[Note: I am no longer happy with this, and intend to post a revised version soon. April 4]
Ethics and morality are important topics, but much ethical discussion and debate is unenlightening and unproductive.
I have serious reservations about philosophical ethics. Whilst a knowledge of some of the rudiments of ethical theory may be useful for articulating issues and problems, there is no clear way of solving problems or deciding between alternative approaches. The academic study of ethics soon becomes (in my experience) an area of rapidly diminishing returns.
Different people have very different ideas about the scope and nature of ethics, often talking at cross purposes or seeking to promote a cherished agenda by any means, including personal abuse.*
Rather than elaborating ambitious theories or contributing to the revival of Aristotelian or other classical approaches, I am drawn simply to look at how adjectives like 'ethical' and 'moral', auxiliaries like 'should' and nouns like 'obligation' or 'duty' are actually used in ordinary day-to-day contexts, and the implicit social rules with which such expressions are associated.
Every society, every social group incorporates implicit rules of behavior. These rules (some relating to etiquette or manners, others to morality) can be studied and described like any other aspect of social life.
Prescriptive (as distinct from descriptive) approaches involve the individual actually making or accepting or rejecting moral judgements or using or applying moral language or concepts.
Deontic logic traditionally divides behaviors into three broad classes: obligatory, impermissible and optional. It's a complex branch of logic, but the real complications and challenges of moral thinking are not so much logical as contextual. Because, obviously, the general situation and the specific position(s) of the individual(s) involved need to be taken into account.
Times have changed since F.H. Bradley wrote his famous essay, 'My station and its duties' [included in his Ethical Studies (1876)], but the basic principle of the contextuality of ethics still applies. A person's duties or obligations derive in large part from (or at least cannot be assessed without taking into account) his or her positions in complex societal, professional and familial structures.
Kant talked about a categorical imperative, but I don't think we can get beyond hypothetical imperatives. In other words, if you (in such and such a situation) want such and such an outcome, do this or that. With respect to social relations, this way of thinking is never straightforward or foolproof, and requires judgement and insight to be applied successfully.
The kind of (implicit) rule-based approach to ethical thinking and manners which I am advocating is consistent with a very modest view of rights. If you break society's implicit rules whenever it suits you, you forfeit your right to the benefits and protections those rules might potentially provide.
The key question in ethics is a first-person question: what should I do (or refrain from doing)? I say this is the key question in ethics, but such a question (and this is reflected in the ambiguity of the word 'should') transcends ethics or morality.
Ethical or moral questions often merge into questions of etiquette, aesthetics and prudence as well as other areas or dimensions of life. There are no clearcut divisions between ethical and other considerations, in other words, and a certain type of (marginally unacceptable) behavior may be condemned by some as immoral, while others might prefer to call it ugly, unwise or just bad form. Others may see it in a positive light.
Even very serious moral transgressions (like the indiscriminate killing of civilians) are sometimes seen by people in the grip of certain ideologies or belief-systems as praiseworthy.
Most of us, of course, will condemn such ideologies as noxious and depraved. I certainly do. It is not really a problem that we can't prove our view correct and its converse incorrect in some objective, theoretical sense (though many think it is). Ethics is just not like that.
Quite simply, there is no absolute or objective ethical authority, and nor is there any objective method of determining 'moral truths'.
* Here is a summary of a recent controversy involving some very silly and intemperate assertions on the part of one of the protagonists.
Friday, January 18, 2013
Monday, January 7, 2013
Does mathematics pose problems for physicalism?
For those who want to see the world as being comprised at a fundamental level entirely of such processes as physics and the other sciences might model or describe, mathematics seems to pose problems.
Some say that our moral sense, or love and emotion, or our perception of beauty somehow undermine a physicalist viewpoint. But they don't really. All these things can be understood as complex products of simpler physical processes (evolution, biology, social interaction, etc.).
And the realm of the mystic may be timeless, but is subjective – or at least cannot be shown to have an objective existence.
But mathematics seems to take us into a non-empirical but demonstrably objective realm.
Mathematics works in many ways like a branch of science (and of course is an inextricable part of science), but is essentially concerned with abstract patterns and relations rather than with the empirical world directly.
