According to the recently released annual survey by the Apiary Inspectors of America (AIA) and the Agricultural Research Service (ARS), more than a third of U.S. managed honeybee colonies—those set up for intensified pollination of commercial crops—failed to survive this past winter. Since 2006, the decline of the U.S.’s estimated 2.4 million beehives—commonly referred to as colony collapse disorder (CCD)—has led to the disappearance of hundreds of thousands of colonies: Hives are found empty with honey, larvae, and the queen intact, but with no bees and no trail left behind. The cause remains unknown, but appears to be a combination of factors impacting bee health and increasing their susceptibility to disease. Heavy losses associated with CCD have been found mainly with larger migratory commercial beekeepers, some of whom have lost 50-90 percent of their colonies.
A “keystone” species—one that has a disproportionate effect on the environment relative to its biomass—bees are our key to global food security and a critical part of the food chain. Flowering plants that produce our food depend on insects for pollination. There are other pollinators—butterflies, moths, beetles, flies, and birds—but the honeybee is the most effective, pollinating over 100 commercial crops nationwide, including most fruit, vegetables, and nuts, as well as alfalfa for cattle feed and cotton, with a value estimated between $15-$20 billion annually. As much as one of every three bites of food we eat comes from food pollinated by insects. Without honeybees, our diet would be mostly meatless, consisting of rice and cereals, and we would have no cotton for textiles. The entire ecosystem and the global food economy potentially rests on their wings.
Experts now believe bees are heading for extinction and are racing to pinpoint the culprit, increasingly blaming pesticide usage. U.S. researchers have reported finding 121 different pesticides in samples of bees, wax, and pollen. New parasites, pathogens, fungi, and poor nutrition stemming from intensive farming methods are also part of the equation. Three years ago, U.S. scientists unraveled the genetic code of the honeybee and uncovered the DNA of a virus transmitted by the Varroa mite—Israeli acute paralysis virus (IAPV)—found in almost all of the hives impacted by CCD. Researchers have also found the fungus Nosema ceranae and other pathogens such as chalkbrood in some affected hives throughout the country. Other reported theories include the effects of shifting spring blooms and earlier nectar flow associated with broader global climate and temperature changes, the effects of feed supplements from genetically modified crops, such as high-fructose corn syrup (HFCS), and the effects of cell phone transmissions and radiation from power lines that may be interfering with a bee’s navigational capabilities. (Last year, a study revealed that a contaminant from heat-exposed HFCS might be killing off the bees.) However, according to a recent congressional report on CCD, contributions of these possible factors have not been substantiated.
The industrial bee business and the demands of intensified food production could also be playing a role in the bees’ demise. Widespread migratory stress brought about by increased needs for pollination could be weakening the bees’ immune systems. Most pollination services are provided by commercial migratory beekeepers who travel from state to state and provide pollination services to crop producers. These operations are able to supply a large number of bee colonies during the critical phase of a crop’s bloom cycle, when bees pollinate as they collect nectar. A hive might make five cross-country truck trips each year, chasing crops, and some beekeepers can lose up to 10 percent of their queens during one cross country trip. Bees are overworked and stressed out.
California’s almond crop is a prime example of our reliance on bees’ industriousness for our agriculture success. The state grows 80 percent of the world’s almonds, making it our largest agricultural export and bringing in a whopping $1.9 billion last year. The crop—with nearly 740,000 acres of almond trees planted—uses 1.3 million colonies of bees, approximately one half of all bees in the U.S., and is projected to grow to 1.5 million colonies. The U.S. Department of Agriculture is now predicting that Central Valley almond growers will produce about 1.53 billion pounds of almonds this year, up 8.5 percent last year. To meet the demand, bee colonies are trucked farther and more often than ever before and demand for bees has dramatically outstripped supply. Bee colonies, which a decade ago rented for $60, cost as much as $170 this February in California.
Few organic beekeepers have reported bee losses, suggesting that natural and organic bee keeping methods may be the solution. In addition, organic farmers who maintain wildlife habitat around their farms are helping to encourage bees to pollinate their crops. “The main difference between our farm and our conventional neighbors is the amount of wildlife and insect habitat that we have around the edge of our farm,” said Greg Massa, who manages Massa Organics, a fourth generation 90-acre certified organic rice farm near Chico. Massa started growing organic almonds six years ago, and works with a small, organic beekeeper in Oregon who brings in 30 hives to his farm. Massa’s farm has a large wildlife corridor which has been revegetated with native plants and covered in mustard, wild radish, and vetch, a favorite of bees and also a good nitrogen source for his rice crop.
Time might be running out for the bees, but there are simple actions we can take to make a difference. First, support organic farmers who don’t use pesticides and whose growing methods work in harmony with the natural life of bees. In particular, buy organic almonds. Don’t use pesticides in your home garden, especially at mid-day when bees most likely forage for nectar. You can also plant good nectar sources such as red clover, foxglove, bee balm, and other native plants to encourage bees to pollinate your garden. Provide clean water; even a simple bowl of water is beneficial. Buy local honey; it keeps small, diversified beekeepers in business, and beekeepers keep honeybees thriving. In addition, you can start keeping bees yourself. Backyard and urban beekeeping can actively help bring back our bees. Finally, you can work to preserve more open cropland and rangeland. Let’s use our political voices to support smart land use, the impact of which will not only result in cleaner water, soil, and air, but also just might help save the humble honeybee.


