c on day 2 => s1 is identical to s2 =>  s2 exists on day 2. Contradiction.
      • s2 is identical to c on day 3 => c is c’, contradicting NI.
  • What are the solutions?
    • c and  are not identical:
      • c exists prior to the existence of .
      • s1 possesses the property of being destroyed while c does not.
      •  possesses the property of being squeezed into a ball in the future while does not.
      • Frame the issue in terms of c and s that (partially) coincide throughout their entire existence.
      • c is a temporally extended object whose day 1 stage is identical to  and whose day 2 stage is identical to s2 => since day 1 and day 2 are different, s1 and s2 are not NI.
      • Counterpart theory: different concepts are associated with different counterpart relations and hence with different criteria of trans-world identity.
  • The Ship of Theseus Paradox
    • What is the paradox?
      • A wooden ship restored by replacing all its planks and beams.
      • Does the ship remain same?
  • What are the views?
    • The restored ship appears to qualify equally to be the original, but not the same ship.
      • Hobbes.
      • Wiggins (1967) and Parfit (1984): brain duplication scenarios.
      • The restored ship is identical to the original one, since it exhibits a greater degree of spatio-temporal continuity with the original (Wiggins 1967).
        • Problem of intuition: identity is preserved by spatio-temporal continuity v.s. identity is preserved in the process of dismantlement and reassembly.
      • The restored ship is not identical to the original one.
        • Kripke (1980): Table T is made out of wood H; In world w, T is made out of H’; In world w’, T is made out of H, and T’ is made out of H’. Since T and T’ are not identical in w’, table made out of H’ in w is not T.
        • Analogy: In actual world: original ship O, and remodeled ship S; In world w, S’ is built out of the same parts of S. Since S’ and O are different in w, S is not identical to O. (Assumption: S and S’ are the same ship.)
        • Additional paradox from Kripkean argument: S eventuates from O by replacing one part of O one day at a time. By transitivity of identity, O and S are the same.
          • Kripke reply: whether O could change in S is irrelevant.
  • Connections between two issues: the ship of Theseus problem & the question of the necessity of origin.
    • Modified ship of Theseus problem:
      • Two ships: O and O’, and O’ never sets sail; Planks are removed from O’ and used to replace corresponding planks of O, resulting in S. Do O and O’ have equal claim to be S?
      • Criticisms:
        • Conflict with the common sense principle (1) that the material of an object can be totally replenished or replaced without affecting its identity (Salmon 1979).
        • Conflict with the additional common sense principle (2) that replacement by a single part or small portion preserves identity.
          • Counter example of (2) :
            • Two exactly similar sandals A and B;
            • A is brand new and B is worn out;
            • Parts of A and B are exchanged => A’ and B’;
            • By ND, A and A’ are distinct, and B and B’ are distinct;
            • Contradicting with intuition.

In this essay, I will explain how Darwin’s theory of natural selection has effectively changed people’s conception of the biological nature of reality. Firstly, I will show that it removes the purpose from the world by considering the appearance of design as a mindless mechanical causation, which denies the existence of an intelligent designer and thus demystifies the adaptation of nature. Secondly, I will explain how it changes the view of humanity progress by considering the evolutionary progress in the local sense and adaptability as an environmental contingent trait.

The biological nature is composed of various organisms, and each of them has complex functions which seem to be designed to have the purpose of fitting organisms well into the environment, which we call “adaptation” today. Before Darwin, the explanation of this diversity, complexity and appearance of purpose of design in nature was dominated by teleology. One representative view is Paley’s argument from design. This argument appeals these features in the realm of living things to the existence of an omnipotent, omniscient and benevolent divine designer, namely the theistic God, who implements the design. Darwin’s theory of natural selection also tries to explain the same set of data with all three of these features, but in a non-teleological view.

Firstly, one of the fundamental assumptions of natural selection is that the appearance of design is produced by a purely causal, mechanical and non-intentional process of random variation combined with passive environmental filtration.

In particular, in contrast to Paley’s argument that the novel traits are directed by a designer, Darwin proposes that they occur at random. In Darwin’s view, the variations in every hereditary trait of an organism are not causally driven by any needs, benefits or advantage or with any foresights or intentions, but rather a random event. In this sense, the appearance of novel traits is not directed by a designer to make the organism better fitted in the environment.

Moreover, Argument from Design implies that the environment positively generates the best adapted traits, while Darwin denies any purpose in the environment. Natural selection is a passive process such that the environment passively filters traits that are mostly maladapted. As organisms reproduce, the genes of these “worst” traits are unlikely to be preserved in the next generation, so their proportion in the population is shrinking. To the contrary, the other “better” traits pass on to the next generations and gradually dominate the population. For example, it is not the arctic environment that picks the white bear, but the bears of other colors are not likely to survive since they cannot blend in white environment.

Finally, the Argument from Design contradicts with the fact of the presence of imperfect adaptations, which, however, can be nicely explained by random variation and passive filtration of natural selection. For example, our eye is not perfect as it has a blind spot in which the optic nerve attaches to the back of the retina, resulting in its insensitivity to light. According to Darwin’s theory, many kinds of adaptions have to occur for survival and reproduction, and the solutions to the adaption have to be “quick and dirty” to prevent extinction during the struggle with the environment. Since the “solutions” only emerge by random chance, they might not be the best ones, but the ones that occur first to be just good enough to survive are selected for. Once a “quick and dirty” solution works in the environment, it is inherited by subsequent generations and becomes hard to get rid of. On the other hand, if there is an omnipotent, omniscient and benevolent designer as the teleogists suggest, then this kind of adaptations should not have been existent.

