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Art centres fulfil many functions in remote regions as a source of Indigenous identity and creativity; as a link to the global art market; as centres for community engagement and participation; and as a source of social capital providing a range of services for local communities. They are dependent on funding from State and Federal authorities and they are identified as one of the success stories in remote community development. However, they face an uncertain future in the light of their multiple functions and their position as both a source of traditional identity and a link to an external art market. The article highlights the challenges faced by government in the evaluation of their effectiveness and contribution; and in particular discusses the suitability of the hybrid economy model as a representation of their functions.
Glaciers in Alaska are currently losing mass at a rate of ~−50 Gt a−1, one of the largest ice loss rates of any regional collection of mountain glaciers on Earth. Existing projections of Alaska's future sea-level contributions tend to be divergent and are not tied directly to regional observations. Here we develop a simple, regional observation-based projection of Alaska's future sea-level contribution. We compute a time series of recent Alaska glacier mass variability using monthly GRACE gravity fields from August 2002 through December 2014. We also construct a three-parameter model of Alaska glacier mass variability based on monthly ERA-Interim snowfall and temperature fields. When these three model parameters are fitted to the GRACE time series, the model explains 94% of the variance of the GRACE data. Using these parameter values, we then apply the model to simulated fields of monthly temperature and snowfall from the Community Earth System Model, to obtain predictions of mass variations through 2100. We conclude that mass loss rates may increase between −80 and −110 Gt a−1 by 2100, with a total sea-level rise contribution of 19 ± 4 mm during the 21st century.
Nations love to go to war, argue leftist pacifists in democratic Western societies. By this account, governments cannot resist the temptation to assert their selfish interests by violent means. Political leaders use the language of just war to hide their real intentions: imperialistic domination and economic profit. These pacifists charge that with the Iraq war, the disastrous consequences of such politics have become hideously clear again.
Over the past two decades, thousands of studies have demonstrated that Blacks receive lower quality medical care than Whites, independent of disease status, setting, insurance, and other clinically relevant factors. Despite this, there has been little progress towards eradicating these inequities. Almost a decade ago we proposed a conceptual model identifying mechanisms through which clinicians' behavior, cognition, and decision making might be influenced by implicit racial biases and explicit racial stereotypes, and thereby contribute to racial inequities in care. Empirical evidence has supported many of these hypothesized mechanisms, demonstrating that White medical care clinicians: (1) hold negative implicit racial biases and explicit racial stereotypes, (2) have implicit racial biases that persist independently of and in contrast to their explicit (conscious) racial attitudes, and (3) can be influenced by racial bias in their clinical decision making and behavior during encounters with Black patients. This paper applies evidence from several disciplines to further specify our original model and elaborate on the ways racism can interact with cognitive biases to affect clinicians' behavior and decisions and in turn, patient behavior and decisions. We then highlight avenues for intervention and make specific recommendations to medical care and grant-making organizations.
§1. I propose to address not so much Gödel's own philosophy of mathematics as the philosophical implications of his work, and especially of his incompleteness theorems. Now the phrase “philosophical implications of Gödel's theorem” suggests different things to different people. To professional logicians it may summon up thoughts of the impact of the incompleteness results on Hilbert's program. To the general public, if it calls up any thoughts at all, these are likely to be of the attempt by Lucas [1961] and Penrose [1989] to prove, if not the immortality of the soul, then at least the non-mechanical nature of mind. One goal of my present remarks will be simply to point out a significant connection between these two topics.
But let me consider each separately a bit first, starting with Hilbert. As is well known, though Brouwer's intuitionism was what provoked Hilbert's program, the real target of Hilbert's program was Kronecker's finitism, which had inspired objections to the Hilbert basis theorem early in Hilbert's career. (See the account in Reid [1970].) But indeed Hilbert himself and his followers (and perhaps his opponents as well) did not initially perceive very clearly just how far Brouwer was willing go beyond anything that Kronecker would have accepted. Finitism being his target, Hilbert made it his aim to convince the finitist, for whom no mathematical statements more complex than universal generalizations whose every instance can be verified by computation are really meaningful, of the value of “meaningless” classical mathematics as an instrument for establishing such statements.
REALISM VS NOMINALISM
Philosophy is a subject in which there is very little agreement. This is so almost by definition, for if it happens that in some area of philosophy inquirers begin to achieve stable agreement about some substantial range of issues, straightaway one ceases to think of that area as part of “philosophy,” and begins to call it something else. This happened with physics or “natural philosophy” in the seventeenth century, and has happened with any number of other disciplines in the centuries since. Philosophy is left with whatever remains a matter of doubt and dispute.
Philosophy of mathematics, in particular, is an area where there are very profound disagreements. In this respect philosophy of mathematics is radically unlike mathematics itself, where there are today scarcely ever any controversies over the correctness of important results, once published in refereed journals. Some professional mathematicians are also amateur philosophers, and the best way for an observer to guess whether such persons are talking mathematics or philosophy on a given occasion is to look whether they are agreeing or disagreeing.
One major issue dividing philosophers of mathematics is that of the nature and existence of mathematical objects and entities, such as numbers, by which I will always mean positive integers 1, 2, 3, and so on. The problem arises because, though it is common to contrast matter and mind as if the two exhausted the possibilities, numbers do not fit comfortably into either the material or the mental category.
TWO SENSES OF “FOUNDATIONS OF MATHEMATICS”
Does mathematics requires a foundation? The first thing that must be said about the question is that the expression “foundations of mathematics” is ambiguous. Let me explain.
Modern mathematicians inherited from antiquity an ideal of rigor, according to which each mathematical theorem should be deduced from previously admitted results, and ultimately from an explicit list of postulates. It also inherited a further ideal according to which the postulates should be self-evidently true. During the great creative period of early modern mathematics, there were and probably had to be many departures from both ideals. But during the century before last, as mathematicians were driven or drawn to consider less familiar mathematical structures, from hyperbolic spaces to hypercomplex numbers, the need for rigor was increasingly felt, and higher standards were eventually instituted. But while the ideal of rigor may be claimed to have been realized, the ideal of selfevidence was not.
Considering only the ideal of rigor, the working mathematician's understanding of its requirements, of what is permissible in the way of modes of definition and modes of deduction of new mathematical notions and results from old, is largely implicit. Logic, which investigates such matters, and fixes explicit canons, is a subject in which the algebraist, analyst, or geometer need never take a formal course. Nor are mathematicians in practice much concerned with tracing back the chain of definitions and deductions beyond the recent literature in their fields to the ultimate primitives and postulates.
THE QUESTION
Which if any of the many systems of modal logic in the literature is it whose theorems are all and only the right general laws of necessity? That depends on what kind of necessity is in question, so I should begin by making distinctions.
A first distinction that must be noted is between metaphysical necessity or inevitability – “what could not have been otherwise” – and logical necessity or tautology – “what it is self-contradictory to say is otherwise.” The stock example to distinguish the two is this: “Water is a compound and not an element.” Water could not have been anything other than what it is, a compound of hydrogen and oxygen; but there is no self-contradiction in saying, as was often said, that water is one of four elements along with earth and air and fire.
The logic of inevitability might be called mood logic, by analogy with tense logic. For the one aims to do for the distinction between the indicative “it is the case that…” and the subjunctive “it could have been the case that…,” something like what the other does for the distinction between the present “it is the case that…” and the future “it will be the case that…” or the past “it was the case that…” The logic of tautology might be called endometalogic, since it attempts to treat within the object language notions that classical logic treats only in the metalanguage.
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