Nonsteroidal anti-inflammatory drugs (NSAIDs) are used to treat pain, fever, and inflammation. Traditional NSAIDs block COX-1 and COX-2 enzymes that the body uses to manufacture substances called prostaglandins. Since COX-1 prostaglandins are stomach-protective, blocking this enzyme is associated with gastrointestinal toxicity, a known side effect of these drugs. Newer NSAIDs (called COX-2 inhibitors) block primarily COX-2 prostaglandins associated with pain, fever, and inflammation, and might be less risky to the stomach. However, this is not proven, and some COX-2s have been taken off the market due to excess risk of heart attacks attributable to their use. Drugs in this family include:
- Aspirin, alternatively called acetylsalicylic acid or ASA (Adprin-B, Anacin, Arthritis Foundation Aspirin, Ascriptin, Aspergum, Asprimox, Bayer, BC, Bufferin, Buffex, Cama, Cope, Easprin, Ecotrin, Empirin, Equagesic, Fiorinal, Fiorital, Halfprin, Heartline, Genprin, Lanorinal, Magnaprin, Measurin, Micrainin, Momentum, Norwich, St. Joseph, Zorprin)
- Celecoxib (Celebrex)
- Choline salicylate (Arthropan)
- Choline salicylate/magnesium salicylate (Tricosal, Trilisate)
- Diclofenac potassium (Cataflam, Voltaren Rapide)
- Diclofenac sodium (Arthrotec, Voltaren, Voltaren SR, Voltaren-XR)
- Diclofenac sodium/misoprostol (Arthrotec)
- Diflunisal (Dolobid)
- Etodolac (Lodine, Lodine XL)
- Fenoprofen calcium (Nalfon)
- Flurbiprofen (Ansaid)
- Ibuprofen (Advil, Arthritis Foundation Ibuprofen, Bayer Select Ibuprofen, Dynafed IB, Genpril, Haltran, IBU, Ibuprin, Ibuprohm, Menadol, Midol IB, Motrin, Nuprin, Saleto)
- Indomethacin (Indochron E-R, Indocin, Indocin SR, Indomethacin, Indomethacin SR, Novo-Methacin)
- Ketoprofen (Actron, Orudis, Orudis KT, Oruvail)
- Ketorolac tromethamine (Toradol)
- Magnesium salicylate (Doan's, Magan, Mobidin, Backache Maximum Strength Relief, Bayer Select Maximum Strength Backache, Momentum Muscular Backache Formula, Nuprin Backache, Mobigesic, Magsal)
- Meclofenamate sodium (Mecolfen, Meclomen)
- Mefenamic acid (Ponstan, Ponstel)
- Nabumetone (Relafen)
- Naproxen (EC-Naprosyn, Napron X, Naprosyn)
- Naproxen sodium (Aleve, Anaprox, Anaprox DS, Naprelan)
- Oxaprozin (Daypro)
- Piroxicam (Feldene)
- Salsalate or salicylic acid (Amigesic, Argesic-SA, Arthra-G, Disalcid, Marthritic, Mono-Gesic, Salflex, Salgesic, Salsitab)
- Sodium salicylate (Pabalate)
- Sodium thiosalicylate (Rexolate)
- Sulfasalazine (Azulfidine EN-tabs, Salazopyrin, SAS-500)
- Sulindac (Clinoril)
- Tolmetin sodium (Tolectin, Tolectin DS)
- and others
Besides reducing pain and inflammation, aspirin and, to a lesser extent, other NSAIDs interfere with cells in the blood called platelets, which facilitate clotting.
Arginine is an amino acid found in many foods, including dairy products, meat, poultry, and fish. Supplemental arginine has been proposed as a treatment for various conditions, including heart problems.
Arginine has been found to stimulate the body's production of gastrin, a hormone that increases stomach acid.
Because excessive acid can irritate the stomach, there are concerns that arginine could be harmful for individuals taking drugs that are also hard on the stomach (such as NSAIDs).
It may be best not to mix arginine with NSAIDs unless approved by your doctor.
The herb feverfew
is primarily used for the prevention and treatment of migraine headaches.
NSAIDs are also used for migraines, so there is a chance that some individuals might use both the herb and drug at once, a combination that may present risks.
The biggest concern with NSAIDs is that they can cause stomach ulcers, which may progress to bleeding or perforation without pain or other warning symptoms. This stomach damage is due to drug interference with the body's protective prostaglandins. Newer NSAIDs called COX-2 inhibitors may be less likely to produce this side effect.
Feverfew also affects prostaglandins.
Thus, combining it with an NSAID might increase the risk of stomach problems.
The herb garlic
is taken to lower cholesterol, among many other proposed uses.
One of the possible side effects of garlic is a decreased ability of the blood to clot, leading to an increased bleeding tendency.
Therefore, you should not combine garlic and aspirin or other NSAIDs except under medical supervision.
The herb ginkgo is used to treat Alzheimer's disease and ordinary age-related memory loss, among many other uses. Some evidence suggests that ginkgo might also decrease the ability of the blood to clot, probably through effects on platelets.
However, one double-blind study found that ginkgo does
increase the anticoagulant effects of aspirin;
another found that while it did not interact with the antiplatelet drug
. But, the herb did interact slightly with the related drug cilostazol.
Taken together, this evidence still suggests that one should not take ginkgo while using aspirin or other NSAIDs except under medical supervision.
A sugarcane-derived form of the supplement policosanol is used to reduce cholesterol levels. It also interferes with platelet clumping, creating potential benefit as well as a risk of interactions with blood-thinning drugs.
For example, a 30-day, double-blind, placebo-controlled trial of 27 individuals with high cholesterol levels found that policosanol at 10 mg daily markedly reduced the ability of blood platelets to clump together.
Another double-blind, placebo-controlled study of 37 healthy volunteers found evidence that the blood-thinning effect of policosanol increased as the dose was increased—the larger the policosanol dose, the greater the effect.
Yet another double-blind placebo-controlled study of 43 healthy volunteers compared the effects of policosanol (20 mg daily), aspirin (100 mg daily), and policosanol and aspirin combined at these same doses.
The results again showed that policosanol substantially reduced the ability of blood platelets to stick together, and that the combined therapy exhibited additive effects.
Based on these findings, it would be advisable to avoid combining aspirin or other NSAIDs with sugarcane policosanol except under medical supervision.
: Beeswax policosanol is substantially different from sugarcane policosanol, and is described separately
PC-SPES is an herbal combination that has shown promise for the treatment of prostate cancer. One case report suggests that PC-SPES might increase risk of bleeding complications if combined with blood-thinning medications.
Subsequent evidence has indicated that PC-SPES contains the strong prescription blood thinner warfarin, making this interaction inevitable.
Potassium citrate and other forms of citrate (for example, calcium citrate, magnesium citrate) may be used to prevent kidney stones. These agents work by making the urine less acidic.
This effect on the urine may lead to decreased blood levels and therapeutic effects of several drugs, including aspirin and other salicylates (choline salicylate, magnesium salicylate, salsalate, sodium salicylate, sodium thiosalicylate).
It may be advisable to avoid these citrate compounds during therapy with aspirin or salicylates except under medical supervision.