Nonetheless, as a human activity even pure mathematics is clearly a part of the empirical world.
In fact, as digital computers become more fully integrated into mathematical research and practice, and discrete mathematics continues (as I suspect it will) to replace continuous as the basis for our most plausible and accurate descriptions of reality (since physical reality at its most fundamental levels appears to be discontinuous), the view of mathematics as timeless and Platonistic will most likely fade.
Be that as it may, for various reasons many still adhere to a full-fledged mathematical platonism, and see the existence of mathematics and our access to mathematical truths (which on some views gives rise to what has become known as the 'access problem') as evidence of the inadequacy of physicalism; even sometimes as evidence for a religious or spiritual view of reality.
There are, of course, many competing philosophies of mathematics, some of them (like platonism) realist (in the sense of accepting the real existence of abstract mathematical objects), others anti-realist. In general, the former approaches seem more or less incompatible with physicalism, and the latter compatible.
As there is no scientific way of deciding between these approaches, the physicalist is really under no pressure. He or she can just point to one or other of those ways of seeing mathematics which do not entail accepting independently-existing abstract objects, etc.
I have alluded in the past to the anti-realist views of the mathematician Timothy Gowers. And I have just come across someone else whose views appeal to me.
Sharon Berry, who has recently completed work on her Ph.D. at Harvard*, is not an anti-realist or anti-platonist like Gowers, but her approach is basically empirical, and the platonism she countenances is sufficiently weak not to put me off too much.
Her dissertation is on the so-called access problem which she addresses in what seems like a refreshingly straightforward and down-to-earth way. She argues that mathematical knowledge can be reduced to 'knowledge of a kind of broadly logical possibility, that is possibility with regard to the most general principles about how any objects can be related by any relations.' She calls this notion 'combinatorial possibility', and claims we can account for our knowledge of combinatorial possibility 'by appealing to general constraints on relationships between concrete physical objects.'
What is particularly interesting about the notion of combinatorial possibility is that it is tightly tied to the empirical world: 'one can infer possibility from actuality.'
Our access to good (but incomplete) methods of reasoning about combinatorial possibility is explained by our experiences with concrete objects, and so – if indeed mathematical knowledge can be reduced to a knowledge of combinatorial possibility – our (partial) access to mathematical truth is also explained in terms of these ordinary experiences.
Berry believes that her approach to the access problem meshes neatly with a relatively robust approach to claims about mathematical objects. 'The key idea is that quantifiers can take on different senses in different contexts. These senses correspond to different standards that we might apply when assessing questions of existence.'
Her view is that lower standards operate in everyday contexts than are required in discussions of 'fundamental ontology'. And lower standards apply also in mathematical discussions.
So long as these higher and lower standards are seen in pragmatic terms (and not in terms of different kinds of objects actually having different degrees of being), this approach seems doubly attractive. It does justice to the subtleties of human communication as well as avoiding the implicit dogmatism of standard realist and anti-realist stances.
Berry herself, taking ontological and metaphysical discourse in general rather more seriously than I am inclined to, may not be entirely happy with my pragmatic interpretation. But her views do certainly reflect empirical and pragmatic tendencies.
As I said, there is probably no way to decide which, if any, of the available positions in the philosophy of mathematics are on the right track and which are not. Some look more plausible than others, it must be said, but such judgments are always going to be affected by prior metaphysical (or anti-metaphysical) tendencies and such like.
Which is not to say that all work in this area lacks significance. Arguably, both Gowers's and Berry's perspectives have significance and value.
As I suggested above, so long as there are plausible positions available which do not entail fully-fledged realism or platonism, the physicalist need not feel that his or her physicalist stance is under threat.
And, so, though I don't feel obliged to make (or capable of making) an unequivocal assessment either of Gowers's or of Berry's approach, I do value them both as possible (and, on the face of it at least, plausible) alternatives to full-blown mathematical platonism.
* Both a short and a long dissertation abstract are included in her CV which is available via her website.
Some say that our moral sense, or love and emotion, or our perception of beauty somehow undermine a physicalist viewpoint. But they don't really. All these things can be understood as complex products of simpler physical processes (evolution, biology, social interaction, etc.).
And the realm of the mystic may be timeless, but is subjective – or at least cannot be shown to have an objective existence.
