Sunday, March 1, 2015
Sunday, February 22, 2015
Infinities have different sizes
Cantor argued that the infinite size of the set of positive integers is smaller than the infinite size of the set of real numbers in the interval from 0 to 1. This (a) established the incorrectness of our intuition that all infinities are the same size, and (b) was the first argument that used a diagonal construction.
The argument is a reductio ad absurdum. Suppose the two sets were the same size. Then by the definition of same size, each real number somewhere in the range from 0 to 1 could be paired up with a positive integer and vice versa. Here is how such a pairing might look:
Consider the diagonal number that is produced by using a decimal point and then selecting the diagonal digits that are highlighted and underlined above:
This number might be somewhere down the list, but the following number definitely won’t be. Take each digit of the diagonal number and add one to it, but if the digit is 9 then replace it with 0.
That new number differs from the nth number in the list at least in its nth digit. It should be on the list but isn’t. That’s the contradiction. For any other table that tries to pair natural numbers with real numbers, there is a similar diagonal construction.
The Euthyphro dilemma (Plato’s Socrates)
What gives a moral truth its authority?
Are actions morally good because God commands them, or does God only command what is morally good?
1) the authority of a moral truth is established by God commanding it, orIf 1 is true, then any moral truths established by God are arbitrary. (God could have commanded something different, and the authority of morality is not based on the reasons why God commanded what he did.)
2) God understands the authority and that leads him to make his commands
If 2 is true, then God is not the source of morality. (God must be referring to some kind of moral reasons, principles, or rules in order to know what is morally good. Morality is not arbitrary on this view because it is based on reasons. God is not the source of morality on this view because the reasons, principles, or rules are the source or authority of morality and God is (presumably) using rationality to infer morality from those reasons, principles, or rules.)
This argument is important because, regardless of one’s religious beliefs, it encourages us to think carefully about what makes something morally good or bad. This kind of thinking is required for us to work out how to behave towards others in our diverse world. And it’s cool because I like to imagine God puzzling over trolley problems and experience machine scenarios (“it just is wrong to push the man!”)
I think the best arguments begin with really simple and uncontroversial premises, which are used to develop much more substantive and interesting conclusions. Alan Gewirth (Reason and Morality, 1978) begins with the simple and uncontroversial thought that each of us considers the aims and purposes of our chosen actions as good (otherwise, why do them?). Each of us, then, should insist that others not interfere with these actions. We are all committed to objecting and resenting others when they prevent us from acting on what we consider good.
So, from the first-person point of view every agent is rationally committed to a) demanding that others not interfere with her actions and b) acknowledging that the basis of this demand is a generic feature of human agency. Therefore, c) every agent has the same basis for making this demand as she does, and d) anyone who made this demand for herself while refusing to acknowledge the standing of others to make it, as well, has contradicted herself.
This general commitment makes freedom of action a moral default. It's not absolute, of course, but it establishes a moral presumption and, for Gewirth, a very strong one so that no one's freedom may be restricted without special justification.
G. Randolph Mayes
1. If successful scientific theories are not accurate descriptions of reality, then their success is a miracle.The idea underlying premise 1 is that the best explanation of the success of science is that it provides accurate descriptions of reality. This is called an inference to the best explanation (IBE).
2. The success of scientific theories ain't a miracle.
3. Therefore, successful scientific theories are accurate descriptions of reality.
I find it compelling in naturalistic terms: It seems right, e.g., that the relative success of organisms with minds seems (partially) best explained by the accuracy with which they represent their environment.
But the principle of IBE also strikes me as a confusion. Simply put: we can't infer that a theory is true or accurate because it is a good explanation. Being true is just part of what we mean when we say that an explanation is good.
There are other criteria, too, e.g., prediction, consilience, and simplicity. So we could just remove truth from this list. But then when we say that realism is the best explanation, what we mean is that it possesses these virtues to the greatest degree. Well, maybe so- compared to no explanation at all. But how good is it? What does it predict? What is unifying or simplifying about it? When you really hold it accountable to explanatory criteria, the no-miracles argument starts to feel like magic.
