Seungbae Park

Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an object that changes its shape from a triangle to a circle, and then back to a triangle with every second.

Nickles (2017) advocates scientific antirealism by appealing to the pessimistic induction over scientific theories, the illusion hypothesis (Quoidbach, Gilbert, and Wilson, 2013), and Darwin’s evolutionary theory. He rejects Putnam’s (1975: 73) no-miracles argument on the grounds that it uses inference to the best explanation. I object that both the illusion hypothesis and evolutionary theory clash with the pessimistic induction and with his negative attitude towards inference to the best explanation. I also argue that Nickles’s positive philosophical theories are subject to Park’s (2017a) pessimistic induction over antirealists.

Selectivism holds that some theoretical contents of most present theories will be preserved in future theories. By contrast, optimistic realism holds that most theoretical contents of most present theories will be preserved in future theories. I construct a pessimistic induction over selectivists to undermine selectivism, and an optimistic induction over optimistic realists to support optimistic realism. The former holds that since the selectivists of the early twentieth century were overly cautious about their present theories, those of the early twenty-first century are also overly cautious about their present theories. The latter holds that since the optimistic realists of the early twentieth century were right about their present theories, those of the early twenty-first century are also right about their present theories.

Sample (2015) argues that scientists ought not to believe that their theories are true because they cannot fulfill the epistemic obligation to take the diachronic perspective on their theories. I reply that Sample’s argument imposes an inordinately heavy epistemic obligation on scientists, and that it spells doom not only for scientific theories but also for observational beliefs and philosophical ideas that Samples endorses. I also delineate what I take to be a reasonable epistemic obligation for scientists. In sum, philosophers ought to impose on scientists only an epistemic standard that they are willing to impose on themselves.

Dellsén (2016a) argues that understanding requires neither justification nor belief. I object that ridding understanding of justification and belief comes with the following costs. (i) No claim about the world can be inferred from what we understand. (ii) We run into either Moore’s paradox or certain disconcerting questions. (iii) Understanding does not represent the world. (iv) Understanding cannot take the central place in epistemology. (v) Understanding cannot be invoked to give an account of scientific progress. (vi) It is not clear how misunderstanding arises.

Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how we can have knowledge about an unchanging object.

In contemporary philosophy of science, the no-miracles argument and the pessimistic induction are regarded as the strongest arguments for and against scientific realism, respectively. In this paper, I construct a new argument for scientific realism which I call the anti-induction for scientific realism. It holds that, since past theories were false, present theories are true. I provide an example from the history of science to show that anti-inductions sometimes work in science. The anti-induction for scientific realism has several advantages over the no-miracles argument as a positive argument for scientific realism.

Saatsi’s minimal realism holds that science makes theoretical progress. It is designed to get around the pessimistic induction, to fall between scientific realism and instrumentalism, and to explain the success of scientific theories. I raise the following two objections to it. First, it is not clear whether minimal realism lies between realism and instrumentalism, given that minimal realism does not entail instrumentalism. Second, it is not clear whether minimal realism can explain the success of scientific theories, given that it is doubtful that theoretical progress makes success likely. In addition to raising these two objections, I develop and criticize a new position that truly falls between realism and instrumentalism.

I criticize Kuhn’s (1962/1970) taxonomic incommensurability thesis as follows. (i) His argument for it is neither deductively sound nor inductively correct. (ii) It clashes with his account of scientific development that employs evolutionary theory. (iii) Even if two successive paradigms are taxonomically incommensurable, they have some overlapping theoretical claims, as selectivists point out. (iv) Since scientific revolutions were rare in the recent past, as historical optimists observe, they will also be rare in the future. Where scientific revolution is rare, taxonomic incommensurability is rare, and taxonomic commensurability is common. For these reasons, taxonomic commensurability rather than incommensurability should be advanced as an image of science.

Scientific antirealism, the view that successful theories are empirically adequate, is untenable in light of the problem of unobserved anomalies that since past scientists could not observe the anomalies that caused the replacement of past theories with present theories, present scientists also cannot observe the anomalies that will cause the replacement of present theories with future theories. There are several moves that antirealists would be tempted to make to get around the problem of unobserved anomalies. All of them, however, are problematic.

After decades of intense debate over the old pessimistic induction (Laudan, 1977; Putnam, 1978), it has now become clear that it has at least the following four problems. First, it overlooks the fact that present theories are more successful than past theories. Second, it commits the fallacy of biased statistics. Third, it erroneously groups together past theories from different fields of science. Four, it misses the fact that some theoretical components of past theories were preserved. I argue that these four problems entitle us to construct what I call the grand pessimistic induction that since the old pessimistic induction has infinitely many hidden problems, the new pessimistic induction (Stanford, 2006) also has infinitely many hidden problems.