One study suggests that reishi impairs platelet clumping.
This creates the potential for an interaction with any blood-thinning medication.
Dong QuaiSt. John's Wort
St. John's wort
is primarily used to treat mild to moderate depression.
The herb dong quai
is often recommended for menstrual disorders such as dysmenorrhea, PMS, and irregular menstruation.
Certain NSAIDs, including most notably piroxicam, can cause increased sensitivity to the sun, amplifying the risk of sunburn or skin rash. Because St. John's wort and dong quai may also cause this problem, taking these herbal supplements during NSAID therapy might add to this risk.
It may be a good idea to wear a sunscreen or protective clothing during sun exposure if you take one of these herbs while using an NSAID.
The substance vinpocetine is sold as a dietary supplement for the treatment of age-related memory loss and impaired mental function.
Vinpocetine is thought to inhibit blood platelets from forming clots.
For this reason, it should not be combined with medications or natural substances that impair the blood’s ability to clot normally, as this may lead to excessive bleeding. One study found only a minimal interaction between the blood-thinning drug warfarin (Coumadin) and vinpocetine, but prudence dictates caution anyway.
Vitamin E appears to add to aspirin's blood-thinning effects. One study suggests that the combination of aspirin and even relatively small amounts of vitamin E (50 mg daily) may lead to a significantly increased risk of bleeding.
In another study of 28,519 men, vitamin E supplementation at a low dose of about 50 IU (international units) daily was associated with an increase in fatal hemorrhagic strokes, the kind of stroke caused by bleeding within the brain.
However, there was a reduced risk of the more common ischemic stroke, caused by obstruction of a blood vessel in the brain, and the two effects were found essentially to cancel each other out.
Weak evidence from one animal study hints that vitamin E might reduce stomach inflammation caused by NSAIDs.
The bottom line: Seek medical advice before combining vitamin E and aspirin.
The herb white willow
, also known as willow bark, is used to treat pain and fever.
White willow contains a substance that is converted by the body into a salicylate similar to aspirin. It is therefore possible that taking NSAIDs and white willow could lead to increased risk of side effects, just as would occur if you combined NSAIDs with aspirin.
Based on their known effects or constituents, the herbs
dong quai(Angelica sinensis)
horse chestnut(Aesculus hippocastanum)
red clover(Trifolium pratense)
, and the substances
(oligomeric proanthocyanidins) might conceivably present an increased risk of bleeding if combined with aspirin.
Potassium citrate, sodium citrate, and potassium-magnesium citrate are sometimes used to prevent
. These supplements reduce urinary acidity and can, therefore, lead to decreased blood levels and effectiveness of NSAIDs.
) and other hot peppers used in chili and various dishes contain as their "hot" ingredient capsaicin, a substance that is thought to be stomach-protective.
For years, people have believed that spicy foods were a cause of stomach ulcers. However, preliminary evidence suggests that cayenne peppers might actually help protect the stomach against ulcers caused by aspirin and possibly other NSAIDs.
In a study involving 18 healthy human volunteers, one group received chili powder, water, and aspirin; the control group received only water and aspirin.
Chili powder was found to significantly protect the stomach against damage from aspirin, a known stomach irritant. It was suggested that this protective effect might result from capsaicin-induced stimulation of blood flow in the lining of the stomach.
Further support for this theory comes from a study in rats, which found that capsaicin protected the stomach against damage caused by aspirin, ethanol (drinking alcohol), and acid.
Increasing the dose of capsaicin brought even greater benefit, as did increasing the time between giving capsaicin and the other agents. An earlier study in rats found that capsaicin exerted similar protection against aspirin damage.
Some researchers have used this data to advocate chili or capsaicin as treatment for peptic ulcer disease,
but check with your doctor before trying to self-treat this serious condition.
Colostrum is the fluid that new mothers' breasts produce during the first day or two after birth. It gives newborns a rich mixture of antibodies and growth factors that help them get a good start.
According to one study involving rats, taking colostrum from cows (bovine colostrum) as a supplement might help protect against the ulcers caused by NSAIDs.
Folate (also known as folic acid) is a B vitamin that plays an important role in many vital aspects of health, including preventing neural tube birth defects and possibly reducing the risk of heart disease. Because inadequate intake of folate is widespread, if you are taking any medication that depletes or impairs folate even slightly, you may need supplementation.
There is some evidence that NSAIDs might produce this effect. In test tube studies, many NSAIDs have been found to interfere with folate activity.
In addition, a study of 25 people with arthritis receiving the drug sulfasalazine found evidence of folate deficiency.
In another report, a woman taking 650 mg of aspirin every 4 hours for 3 days experienced a significant fall in blood levels of folate.
Based on this preliminary evidence, folate supplementation may be warranted if you are taking drugs in the NSAID family.
Licorice root (
), a member of the pea family, has been used since ancient times as both food and medicine.
Preliminary evidence suggests that a specific form of licorice called DGL (deglycyrrhizinated licorice) might help protect the stomach against damage caused by the use of aspirin and possibly other NSAIDs. (DGL is a modified version of licorice that is safer to use.)
In a double-blind study of 9 healthy human volunteers, participants were given aspirin alone (325 mg) or aspirin (325 mg) plus DGL (175 mg).
Stomach damage (as measured by blood loss) was found to be about 20% less when DGL was given with aspirin. As part of the same study, DGL was also found to reduce stomach damage caused by aspirin in rats, though the benefit was small. It is possible that larger doses of DGL might provide greater protection.
Test tube studies suggest that aspirin promotes the loss of vitamin C through the urine,
which could lead to tissue depletion of the vitamin. In addition, low vitamin C levels have been noted in individuals with rheumatoid arthritis, and this has been attributed to aspirin therapy taken for this condition.
If you take aspirin regularly, vitamin C supplementation may be advisable.
The supplement policosanol is a mixture of numerous related substances, and its exact composition varies with its source. Policosanol made from sugar cane appears to reduce cholesterol levels. Policosanol from beeswax may help protect the stomach from damage caused by NSAIDs. However, it is not clear whether beeswax policosanol might amplify the "blood thinning" effect of anti-inflammatory drugs in the same manner as sugarcane policosanol, as described
Based on chondroitin’s chemical similarity to the anticoagulant drug heparin, it has been suggested that chondroitin might have anticoagulant effects as well. There are no case reports of any problems relating to this, and studies suggest that chondroitin has at most a mild anticoagulant effect.