In Ethics: Inventing Right and Wrong, Mackie offers an ‘Error Theory’ for how we have come to be so mistaken about what there is. One part is the Argument from Queerness:
1. If values are objective, then they must be metaphysically similar to other objective things. Objectivity entails that what is objective is real, i.e., is true against the way the world actually is (not against the way we agree it is, or against our practices, desires, perspectives, or semantics). For values to have this kind of objectivity entails “they would be entities or qualities or relations… utterly different from anything else in the universe” (38).
2. If values are objective, then we must be able to know them. But, to know something “utterly different from anything else in the universe,” we’d need “some special faculty of moral perception or intuition, utterly different from our ordinary ways of knowing everything else” (38).
What makes this argument cool, is that Mackie demands that we question how we can know our moral judgments are true. Even obvious prescriptions, like ‘do no harm’, presume an entailment between the fact of pain and the wrongness of it. But this is not self-evident, as intuitionists and moral realists propose. Mackie’s Argument from Queerness jabs at that connection. This is not to say he’s right, but his jab demands we rethink what we take for granted when we declare anything to be wrong or right. It is also cool just ‘cuz of its name.
In Animal Liberation (1975) Peter Singer makes a compelling case for not using or consuming non-human animals when it is not necessary to our survival, because animals experience pain and suffering as we do, they need their lives as much as we do.
We really don’t accept that differences in intelligence between humans make it morally acceptable for some humans to eat or experiment or otherwise subordinate less intelligent humans, because intelligence is not the relevant difference we use to guide our treatment of others. The capacity for suffering is the only relevant difference. In suffering, animals are our equals.
Refusing to acknowledge animal vital interests on the grounds that they are not human or lack other qualities that humans have is a form of discrimination akin to racism and sexism, he calls it speciesism, which has the same recipe-for-exploitation rationale: Ignore or weigh differently the similar, vital interests of members of different groups.
Singer’s argument is cool because he extends the principle of equality that guides our treatment of fellow humans “consider and treat the interests of those who suffer equally” to non-humans. It isn’t fair for racists and sexists to discriminate on the grounds of real or perceived physical or cognitive abilities and then inflict suffering on those whom they subordinate, and it isn’t fair for speciesists. Sure animals eat each other, but unlike animals, we humans are morally responsible for what we do.
Fission and Fusion
Derek Parfit in Reasons and Persons asks us to imagine a fictional case where you are taking a timed exam with two problems left and only enough time remaining to finish one.
But, you can easily trigger a device in your brain—perhaps by raising your eyebrows—that effectively divides your stream of consciousness—and your ability to control your body—in two.
So the left half of you can work on one test problem at the same time as your right half is working on the other test problem.
The way Parfit describes it is great: for example, the left ‘you’ can see in its peripheral vision the right ‘you’ scribbling furiously as the clock ticks down, and can wonder what the right ‘you’ is thinking and feeling. And vice-versa.
This is an illustration of what it might be like to experience a certain kind of ‘division’ or ‘fission’ (in this case, binary fission, of one’s stream of consciousness and bodily control).
Of course, philosophers divide (pun intended) on what such a case might prove or illustrate about personal identity and other matters. (For example, do you literally become two persons? If not, which stream are you?)
But one reason I like the case is that Parfit quickly closes its description by imagining a ‘fusion’ once the test is over. (Perhaps the you—the left ‘you’?—blinks twice?) The individual at the end of the fusion (you?) suddenly remembers everything that happened in both streams.
It’s a great case.
Sunday, February 15, 2015
Option 1: Do nothing and let five die.
Option 2: Flick a switch that redirects the trolley onto a side-track with four innocent people who cannot escape on it, killing them and saving the five
Option 3: Flick a switch that redirects the trolley onto a raised side-track with three innocent large men who cannot escape on it, killing them and saving the five.
Option 4: Push an innocent very large man, who is holding another innocent large man and standing on a footbridge, into the path of the trolley, killing them and saving the five.
Option 5: Push an innocent very large man on a foot bridge into the path of the trolley, killing him and saving the five.The pedestrian takes Option 5, and as a result the innocent very large man dies and the five innocent people are saved.