Secondly, natural selection challenges the Argument from Design by taking away “purpose” from the world, so man is no longer considered to be designed to be perfect. Therefore, the worldview of humanity as well as the evolutionary progress is altered, as natural selection does not rank the level of evolution by the appearance of complexity or the superiority in a given environment.

Before Darwin, human beings are considered to represent the highest achievement of evolutionary progression as they are at the top of the organismal hierarchy. Darwin rejects this view. He never accepts the notion of higher and lower species, or ones that have seen more progress versus ones that have seen less, although Darwin’s theory accepts the views about progress which included evolutionary speculations about the upward progress of living things from primordial beginnings.

Moreover, Argument from Design considers the evolution of species is directed by a divine designer, which implies the process of adaptation is forever progressing. However, natural selection considers the progress in a local sense. In Darwin’s view, there is no long-term, locked-in progress in evolution. The environment can change, leading the best adaptation to maladaptation, or even extinction. For example, the dinosaurs were the dominant terrestrial vertebrates on the earth for 135 million years, but later the radical alteration of environment led to the extinction of most dinosaur groups. In addition, adaptation makes some traits well-suited for a particular environment, but these traits could be a disadvantage if put in another environment. For example, the polar bear with its white coat shows its high adaptability in the Arctic Pole, but in the forest, its white color would contrast sharply with the environment, which would make them an inefficient predator and easier to be shot by hunters.

To conclude, Darwin’s theory denies a teleological explanation of the complexity, diversity and appearance of purpose of the living world, and provides a causal mechanical explanation. It proposes that the appearance of purpose in nature is not designed by some divine intelligence, and human beings are not “pre-programmed” by God to progress, or to be the best of all creatures, as it considers adaptability as an environmentally contingent trait.

In this paper, I will first explain the difference between a deductive argument and an inductive argument. I will compare two arguments which both explain the existence of theistic God, the cosmological argument and the argument from design. I will show that the former is deductive; while the latter is inductive. However, I will argue that the cosmological argument also rests on inductive reasoning.

The difference between a deductive argument and an inductive argument rests on whether the argument has a truth preserving logical structure and whether it creates new knowledge.

A deductively valid argument has a truth preserving logical structure, in other words, if its premises are true, its conclusion must be true. For example:

  1. All men are moral (premise);
  2. Socrates is a man (premise);
  3. Socrates is moral (conclusion).

However, a deductively invalid argument is an argument that its premises do not form the logical necessity to give its conclusion. For example:

  1. Poison can kill people (premise);
  2. Daniel was killed (premise);
  3. Daniel had taken poison (conclusion).

This argument is invalid, as experience tells us that many reasons can cause death, so the conclusion cannot be deduced from the premises.

Furthermore, deductive reasoning does not grant new knowledge, as it draws specific conclusion based on the prior knowledge of its premises, of which the conclusion is merely a subset of existing knowledge.

The cosmological argument is a deductive argument. It states that “(1) every being is a dependent being or an independent being, and (2) not every being can be a dependent being, therefore, (3) there exists a self-existent being”, which can be represented by the following formal logical  structure:

  1. P or Q (premise);
  2. P is not true (premise);
  3. Q holds (conclusion).

We can verify its deductive validity via an intuitive example: an integer is either even or odd, so if an integer is not odd, then it must be even. The conclusion of this argument must be true if the two premises are true.

To the contrary, an inductive argument does not guarantee the truth of its conclusion. It draws general inferences from specific instances, and the truth of its premises provides a reason for accepting the conclusion with some level of probability. For example:

  1. The sun has risen every day in the past (premise);
  2. The sun will rise in the future (conclusion).

Although there is an infinitesimal possibility that the sun could explode tomorrow, this is unlikely to happen by our current knowledge, so the conclusion has high probability to be true.

Since inductive argument give generalizations of current knowledge, the generalized conclusion can then be applied to other new specific conditions with some confidence level. In this way, the inductive argument makes prediction and thus produces new knowledge.

The argument from design rests on inductive reasoning. It proceeds by Inference to the Best Explanation from the complexity, diversity and the appearance of purposes of design in the realm of living things to the existence of a divine designer, namely the theistic God. It is called “best explanation” because alternative explanations such as magic and randomness seem far less plausible by intuition. For example, the human body is a complex biological machine such that each system functions appropriately for a purpose and harmonious cooperate to carry out vital activities, which is unlikely to be caused by some random or magic power. Therefore, among all the alternatives the argument from design is its only probable explanation.

I will argue that cosmological argument (CA) indeed rests on inductive reasoning, because its premises rest on the Principle of Sufficient Reason (PSR), and PSR is an inductive argument.

First, CA(1) rests on PSRa. CA(1) states that “every being is a dependent being or an independent being”, with “dependence” defined as “can be caused by others or composed of others”, and “independence” defined as “can be caused by itself or composed of itself”. In other words, CA(1) proposes that every being can be explained by its causes or its components, and the cause or component can either be some other being or itself. This is based on PSRa. PSRa states that “there must be an explanation of the existence of any being”, which denies the existence of any unexplained being, implying every being must be either explained by others or explained by itself.

Second, CA(2) rests on PSRb. PSRb states that “there must be an explanation of any positive fact whatever”, which requires an explanation of the existence of the collection of all the dependent beings. The collection is either explained by itself, for which implies it is independent, or explained by others, for which the “other” being must be independent. Therefore, PSRb necessitates the existence of at least one independent being, so CA(2) holds.

Finally, PSR is inductive. It comes from the following reasoning:

  1. We observe many beings/facts have had an explanation in the past (premise).
  2. Therefore, every being/fact has and will have an explanation (conclusion).

The conclusion, however, does not exclude the possibility, albeit small, of no explanation. For example, the movement of sub-atomic particles whose cause has not fully explored by scientists might not have explanations. In sum, PSR which cosmological argument rests on is inductive.