Nonetheless, prudence suggests that chondroitin should not be combined with NSAIDs except under physician supervision.


Socrates, an Athenian Greek of the second half of the fifth century bc, wrote no philosophical works but was uniquely influential in the later history of philosophy. His philosophical interests were restricted to ethics and the conduct of life, topics which thereafter became central to philosophy. He discussed these in public places in Athens, sometimes with other prominent intellectuals or political leaders, sometimes with young men, who gathered round him in large numbers, and other admirers. Among these young men was Plato. Socrates' philosophical ideas and - equally important for his philosophical influence - his personality and methods as a 'teacher' were handed on to posterity in the 'dialogues' that several of his friends wrote after his death, depicting such discussions. Only those of Xenophon (Memorabilia,Apology, Symposium) and the early dialogues of Plato survive (for example Euthyphro, Apology, Crito). Later Platonic dialogues such as Phaedo, Symposium and Republic do not present the historical Socrates' ideas; the 'Socrates' appearing in them is a spokesman for Plato's own ideas.
Socrates' discussions took the form of face-to-face interrogations of another person. Most often they concerned the nature of some moral virtue, such as courage or justice. Socrates asked what the respondent thought these qualities of mind and character amounted to, what their value was, how they were acquired. He would then test their ideas for logical consistency with other highly plausible general views about morality and goodness that the respondent also agreed to accept, once Socrates presented them. He succeeded in showing, to his satisfaction and that of the respondent and any bystanders, that the respondent's ideas were not consistent. By this practice of 'elenchus' or refutation he was able to prove that politicians and others who claimed to have 'wisdom' about human affairs in fact lacked it, and to draw attention to at least apparent errors in their thinking. He wanted to encourage them and others to think harder and to improve their ideas about the virtues and about how to conduct a good human life. He never argued directly for ideas of his own, but always questioned those of others. None the less, one can infer, from the questions he asks and his attitudes to the answers he receives, something about his own views.
Socrates was convinced that our souls - where virtues and vices are found - are vastly more important for our lives than our bodies or external circumstances. The quality of our souls determines the character of our lives, for better or for worse, much more than whether we are healthy or sick, or rich or poor. If we are to live well and happily, as he assumed we all want to do more than we want anything else, we must place the highest priority on the care of our souls. That means we must above all want to acquire the virtues, since they perfect our souls and enable them to direct our lives for the better. If only we could know what each of the virtues is we could then make an effort to obtain them. As to the nature of the virtues, Socrates seems to have held quite strict and, from the popular point of view, paradoxical views. Each virtue consists entirely in knowledge, of how it is best to act in some area of life, and why: additional 'emotional' aspects, such as the disciplining of our feelings and desires, he dismissed as of no importance. Weakness of will is not psychologically possible: if you act wrongly or badly, that is due to your ignorance of how you ought to act and why. He thought each of the apparently separate virtues amounts to the same single body of knowledge: the comprehensive knowledge of what is and is not good for a human being. Thus his quest was to acquire this single wisdom: all the particular virtues would follow automatically.
At the age of 70 Socrates was charged before an Athenian popular court with 'impiety' - with not believing in the Olympian gods and corrupting young men through his constant questioning of everything. He was found guilty and condemned to death. Plato's Apology, where Socrates gives a passionate defence of his life and philosophy, is one of the classics of Western literature. For different groups of later Greek philosophers he was the model both of a sceptical inquirer who never claims to know the truth, and of a 'sage' who knows the whole truth about human life and the human good. Among modern philosophers, the interpretations of his innermost meaning given by Montaigne, Hegel, Kierkegaard, and Nietzsche are especially notable.
Socrates, an Athenian citizen proud of his devotion to Athens, lived his adult life there engaging in open philosophical discussion and debate on fundamental questions of ethics, politics, religion and education. Going against the grain of the traditional education, he insisted that personal investigation and reasoned argument, rather than ancestral custom, or appeal to the authority of Homer, Hesiod and other respected poets, was the only proper basis for answering these questions. His emphasis on argument and logic and his opposition to unquestioning acceptance of tradition allied him with such Sophists of a generation earlier as Protagoras, Gorgias and Prodicus, none of whom was an Athenian, but all of whom spent time lecturing and teaching at Athens (see Sophists). Unlike these Sophists Socrates did not formally offer himself or accept pay as a teacher. But many upper-class young Athenian men gathered round him to hear and engage in his discussions, and he had an inspirational and educational effect upon them, heightening their powers of critical thought and encouraging them to take seriously their individual responsibility to think through and decide how to conduct their lives. Many of his contemporaries perceived this education as morally and socially destructive - it certainly involved subverting accepted beliefs - and he was tried in 399 bc before an Athenian popular court and condemned to death on a charge of 'impiety': that he did not believe in the Olympian gods, but in new ones instead, and corrupted the young. Scholars sometimes mention specifically political motives of revenge, based on guilt by association: a number of prominent Athenians who were with Socrates as young men or were close friends did turn against the Athenian democracy and collaborated with the Spartans in their victory over Athens in the Peloponnesian war. But an amnesty passed by the restored democracy in 403 bc prohibited prosecution for political offences before that date. The rhetorician Polycrates included Socrates' responsibility for these political crimes in his Accusation of Socrates (see Xenophon, Memorabilia I 2.12), a rhetorical exercise written at least five years after Socrates' death. But there is no evidence that, in contravention of the amnesty, Socrates' actual accusers covertly attacked him, or his jurors condemned him, on that ground. The defences Plato and Xenophon constructed for Socrates, each in his respective Apology, imply that it was his own questioning mind and what was perceived as the bad moral influence he had on his young men that led to his trial and condemnation.
Socrates left no philosophical works, and apparently wrote none. His philosophy and personality were made known to later generations through the dialogues that several of his associates wrote with him as principal speaker (see Socratic dialogues). Only fragments survive of those by Aeschines of Sphettus and Antisthenes, both Athenians, and Phaedo of Elis (after whom Plato's dialogue Phaedo is named). Our own knowledge of Socrates depends primarily on the dialogues of Plato and the Socratic works of the military leader and historian Xenophon. Plato was a young associate of Socrates' during perhaps the last ten years of his life, and Xenophon knew him during that same period, though he was absent from Athens at the time of Socrates' death and for several years before and many years after.