Select which answer best fits your opinion (chose one and only one response):
A: Given the situation, the pedestrian’s action was morally permissible
B: Given the situation, the pedestrian’s action was not morally permissible
According to many philosophers, including Philippa Foot (1967) and Judith Jarvis Thomson (1976), the vast majority of people realize that pushing the very large man in this kind of situation is not morally permissible (i.e. morally speaking, it’s not OK to push the guy). Empirical research on trolley scenarios like this are largely in agreement; the proportion of respondents reporting that pushing the very large man (killing one to save five) is morally permissible ranges from about 11% (Hauser et al. 2007) to 18% (Kelman and Kreps 2014). BUT, these empirical studies, and the views of Foot and Thomson, are based on versions of the scenario that at least imply that only two options are available to the agent: to push or not to push. For an example of a two-option version, consider the above five-option scenario with options 2, 3, and 4 omitted.
Among the uses of experimental philosophy (doing experiments to help resolve philosophical problems), are:
1) Testing the claims philosophers make about the proportion of people who have this or that intuition, or believe this or that proposition, etc. And,I conducted a paper-based survey of 468 undergraduate students so as to run these kinds of tests in relation to the ‘pushing the very large man’ (AKA ‘foot bridge’) trolley scenario. More specifically, I wanted to find out whether including several, instead of two, options had an effect on how people reported the moral status of pushing the very large man in a ‘foot bridge’ trolley scenario. The basic method for conducting such an investigation is to randomly assign each individual in the sample either the two-option version of the scenario or a several-option version of the same scenario. In my study, I randomly assigned one of the following three versions: the two-option version, the three-option version, or the five-option version.
2) Comparing intuitions about similar scenarios to test whether certain manipulations tend to produce different results (e.g., to test whether a thought experiment inadvertently elicits a bias by the inclusion of some purportedly irrelevant fact)
The five-option scenario above is the same as I used in my study. The three-option version followed the same pattern, but omitted options 2 and 4 from the five-option version. Similarly, the two-option version omitted options 2, 3, and 4.
As you can see in the chart below, the more options in the scenario, the greater the proportion of respondents indicating that pushing the very large man is morally permissible. The differences between the two-option version and the other versions are both statistically significant (p<0.05). The difference between the three- and five-option versions was not statistically significant (p=0.1213). These results mean that we can be 95% or more confident that the differences between two-option version and the other versions are not the product of chance. Notice also, that the majority verdict changes position as we move from the two- to the five-option version. In the two-option version, the majority views pushing the very large man as morally impermissible, but in the five-option case an even greater majority views pushing the very large man as morally permissible. This is interesting result #1.
Why might including several-options in the scenario change the reported judgments in this way? Peter Unger (1996) has argued for ‘Liberationism’, i.e., that including intervening options in established two-option thought experiments can liberate readers’ judgments by inducing them to think more deeply about which option reduces the most harm to innocent people. According to Liberationism, then, reasonable respondents should report more utilitarian judgments about the morality of particular actions in several-option setups compared to two-option setups.
What do you think could have caused this result? Also, assuming the cause of the difference is not pernicious, think about the implications of this finding for the trolley problem and, potentially, all those other famous two-option scenarios!
Interesting result #2 is that 41.8% of respondents to the two-option scenario reported pushing the very large man as morally permissible. This is more than double the proportion found in other published studies of ‘foot bridge’ trolley scenarios, and far more than anecdotal evidence from the ‘coal face’ of undergraduate (raise-your-hand-if-you…) lecturing would suggest. Was my result anomalous? My collaborators conducted some online surveys using very similar scenarios with very similar results. When I observed Genevieve Wallace polling students on this scenario using clickers, the results were also similar to my results here. So, it seems this is a genuine mystery. Why are all the results I have first-hand experience of different to all of the results that I don’t have that experience of?
Please help me solve these mysteries!
Department of Philosophy
Many thanks to Peter Unger and Justin Sytsma for advice and comments on the study set up, analysis, and discussion. Thanks also to the Provost’s Research Incentive Fund for effectively bankrolling the study.
Foot, P. (I967). The Problem of Abortion and the Doctrine of the Double Effect, The Oxford Review, 5: 5-15.
Hauser, M., Cushman, F., Young, L., Kang‐Xing Jin, R., & Mikhail, J. (2007). A Dissociation Between Moral Judgments and Justifications. Mind & language, 22(1): 1-21.
Kelman, M., & Kreps, T. A. (2014). Playing with Trolleys: Intuitions About the Permissibility of Aggregation. Journal of Empirical Legal Studies, 11(2): 197-226.
Thomson, J. J. (1976). Killing, Letting Die, and the Trolley Problem. The Monist, 59: 204-217.