If scientists embrace scientific realism, they can use a scientific theory to explain and predict observables and unobservables. If, however, they embrace scientific antirealism, they cannot use a scientific theory to explain observables and unobservables, and cannot use a scientific theory to predict unobservables. Given that explanation and prediction are means to make scientific progress, scientists can make more scientific progress, if they embrace scientific realism than if they embrace scientific antirealism.

It is supererogatory to refrain from eating meat, just as it is supererogatory to refrain from driving cars, living in apartments, and wearing makeup, for the welfare of animals. If all animals are equal, and if nonhuman omnivores, such as bears and baboons, are justified in killing the members of other species, such as gazelles and buffaloes, for food, humans are also justified in killing the members of other species, such as cows, pigs, and chickens, for food. In addition, it is fair for humans to eat animals because humans are also eaten by animals.

The no-miracles argument (Putnam, 1975) holds that science is successful because successful theories are (approximately) true. Frost-Arnold (2010) objects that this argument is unacceptable because it generates neither new predictions nor unifications. It is similar to the unacceptable explanation that opium puts people to sleep because it has a dormative virtue. I reply that on close examination, realism explains not only why some theories are successful but also why successful theories exist in current science. Therefore, it unifies the disparate phenomena.

Individual realism asserts that our best scientific theories are (approximately) true. In contrast, selective realism asserts that only the stable posits of our best scientific theories are true. Hence, individual realism recommends that we accept more of what our best scientific theories say about the world than selective realism does. The more scientists believe what their theories say about the world, the more they are motivated to exercise their imaginations and think up new theories and experiments. Therefore, individual realism better fosters scientific creativity than selective realism.

McKitrick (2003) proposes that an object has a disposition if and only if there are a manifestation, the circumstances of the manifestation, a counterfactual true of the object, and an overtly dispositional locution referring to the disposition. A disposition is extrinsic if and only if an object has it, but a perfect duplicate of the object might not have it. I present an alternative definition that an object has a disposition if and only if a counterfactual is true of the object that under a certain condition, it would interact with another object in a certain manner. There are three reasons for thinking that my definition is better than her definition. 1. Ockham’s razor favors my definition over McKitrick’s definition. My definition is consistent, while her definition is not, with Lewis’s and her definitions of intrinsic and extrinsic properties. 3. My definition goes well, while her definition does not, with our intuition that an object has a disposition even in a possible world where there is nothing but that object.

Scientific realists and antirealists believe that a successful scientific theory is true and merely empirically adequate, respectively. In contrast, epistemic reciprocalists believe that realists’ positive theories are true, and that antirealists’ positive theories are merely empirically adequate, treating their target agents as their target agents treat other epistemic agents. Antirealists cannot convince reciprocalists that their positive theories are true, no matter how confident they might be that they are true. In addition, reciprocalists criticize antirealists’ positive theories exactly in the way that antirealists criticize their epistemic colleagues’ theories. Reciprocalism is a better epistemic policy than realism and antirealism in the epistemic battleground in which we strive to be epistemically safe vis-à-vis our epistemic colleagues’ theories and strive to convince our epistemic colleagues that our theories are true.

The pessimistic induction over scientific theories holds that present theories will be overthrown as were past theories. The pessimistic induction over scientists holds that present scientists cannot conceive of future theories just as past scientists could not conceive of present theories. The pessimistic induction over realists :4321–4330, 2013) holds that present realists are wrong about present theories just as past realists were wrong about past theories. The pessimistic induction over antirealist theories :3–21, 2014) holds that the latest antirealist explanation of the success of science :891–901, 2003) has hidden problems just as its eight predecessors did. In this paper, I criticize the pessimistic inductions over scientific theories, scientists, and realists, introduce a pessimistic induction over antirealist theories, and then construct two new pessimistic inductions. One is a pessimistic induction over antirealists according to which the author of the latest antirealist proposal cannot see hidden problems with his proposal just as his antirealist predecessors could not see hidden problems with their proposals. The other is the pessimistic induction over pessimists according to which since past pessimists have been wrong about their present scientific theories from the early twentieth century to the early twenty-first century, future pessimists will also be wrong about their present scientific theories from the early twenty-first century to the early twenty-second century.

Both the pessimistic inductions over scientific theories and over scientists are built upon what I call proportional pessimism: as theories are discarded, the inductive rationale for concluding that the next theories will be discarded grows stronger. I argue that proportional pessimism clashes with the fact that present theories are more successful than past theories, and with the implications of the assumptions that there are finitely and infinitely many unconceived alternatives. Therefore, the two pessimistic inductions collapse along with proportional pessimism.