We also have secondary evidence from the comic playwright Aristophanes and from Aristotle. Aristotle, although born fifteen years after Socrates' death, had access through Plato and others to first-hand information about the man and his philosophy. Aristophanes knew Socrates personally; his Clouds (first produced c.423 bc) pillories the 'new' education offered by Sophists and philosophers by showing Socrates at work in a 'thinkery', propounding outlandish physical theories and teaching young men how to argue cleverly in defence of their improper behaviour. It is significant that in 423, when Socrates was about 45 years old, he could plausibly be taken as a leading representative in Athens of the 'new' education. But one cannot expect a comic play making fun of a whole intellectual movement to contain an authentic account of Socrates' specific philosophical commitments.
However, the literary genre to which Plato's and Xenophon's Socratic works belong (along with the other, lost dialogues) also permits the author much latitude; in his Poetics Aristotle counts such works as fictions of a certain kind, alongside epic poems and tragedies. They are by no means records of actual discussions (despite the fact that Xenophon explicitly so represents his). Each author was free to develop his own ideas behind the mask of Socrates, at least within the limits of what his personal experience had led him to believe was Socrates' basic philosophical and moral outlook. Especially in view of the many inconsistencies between Plato's and Xenophon's portraits (see §7 below), it is a difficult question for historical-philosophical interpretation whether the philosophical and moral views the character Socrates puts forward in any of these dialogues can legitimately be attributed to the historical philosopher. The problem of interpretation is made more difficult by the fact that Socrates appears in many of Plato's dialogues - ones belonging to his middle and later periods (see Plato §§10-16) - discussing and expounding views that we have good reason to believe resulted from Plato's own philosophical investigations into questions of metaphysics and epistemology, questions that were not entered into at all by the historical Socrates. To resolve this problem - what scholars call the 'Socratic problem' - most agree in preferring Plato to Xenophon as a witness. Xenophon is not thought to have been philosopher enough to have understood Socrates well or to have captured the depth of his views and his personality. As for Plato, most scholars accept only the philosophical interests and procedures, and the moral and philosophical views, of the Socrates of the early dialogues, and, more guardedly, the Socrates of 'transitional' ones such as Meno and Gorgias, as legitimate representations of the historical personage. These dialogues are the ones that predate the emergence of the metaphysical and epistemological inquiries just referred to. However, even Plato's early dialogues are philosophical works written to further Plato's own philosophical interests. That could produce distortions, also; and Xenophon's relative philosophical innocence could make his portrait in some respects more reliable. Moreover, it is possible, even probable, that in his efforts to help his young men improve themselves Socrates spoke differently to the philosophically more promising ones among them - including Plato - from the way he spoke to others, for example Xenophon. Both portraits could be true, but partial and needing to be combined (see §7). The account of Socrates' philosophy given below follows Plato, with caution, while giving independent weight also to Xenophon and to Aristotle.
Xenophon's Apology of Socrates, Symposium and Memorabilia (or Memoirs) may well reflect knowledge of Plato's own Apology and some of his early and middle period dialogues, as well as lost dialogues of Antisthenes and others. Xenophon composed the Memorabilia over many years, beginning only some ten years after Socrates' death, avowedly in order to defend Socrates' reputation as a good man, a true Athenian gentleman, and a good influence upon his young men. The same intention motivated hisApology and Symposium. Anything these works contain about Socrates' philosophical opinions and procedures is ancillary to that apologetic purpose. Plato's Apology, of course, is similarly apologetic, but it and his other early dialogues are carefully constructed discussions, strongly focused upon questions of philosophical substance. Plato evidently thought Socrates' philosophical ideas and methods were central to his life and to his mission. Xenophon's and Plato's testimony are agreed that Socrates' discussions consistently concerned the aretai, the recognized 'virtues' or excellences of character (see Aret), such as justice, piety, self-control or moderation (sophrosyn), courage and wisdom; what these individual characteristics consist in and require of a person, what their value is, and how they are acquired, whether by teaching or in some other way. In his Apology and elsewhere Plato has Socrates insist that these discussions were always inquiries, efforts made to engage his fellow-discussants in coming jointly to an adequate understanding of the matters inquired into. He does not himself know, and therefore cannot teach anyone else - whether by means of these discussions or in some other way - either how to be virtuous or what virtue in general or any particular virtue is. Furthermore, given his general characterization of virtue (see §§4-5), Plato's Socrates makes a point of suggesting the impossibility in principle of teaching virtue at all, by contrast with the Sophists who declared they could teach it. Virtue was not a matter of information about living or rote techniques of some sort to be handed on from teacher to pupil, but required an open-ended personal understanding that individuals could only come to for themselves. Xenophon, too, reports that Socrates denied he was a teacher of aret, but he pays no attention to such issues of philosophical principle. He does not hesitate to show Socrates speaking of himself as a teacher (see Apology 26, Memorabilia I 6.13-14), and describes him as accepting young men from their fathers as his pupils (but not for a fee), and teaching them the virtues by displaying his own virtues to them for emulation, as well as through conversation and precepts. Perhaps Socrates did not insist on holding to strict philosophical principles in dealing with people on whom their point would have been lost.
In his Apology Plato's Socrates traces his practice of spending his days discussing and inquiring about virtue to an oracle delivered at the shrine of Apollo at Delphi. Xenophon also mentions this oracle in his Apology. A friend of Socrates', Chaerephon, had asked the god whether anyone was wiser than Socrates; the priestess answered that no one was. Because he was sure he was not wise at all - only the gods, he suspected, could actually know how a human life ought to be led - Socrates cross-examined others at Athens with reputations for that kind of wisdom. He wanted to show that there were people wiser than he and thus discover the true meaning of the oracle - Apollo was known to speak in riddles requiring interpretation to reach their deeper meaning. In the event, it turned out that the people he examined were not wise, since they could not even give a self-consistent set of answers to his questions: obviously, true knowledge requires at least that one think and speak consistently on the subjects one professes to know. So he concluded that the priestess's reply had meant that of all those with reputations for wisdom only he came close to deserving it; he wisely did not profess to know these things that only gods can know, and that was wisdom enough for a human being. Because only he knew that he did not know, only he was ready earnestly to inquire into virtue and the other ingredients of the human good, in an effort to learn. He understood therefore that Apollo's true intention in the oracle had been to encourage him to continue his inquiries, to help others to realize that it is beyond human powers actually to know how to live - that is the prerogative of the gods - and to do his best to understand as far as a human being can how one ought to live. The life of philosophy, as led by him, was therefore something he was effectively ordered by Apollo to undertake.