Thomson, J. J. (1985). The Trolley Problem. Yale Law Journal, 94: 1395-1415.
Unger, P. (1996). Living High and Letting Die: Our Illusion of Innocence. Oxford University Press: New York.
Friday, February 13, 2015
I’m sorry about all this sneaking around, and having to meet up at strange times. But, you know that my family is still very important to me. If they knew… well, you know what I mean. It would break their hearts if they knew how I felt about you. Anyway, I’m writing to you now just to make sure you know how I really feel. Forgive me if this all sounds a bit emotional, but I’m only human.
I love you. It’s true, and I want you to know that. So, here follows my justification for why you should believe it.
As we get older, growing together, I continue to learn about you and, in your light, about myself. Even in those times when I only saw you from afar, I knew it was meant to be. Even when you taunted me with your exotic turns of phrase, I knew it was love. Your influence over my thoughts was inescapable, as if I had no free will.
I'm so glad I caught you in the end. Now we can influence each other. I have already noticed that we are starting to think alike. Sometimes I can predict your objections. Occasionally we seem to meld into a sublime synthesis. We even talk alike. We’re playing the same language game.
Now we’re together, our influence on each other will grow. I'm looking forward to it. At the very least we will be better able to appreciate a fuller view of what is and what might be. But, I expect we'll receive so much more from our lives together.
We are building a deep, secure, and thoroughly loving connection. Through this connection, I feel safe while you envelop me, drawing me into your enigmatic depths. At your core is a most profound beauty, moral virtue, and unrelentingly logical view of the world. Tears well in my eyes as I envisage the many years we'll share. I want to be influenced by you. I want to share with you, and be a part of you.
In fact, I fantasize of perfectly merging with you, and then everything, so we can become the blobject. I know a part of you doesn’t believe in the blobject, but it would be perfect! And, since existence is an aspect of perfection, I know the blobject exists.
I know it hasn’t always been easy between us. We may have taken each other for granted from time to time. We have irritated each other, and we will irritate each other. You can be cold and overly rational. And I can be silly, holding on to my intuitions more tightly than the evidence reasonably permits. But, we will also love each other. You will fascinate and inspire me. You will continue to be the object of my intellectual desire and the number one reason for me to come into work every day.
Philosophy, my love, you complete me.
Saturday, February 7, 2015
In order to enjoy the benefits of University recognition, student groups must declare that membership and leadership positions are open to any enrolled student. InterVarsity refused to file the declaration. The group requires students who hold leadership positions – positions that may involve teaching and ministering to members – to affirm its traditional views on Biblical Christianity.
The move to enforce this “all comers” policy harms meaningful freedom of association on CSU campuses. It means that College Democrats may not require members to maintain a commitment to progressive causes in order to be eligible for leadership positions. They must be open even to conservative NASCAR fans. College Republicans may not require a commitment to conservative principles of its leaders. An influx of evangelistic Nancy-Pelotheists could undermine its mission. Likewise, the new policy opens leadership positions in the Secular Student Alliance to faith healers, those in the Queer-Straight Alliance to homophobes and those in the Environmental Student Organization to climate change deniers.
These would be unwelcome developments. Universities advance their educational goals in part by promoting a diverse and vibrant intellectual community among students. Meaningfully free inquiry requires universities to afford its students wide-ranging opportunities to associate freely in their pursuit of academic and practical ideals and values. But such pursuit requires the ability of these associations to exclude others – yes, discriminate – on “doctrinal” grounds that are relevant to the group’s distinctive mission. When CSU forbids this, and when it derecognizes InterVarsity, it advertises the fact that its goal is not to foster an environment where all sorts of ideas can be investigated openly and fairly. It suggests its goal is to impose a specific idea about what falls within the bounds of legitimate investigation on campus.
Of course, the CSU doesn’t really forbid all discrimination on grounds that are relevant to a group’s mission. Sensibly enough, the policy already carves out exceptions for some student organizations. And, should students engage in the kind of shenanigans I speculate about above, university administrators would likely intervene to protect organizations with aims and values that they regard as legitimate. InterVarsity is not among those. Nor perhaps are other organizations, religious or otherwise, that are observant, unpopular or weird enough to make people uncomfortable.