I attempt to rebut the following standard objections against cultural relativism: 1. It is self-defeating for a cultural relativist to take the principle of tolerance as absolute; 2. There are universal moral rules, contrary to what cultural relativism claims; 3. If cultural relativism were true, Hitler’s genocidal actions would be right, social reformers would be wrong to go against their own culture, moral progress would be impossible, and an atrocious crime could be made moral by forming a culture which approves of it; 4. Cultural relativism is silent about how large a group must be in order to be a culture, and which culture we should follow when we belong to two cultures with conflicting moralities.

According to some psychological studies, women approaching ovulation feel the increased desire to have short-term sexual affairs with “sexy cads” while they are in long-term relations with “good dads.” I argue that this psychological property is a vestige of our evolutionary history. Early hominid females occasionally acquired good genes from top-ranking males while they were in long-term relations with low-ranking males. The Paleolithic living conditions indicate that women with the foregoing psychological trait were more likely to have viable children than those without it. Sexy cads are the descendents of the top-ranking males, and good dads are the descendents of the low-ranking males. Sexy cads and good dads will continue to coexist in the future, developing better methods to detect cheaters and to escape detection.

Van Fraassen (1980) and Winther (2009) claim that we can explain phenomena in terms of scientific theories without believing that they are true. I argue that we ought to believe that they are true in order to use them to explain and understand phenomena. A scientific antirealist who believes that scientific theories are merely empirically adequate cannot use them to explain or to understand phenomena. The mere belief that they are empirically adequate produces neither explanation nor understanding of phenomena. Explanation and understanding are the benefits of science only a scientific realist is entitled to.

Dawes (2013) claims that we ought not to believe but to accept our best scientific theories. To accept them means to employ them as premises in our reasoning with the goal of attaining knowledge about unobservables. I reply that if we do not believe our best scientific theories, we cannot gain knowledge about unobservables, our opponents might dismiss the predictions derived from them, and we cannot use them to explain phenomena. We commit an unethical speech act when we explain a phenomenon in terms of a theory we do not believe.

Hempel, Popper, and Kuhn argue that to be scientific is to be testable, to be falsifiable, and most nearly to do normal science, respectively. I argue that to be scientific is largely to be interactive, offering some examples from science to show that the ideas from different fields of science interact with one another. The results of the interactions are that hypotheses become more plausible, new phenomena are explained and predicted, we understand phenomena from a new perspective, and our worldview becomes simpler. I also argue that given that the interactions are impressive features of science, astrology and religion would be regarded as science, provided that there are similar interactions in those enterprises.

I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism.

Suppose that scientific realists believe that a successful theory is approximately true, and that constructive empiricists believe that it is empirically adequate. Whose belief is more likely to be false? The problem of underdetermination does not yield an answer to this question one way or the other, but the pessimistic induction does. The pessimistic induction, if correct, indicates that successful theories, both past and current, are empirically inadequate. It is arguable, however, that they are approximately true. Therefore, scientific realists overall take less epistemic risk than constructive empiricists.

Psychopaths are brutal individuals, having no empathetic concern for others. Initially, the existence of psychopaths seems to be a mystery from an evolutionary point of view. On close examination, however, it can be accommodated by evolutionary theory. Brutal individuals excelled meek individuals in the desperate circumstances where they had to fight their competitors over natural resources for survival and reproduction. This evolutionary explanation of psychopaths receives support from Pinker's observation of the history of brutality. We have good reasons for predicting that psychopaths are likely to die out in the future.

Bird argues that scientific progress consists in increasing knowledge. Dellsén objects that increasing knowledge is neither necessary nor sufficient for scientific progress, and argues that scientific progress rather consists in increasing understanding. Dellsén also contends that unlike Bird’s view, his view can account for the scientific practices of using idealizations and of choosing simple theories over complex ones. I argue that Dellsén’s criticisms against Bird’s view fail, and that increasing understanding cannot account for scientific progress, if acceptance, as opposed to belief, is required for scientific understanding.

Scientific realists believe both what a scientific theory says about observables and unobservables. In contrast, scientific antirealists believe what a scientific theory says about observables, but not about unobservables. I argue that scientific realism is a more useful doctrine than scientific antirealism in science classrooms. If science teachers are antirealists, they are caught in Moore’s paradox when they help their students grasp the content of a scientific theory, and when they explain a phenomenon in terms of a scientific theory. Teachers ask questions to their students to check whether they have grasped the content of a scientific theory. If the students are antirealists, they are also caught in Moore’s paradox when they respond positively to their teachers’ questions, and when they explain a phenomenon in terms of a scientific theory. Finally, neither teachers nor students can understand phenomena in terms of scientific theories, if they are antirealists.