But mathematics seems to take us into a non-empirical but demonstrably objective realm.
Mathematics works in many ways like a branch of science (and of course is an inextricable part of science), but is essentially concerned with abstract patterns and relations rather than with the empirical world directly.
Nonetheless, as a human activity even pure mathematics is clearly a part of the empirical world.
In fact, as digital computers become more fully integrated into mathematical research and practice, and discrete mathematics continues (as I suspect it will) to replace continuous as the basis for our most plausible and accurate descriptions of reality (since physical reality at its most fundamental levels appears to be discontinuous), the view of mathematics as timeless and Platonistic will most likely fade.
Be that as it may, for various reasons many still adhere to a full-fledged mathematical platonism, and see the existence of mathematics and our access to mathematical truths (which on some views gives rise to what has become known as the 'access problem') as evidence of the inadequacy of physicalism; even sometimes as evidence for a religious or spiritual view of reality.
There are, of course, many competing philosophies of mathematics, some of them (like platonism) realist (in the sense of accepting the real existence of abstract mathematical objects), others anti-realist. In general, the former approaches seem more or less incompatible with physicalism, and the latter compatible.
As there is no scientific way of deciding between these approaches, the physicalist is really under no pressure. He or she can just point to one or other of those ways of seeing mathematics which do not entail accepting independently-existing abstract objects, etc.
I have alluded in the past to the anti-realist views of the mathematician Timothy Gowers. And I have just come across someone else whose views appeal to me.
Sharon Berry, who has recently completed work on her Ph.D. at Harvard*, is not an anti-realist or anti-platonist like Gowers, but her approach is basically empirical, and the platonism she countenances is sufficiently weak not to put me off too much.
Her dissertation is on the so-called access problem which she addresses in what seems like a refreshingly straightforward and down-to-earth way. She argues that mathematical knowledge can be reduced to 'knowledge of a kind of broadly logical possibility, that is possibility with regard to the most general principles about how any objects can be related by any relations.' She calls this notion 'combinatorial possibility', and claims we can account for our knowledge of combinatorial possibility 'by appealing to general constraints on relationships between concrete physical objects.'
What is particularly interesting about the notion of combinatorial possibility is that it is tightly tied to the empirical world: 'one can infer possibility from actuality.'
Our access to good (but incomplete) methods of reasoning about combinatorial possibility is explained by our experiences with concrete objects, and so – if indeed mathematical knowledge can be reduced to a knowledge of combinatorial possibility – our (partial) access to mathematical truth is also explained in terms of these ordinary experiences.
Berry believes that her approach to the access problem meshes neatly with a relatively robust approach to claims about mathematical objects. 'The key idea is that quantifiers can take on different senses in different contexts. These senses correspond to different standards that we might apply when assessing questions of existence.'
Her view is that lower standards operate in everyday contexts than are required in discussions of 'fundamental ontology'. And lower standards apply also in mathematical discussions.
So long as these higher and lower standards are seen in pragmatic terms (and not in terms of different kinds of objects actually having different degrees of being), this approach seems doubly attractive. It does justice to the subtleties of human communication as well as avoiding the implicit dogmatism of standard realist and anti-realist stances.
Berry herself, taking ontological and metaphysical discourse in general rather more seriously than I am inclined to, may not be entirely happy with my pragmatic interpretation. But her views do certainly reflect empirical and pragmatic tendencies.
As I said, there is probably no way to decide which, if any, of the available positions in the philosophy of mathematics are on the right track and which are not. Some look more plausible than others, it must be said, but such judgments are always going to be affected by prior metaphysical (or anti-metaphysical) tendencies and such like.
Which is not to say that all work in this area lacks significance. Arguably, both Gowers's and Berry's perspectives have significance and value.
As I suggested above, so long as there are plausible positions available which do not entail fully-fledged realism or platonism, the physicalist need not feel that his or her physicalist stance is under threat.
And, so, though I don't feel obliged to make (or capable of making) an unequivocal assessment either of Gowers's or of Berry's approach, I do value them both as possible (and, on the face of it at least, plausible) alternatives to full-blown mathematical platonism.
* Both a short and a long dissertation abstract are included in her CV which is available via her website.
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