We must remember that Socrates was on trial on a charge of 'impiety'. In tracing his philosophical vocation back to Apollo's oracle, and linking it to a humble recognition of human weakness and divine perfection, he was constructing a powerful rebuttal of the charges brought against him. But it cannot be literally true - if that is what he intended to say - that Socrates began his inquiries about virtue only after hearing of the oracle. Chaerephon's question to Apollo shows he had established a reputation in Athens for wisdom before that. That reputation cannot have rested on philosophical inquiries of another sort. In Plato's Phaedo Socrates says he had been interested as a young man in philosophical speculations about the structure and causes of the natural world, but he plainly did not take those interests very far; and in any event, his reputation was not for that kind of wisdom, but wisdom about how to lead a human life. In fact we do not hear of the duty to Apollo in Xenophon, or in other dialogues of Plato, where we might expect to find it if from the beginning Socrates thought Apollo had commanded his life of philosophizing. However, we need not think Socrates was false to the essential spirit of philosophy as he practised it if in looking back on his life under threat of condemnation for impiety he chose, inaccurately, to see it as initially imposed on him by Apollo's oracle.
Despite its impressiveness, Socrates' speech failed to convince his jury of 501 male fellow citizens, and he died in the state prison by drinking hemlock as required by law. His speech evidently offended the majority of the jurors by its disdain for the charges and the proceedings; Xenophon explains his lofty behaviour, which he thinks would otherwise have been lunatic - and damaging to his reputation - by reporting that he had told friends in advance that as a 70-year-old still in possession of his health and faculties it was time for him to die anyhow, before senility set in. Furthermore, his 'divine sign' - the 'voice' he sometimes heard warning him for his own good against a contemplated course of action - had prevented him from spending time crafting a defence speech. (This voice seems to have been the basis for the charge of introducing 'new' gods.) So he would do nothing to soften his manner in order to win his freedom. Even if this story is true, Plato could be right that Socrates put on a spirited, deeply serious defence of his life and beliefs - one that he thought should have convinced the jurors of his innocence, if only they had judged him intelligently and fairly.
In cross-examining those with reputations for wisdom about human affairs and showing their lack of it, Socrates employed a special method of dialectical argument that he himself had perfected, the method of 'elenchus' - Greek for 'putting to the test' or 'refutation'. He gives an example at his trial when he cross-examines Meletus, one of his accusers (Plato, Apology 24d-27e). The respondent states a thesis, as something he knows to be true because he is wise about the matter in question. Socrates then asks questions, eliciting clarifications, qualifications and extensions of the thesis, and seeking further opinions of the respondent on related matters. He then argues, and the respondent sees no way not to grant, that the original thesis is logically inconsistent with something affirmed in these further responses. For Socrates, it follows at once that the respondent did not know what he was talking about in stating his original thesis: true knowledge would prevent one from such self-contradiction. So the respondent suffers a personal set-back; he is refuted - revealed as incompetent. Meletus, for example, does not have consistent ideas about the gods or what would show someone not to believe in them, and he does not have consistent ideas about who corrupts the young, and how; so he does not know what he is talking about, and no one should take his word for it that Socrates disbelieves in the gods or has corrupted his young men. In many of his early dialogues Plato shows Socrates using this method to examine the opinions of persons who claim to be wise in some matter: the religious expert Euthyphro on piety (Euthyphro), the generals Laches and Nicias on courage (Laches), the Sophist Protagoras on the distinctions among the virtues and whether virtue can be taught (Protagoras), the rhapsodist Ion on what is involved in knowing poetry (Ion), the budding politician Alcibiades on justice and other political values (Alcibiades), the Sophist Hippias on which was the better man, Odysseus or Achilles (Lesser Hippias), and on the nature of moral and aesthetic beauty (Greater Hippias). They are all refuted - shown to have mutually inconsistent ideas on the subject discussed (see Plato §§4, 6, 8-9).
But Socrates is not content merely to demonstrate his interlocutor's lack of wisdom or knowledge. That might humiliate him into inquiring further or seeking by some other means the knowledge he has been shown to lack, instead of remaining puffed up with self-conceit. That would be a good thing. But Socrates often also indicates clearly that his cross-examination justifies him and the interlocutor in rejecting as false the interlocutor's original thesis. Logically, that is obviously wrong: if the interlocutor contradicts himself, at least one of the things he has said must be false (indeed, all of them could be), but the fact alone of self-contradiction does not show where the falsehood resides. For example, when Socrates leads Euthyphro to accept ideas that contradict his own definition of the pious as whatever pleases all the gods, Socrates concludes that that definition has been shown to be false (Euthyphro 10d-11a), and asks Euthyphro to come up with another one. He does not usually seem to consider that perhaps on further thought the additional ideas would seem faulty and so merit rejection instead.
Socrates uses his elenctic method also in discussion with persons who are not puffed up with false pride, and are quite willing to admit their ignorance and to reason out the truth about these important matters. Examples are his discussions with his long-time friend Crito on whether he should escape prison and set aside the court's death sentence (Plato, Crito), and with the young men Charmides, on self-control (Charmides), and Lysis and Menexenus, on the nature of friendship (Lysis). Socrates examines Crito's proposal that he escape on the basis of principles that he presents to him for his approval, and he, together with Crito (however half-heartedly), rejects it when it fails to be consistent with them. And he examines the young men's successive ideas about these virtues, rejecting some of them and refining others, by relying on their own acceptance of further ideas that he puts to them. Again, he is confident that the inconsistencies brought to light in their ideas indicate the inadequacy of their successive proposals as to the nature of the moral virtue in question.