Large or wildly popular groups will not be affected at all by the new policy. They have statements of purpose that the masses either resoundingly endorse or do not really care about one way or the other. So club sports and groups like the Anti-Cancer Society and the Society for the Appreciation of Beer Pong will do just fine in the new campus environment. Groups like these don’t need to require a set of specific affirmations from members or leaders in order to pursue their organizational missions.
Many other groups don’t have broad popular support on campus. They have distinctive aims and values, some of which are fairly controversial, which they seek to further through their organizational activities. Such groups – those with political affiliations, social justice concerns or ethnic identities – likely can reliably count on benevolent university administrators to protect their organizational missions, at least for now.
Disfavored organizations cannot, and so far we know this includes InterVarsity at CSU. But this is not true everywhere. For example, Ohio State University provides an exemption to accommodate religious organizations like InterVarsity so that “A student organization formed to foster or affirm the sincerely held religious beliefs of its members may adopt eligibility criteria for its Student Officers that are consistent with those beliefs.” CSU should do the same. The effect of this alternative way forward would be to treat religious groups the way CSU already treats other student groups that have a distinctive mission.
Protecting open inquiry only for those with officially sanctioned views runs counter to the traditionally recognized aims of a university. If students on CSU campuses have genuine freedom of association in order to promote intellectual inquiry, this entails that they can exclude others. When they do, their reasons may seem unfair, arbitrary or worse to at least some people. But when this is forbidden, freedom of association is meaningless and intellectual inquiry becomes a kind of ideological conformity-lite.
Sunday, February 1, 2015
Hilary Putnam once asked a funny question: If all of the things we have heretofore called cats turned out to be robots from Mars, would we have discovered that all cats are robots or, rather, that there are no cats? Putnam went with cats are robots, and on the basis of this intuition he argued that the extension of a term- the set of objects to which it refers- is not determined by our concept of it, but rather by its paradigm cases.
This view is now known as semantic externalism, and I'm largely down with it. Though I actually think it's a mistake to discuss things like this as if we were discovering the real meaning of meaning. The truth about meanings is that they are conventional and we can change them anytime we agree to. If scientists decided in such a case that there were no cats, and invented a new term to refer to these robot thingies instead, no grievous error would have occurred that philosophers would be required to go back and set straight. I see Putnam not so much as having discovered part of the real meaning of meaning, but rather as having made a strong, useful proposal for rationalizing some of the conventions by which we allow meanings to change.
Putnam's robot cat example can seem pretty out there to someone not acquainted with the crazy thought experiments philosophers use in an effort to clean up our conceptual framework. But the history of science and philosophy is replete with similar episodes in which we need to determine whether some phenomenon doesn't exist, or, rather, is just very different than we had supposed, i.e., veditwhasup.*
Here is a slightly different take on robot cats- which I believe is compatible with Putnam's views- in terms of the concept of explanation. What I'll suggest is that whether we decide that a phenomenon doesn't exist or is just veditwhasup depends a great deal on the explanatory context.
Start with witches. Although a large chunk of humanity still believes in witches, in a scientifically enlightened community it is uncontroversial to say that there are none. How did we get from a position of near universal belief in witches, to the view that witches don't exist? I say the reason we say there are no witches is that the phenomena to be explained have disappeared. There was a time when we were in dire need of an explanation of how people get turned into newts. The widely accepted explanation is that it was due to witchcraft. Since then, we have come to doubt that humans do get turned into newts. Hence, we are no longer in need of witches to explain this.
Last year I discussed a few important scientific episodes in which the phenomenon to be explained was determined to be an illusion. Some of these cases we may understand in a manner that is analogous to the above. For example, we do not say that planetary epicycles are veditwhasup. We say that they don't occur, because retrograde, the phenomenon they were invoked to explain, is an illusion. We do not say that the designer of plants and animals is just veditwhasup, because we have come to realize that design itself is an illusion. For the same reason we no longer require the gods as an explanation of fate. If you ask why some things are fated to happen, regardless of what we do to prevent them, you are laboring under an illusion.
However, this particular explanatory model does not fit all the cases, even in the realm of superstition. For example, epilepsy was once widely explained by reference to demonic possession. But we did not reject possession on the grounds that epileptic fits are illusions. Similarly, in science we did not reject the existence of caloric and phlogiston because heating, cooling and combustion do not occur. We no longer believe in humors nor miasmas, but that is not because there is no such thing as the diseases they explained. We reject the élan vital and the soul, but that is not because we no longer believe in the unity of consciousness or the self-organizing properties of living systems.