In many of his discussions, both with young men and the allegedly wise, Socrates seeks to know what some morally valuable property is - for example, piety, courage, self-control or friendship (see §5). Rejecting the idea that one could learn this simply from attending to examples, he insisted on an articulated 'definition' of the item in question - some single account that would capture all at once the presumed common feature that would entitle anything to count as a legitimate instance. Such a definition, providing the essence of the thing defined, would give us a 'model' or 'paradigm' to use in judging whether or not some proposed action or person possesses the moral value so defined (Euthyphro 6d-e). Aristotle says (in Metaphysics I, 6) that Socrates was the first to interest himself in such 'universal definitions', and traces to his interest in them Plato's first impetus towards a theory of Forms, or 'separated' universals (see Plato §10).
In none of his discussions in Plato's early works does Socrates profess to think an adequate final result has actually been established - about the nature of friendship, or self-control, or piety, or any of the other matters he inquires about. Indeed, on the contrary, these works regularly end with professions of profound ignorance about the matter under investigation. Knowledge is never attained, and further questions always remain to be considered. But Socrates does plainly think that progress towards reaching final understanding has taken place (even if only a god, and no human being, could ever actually attain it). Not only has one discovered some things that are definitely wrong to say; one has also achieved some positive insights that are worth holding onto in seeking further systematic understanding. Given that Socrates' method of discussion is elenctic throughout, what does he think justifies this optimism?
On balance, our evidence suggests that Socrates had worked out no elaborate theory to support him here. The ideas he was stimulated to propound in an elenctic examination which went against some initial thesis seemed to him, and usually also to the others present, so plausible, and so supportable by further considerations, that he and they felt content to reject the initial thesis. Until someone came up with arguments to neutralize their force, it seemed the thesis was doomed, as contrary to reason itself. Occasionally Socrates expresses himself in just those terms: however unpalatable the option might seem, it remains open to someone to challenge the grounds on which his conclusions rest (see Euthyphro 15c, Gorgias 461d-462a, 509a, Crito 54d). But until they do, he is satisfied to treat his and his interlocutor's agreement as a firm basis for thought and action. Later, when Plato himself became interested in questions of philosophical methodology in his Meno, this came to seem a philosophically unsatisfactory position; Plato's demand for justification for one's beliefs independent of what seemed on reflection most plausible led him to epistemological and metaphysical inquiries that went well beyond the self-imposed restriction of Socratic philosophy to ethical thought in the broadest sense. But Socrates did not raise these questions. In this respect more bound by traditional views than Plato, he had great implicit confidence in his and his interlocutors' capacity, after disciplined dialectical examination of the issues, to reach firm ground for constructing positive ideas about the virtues and about how best to lead a human life - even if these ideas never received the sort of final validation that a god, understanding fully the truth about human life, could give them.
The topics Socrates discussed were always ethical, and never included questions of physical theory or metaphysics or other branches of philosophical study. Moreover, he always conducted his discussions not as theoretical inquiries but as profoundly personal moral tests. Questioner and interlocutor were equally putting their ways of life to what Socrates thought was the most important test of all - their capacity to stand up to scrutiny in rational argument about how one ought to live. In speaking about human life, he wanted his respondents to indicate what they truly believed, and as questioner he was prepared to do the same, at least at crucial junctures. Those beliefs were assumed to express not theoretical ideas, but the very ones on which they themselves were conducting their lives. In losing an argument with Socrates you did not merely show yourself logically or argumentatively deficient, but also put into question the very basis on which you were living. Your way of life might ultimately prove defensible, but if you cannot now defend it successfully, you are not leading it with any such justification. In that case, according to Socrates' views, your way of life is morally deficient. Thus if Menexenus, Lysis and Socrates profess to value friendship among the most important things in life and profess to be one another's friends, but cannot satisfactorily explain under pressure of elenctic investigation what a friend is, that casts serious doubt on the quality of any 'friendship' they might form (Plato, Lysis 212a, 223b). Moral consistency and personal integrity, and not mere delight in argument and logical thought, should therefore lead you to repeated elenctic examination of your views, in an effort to render them coherent and at the same time defensible on all sides through appeal to plausible arguments. Or, if some of your views have been shown false, by conflicting with extremely plausible general principles, it behoves you to drop them - and so to cease living in a way that depends upon accepting them. In this way, philosophical inquiry via the elenchus is fundamentally a personal moral quest. It is a quest not just to understand adequately the basis on which one is actually living, and the personal and moral commitments that this contains. It is also a quest to change the way one lives as the results of argument show one ought to, so that, at the logical limit of inquiry, one's way of life would be completely vindicated. Accordingly, Socrates in Plato's dialogues regularly insists on the individual and personal character of his discussions. He wants to hear the views of the one person with whom he is speaking. He dismisses as of no interest what outsiders or most people may think - provided that is not what his discussant is personally convinced is true. The views of 'the many' may well not rest on thought or argument at all. Socrates insists that his discussant shoulder the responsibility to explain and defend rationally the views he holds, and follow the argument - reason - wherever it may lead.
We learn a good deal about Socrates' own principles from both Plato and Xenophon. Those were ones that had stood up well over a lifetime of frequent elenctic discussions and had, as he thought, a wealth of plausible arguments in their favour. Foremost is his conviction that the virtues - self-control, courage, justice, piety, wisdom and related qualities of mind and soul - are essential if anyone is to lead a good and happy life. They are good in themselves for a human being, and they guarantee a happy life, eudaimonia - something that he thought all human beings always wanted, and wanted more than anything else. The virtues belong to the soul - they are the condition of a soul that has been properly cared for and brought to its best state. The soul is vastly more important for happiness than are health and strength of the body or social and political power, wealth and other external circumstances of life; the goods of the soul, and pre-eminently the virtues, are worth far more than any quantity of bodily or external goods. Socrates seems to have thought these other goods are truly good, but they only do people good, and thereby contribute to their happiness, under the condition that they are chosen and used in accordance with virtues indwelling in their souls (see Plato, Apology 30b, Euthydemus 280d-282d, Meno 87d-89a).
More specific principles followed. Doing injustice is worse for oneself than being subjected to it (Gorgias 469c-522e): by acting unjustly you make your soul worse, and that affects for the worse the whole of your life, whereas one who treats you unjustly at most harms your body or your possessions but leaves your soul unaffected. On the same ground Socrates firmly rejected the deeply entrenched Greek precept to aid one's friends and harm one's enemies, and the accompanying principle of retaliation, which he equated with returning wrongs for wrongs done to oneself and one's friends (Crito 49a-d). Socrates' daily life gave witness to his principles. He was poor, shabbily dressed and unshod, and made do with whatever ordinary food came his way: such things matter little. Wealth, finery and delicacies for the palate are not worth panting after and exerting oneself to enjoy. However, Socrates was fully capable of relishing both refined and plain enjoyments as occasion warranted (see §7).