In these, and many other cases, the reason we have stopped believing in these entities is that we have hit upon radically different and better explanation of the phenomenon in question. When this occurs, it often makes sense to reject the existence of the entities we are appealing to in explaining the phenomenon, but not the ones we are trying to explain.
What's interesting is that this is very often exactly what people do recommend.
For example, philosophers and scientists often claim that if determinism is true there is no such thing as free will. But if free will is just the remarkable human ability for deliberative choice, of course it exists. All we have rejected is a ghost in the machine explanation of it. A similar point holds for the concept of knowledge. People often conclude that there is no such thing as knowledge when they learn that certainty is unachievable or that the notion of our ideas resembling an external reality makes no sense. But all this means is that we had a false explanation of how knowledge works. Veditwhasup. Again, people often claim that there is no such thing as human altruism when they learn that people get pleasure from helping others. But this is foolish. Human cooperation and self-sacrifice happens. We just had a very wrong idea of how.
In sum, there are two good reasons for thinking that some theoretical entity or process we previously accepted does not exist. The first is that it explains as real what we have come to regard as an illusion. The second is that we have developed better and fundamentally different explanations of the reality in question. Failing either of these, I would suggest raising the following question. Could it just be veditwhasup?
Department of Philosophy
Sacramento State University
*Either of Old Saxon origin or coined by me just now as an acronym for the purpose of staying under the 1,000 word limit imposed by this blog.
Sunday, December 14, 2014
This seriously distorts the issue by ignoring the fact that the Internet is a commons. Although the idea of the commons can be traced back to Roman times, it currently gets relatively little attention in the media, in politics and even in contemporary works of political theory and philosophy. As a result, the general public has at best a rather cloudy understanding of the concept. (I include myself in that category.) The lone exceptions might be found in some works on environmental preservation and related utopian thinking about alternative futures. This is regrettable. The commons are actually very valuable attributes of most contemporary societies but in predominantly capitalist countries like ours, they are under constant threat of enclosure by mega-corporations that have undue influence over lawmakers. Internet neutrality is just one such case among many. For a good account of the scope of the threat, see David Bollier’s Silent Theft.
Rather than attempt a careful definition of the commons (I don’t have one), I will focus on two of its central features worth noting. A commons is a highly valued public asset or pattern of behavior that is (a) regarded as of such high value that it is felt by the public that special effort ought to be made to ensure that it can be experienced or practiced by future generations in perpetuity and (b) it cannot be privately owned or controlled without risking deleterious consequences to its value as a common public asset. The commons are, or should be, off-market. Some commons are publicly owned (parks, rivers, lakes, forests), other commons are unowned but their use can be regulated in ways that preserve their value to the public (the human genome, Antarctica, the free electoral process in democracies, basic scientific research).
The Internet is clearly a commons of inestimable value. Thanks to the technology, it is probably the first truly international commons. It has made information on almost every conceivable subject readily accessible to a significant and rapidly growing portion of the world’s population, along with the opportunity to engage in an open-ended electronic conversation about the reliability and significance of that information. The desire of some ISPs to fast-track – at their discretion – some of the more lucrative Internet sites would clearly diminish the value of the Internet commons to all other users. And if such a special permission were granted, it would very likely not be the last.
Moreover, fast-tracking would be profoundly unfair. The ISPs did not create the Internet. It was the work of a research arm of the Defense Department along with the collaboration of some American research universities, mostly taxpayer financed public entities. Nor did the ISPs build or pay for the satellite infrastructure that is the backbone hardware of the Internet. The ISPs just dropped in at the end of the line to make the connections between their microwave towers and individual homes and offices. Fast-tracking would be an outrageous enclosing of an invaluable commons.
One possible objection to this argument for Internet neutrality is that it turns a blind eye to the vast amount of Internet traffic that is far from anything one could reasonably consider a common public good, e.g. the streaming of Hollywood movies, pornography, and the widespread us of the social media for trivial ends. The point can be granted but it does not detract from the fact that a substantial part of the Internet serves the commons. We can all live with the fact that another part of the Internet serves relatively trivial personal ends.