The Greeks recognized a series of specially prized qualities of mind and character as aretai or virtues. Each was regarded as a distinct, separate quality: justice was one thing, concerned with treating other people fairly, courage quite another, showing itself in vigorous, correct behaviour in circumstances that normally cause people to be afraid; and self-control or moderation, piety and wisdom were yet others. Each of these ensured that its possessor would act in some specific ways, regularly and reliably over their lifetime, having the justified conviction that those are ways one ought to act - agathon (good) and kalon (fine, noble, admirable or beautiful) ways of acting. But each type of virtuous person acts rightly and well not only in regularly recurring, but also in unusual and unheralded, circumstances; the virtue involves always getting something right about how to live a good human life. Socrates thought these virtues were essential if one was to live happily (see §4). But what exactly were they? What was it about someone that made them just, or courageous, or wise? If you did not know that, you would not know what to do in order to acquire those qualities. Furthermore, supposing you did possess a virtue, you would have to be able to explain and defend by argument the consequent ways in which you lived - otherwise your conviction that those are ways one ought to act would be shallow and unjustified. And in order to do that you would have to know what state of mind the virtue was, since that is essential to them (see Plato, Charmides 158e-159a). Consequently, in his discussions Socrates constantly asked for 'definitions' of various virtues: what is courage (Laches); what is self-control or moderation (Charmides), what is friendship (Lysis) and what is piety (Euthyphro). As this context shows, he was asking not for a 'dictionary definition', an account of the accepted linguistic understanding of a term, but for an ethically defensible account of an actual condition of mind or character to which the word in common use would be correctly applied. In later terminology, he was seeking a 'real' rather than a 'nominal' definition (see Definition; Plato §§6-9).
Socrates objected to definitions that make a virtue some external aspect of a virtuous action (such as the manner in which it is done - for example its 'quiet' or measured quality in the case of moderation, Charmides 160b-d), or simply the doing of specific types of action, described in terms of their external circumstances (such as, for courage, standing one's ground in battle; Laches 190e-191d). He also objected to more psychological definitions that located a virtue in some non-rational and non-cognitive aspect of the soul (for example, in the case of courage, the soul's endurance or strength of resistance) (Laches 192d-193e). For his own part, he regularly shows himself ready to accept only definitions that identify a virtue with some sort of knowledge or wisdom about what is valuable for a human being. That 'intellectualist' expectation about the nature of virtue, although never worked out to his satisfaction in any Platonic dialogue, is central to Socrates' philosophy.
Given that in his discussions he is always the questioner, probing the opinions of his respondent and not arguing for views of his own, we never find Socrates stating clearly what led him to this intellectualism. Probably, however, it was considerations drawn from the generally agreed premise that each virtue is a condition motivating certain voluntary actions, chosen because they are good and fine or noble. He took it that what lies behind and produces any voluntary action is the idea under which it is done, the conception of the action in the agent's mind that makes it seem the thing to do just then. If so, each virtue must be some state of the mind, the possessor of which constantly has certain distinctive general ideas about how one ought to behave. Furthermore, since virtues get this right, these are true ideas. And since a virtuous person acts well and correctly in a perfectly reliable way, they must be seated so deeply in the mind as to be ineradicable and unwaveringly present. The only state of mind that meets these conditions is knowledge: to know a subject is not just to be thoroughly convinced, but to have a deep, fully articulated understanding, being ready with explanations to fend off objections and apparent difficulties and to extend old principles into new situations, and being prepared to show with the full weight of reason precisely why each thing falling under it is and must be so. Each virtue, then, must be knowledge about how one ought to behave in some area of life, and why - a knowledge so deep and rationally secure that those who have it can be counted upon never to change their minds, never to be argued out of or otherwise persuaded away from, or to waver in, their conviction about how to act.
In Plato's Protagoras Socrates goes beyond this, and identifies himself with the position, rejected by Protagoras in their discussion, that the apparently separate virtues of justice, piety, self-control, courage and wisdom are somehow one and the same thing - some single knowledge (361a-b). Xenophon too confirms that Socrates held this view (Memorabilia III 9.5). Protagoras defends the position that each of the virtues is not only a distinct thing from each of the others, but so different in kind that a person could possess one of them without possessing the others (329d-e). In opposing him, Socrates sometimes speaks plainly of two allegedly distinct virtues being 'one' (333b). Given this unity of the virtues, it would follow that a person could not possess one without having them all. And in speaking of justice and piety in particular, Socrates seems to go further, to imply that every action produced by virtue is equally an instance of all the standardly recognized virtues: pious as well as just, wise and self-controlled and courageous also. Among his early dialogues, however, Plato's own philosophical interests show themselves particularly heavily in the Protagoras, so it is doubtful how far the details of his arguments are to be attributed to the historical Socrates. The issues raised by Socrates in the Protagoras were, none the less, vigorously pursued by subsequent 'Socratic' philosophers (as Plutarch's report in On Moral Virtue 2 demonstrates). And the positions apparently adopted by Plato's Socrates were taken up and ingeniously defended by the Stoic philosopher Chrysippus (see Stoicism §16). As usual, because of his questioner's role, it is difficult to work out Socrates' grounds for holding to the unity of virtue; and it is difficult to tell whether, and if so how, he allowed that despite this unity there were some real differences between, say, justice and self-control, or courage and piety. Apparently he thought the same body of knowledge - knowledge of the whole of what is and is not good for human beings, and why it is so or not - must at least underlie the allegedly separate virtues. If you did not have that vast, comprehensive knowledge you could not be in the state of mind which is justice or in that which is courage, and so on; and if you did have it you would necessarily be in those states of mind. It seems doubtful whether Socrates himself progressed beyond that point. Efforts to do that were made by Chrysippus and the other philosophers referred to above. And despite denying that all virtues consist in knowledge, Plato in the Republic and Aristotle in Nicomachean Ethics VI follow Socrates to the extent of holding, in different ways, that you need to have all the virtues in order to have any one.
In Plato's Protagoras Socrates also denies the possibility of weakness of will - being 'mastered' by some desire so as to act voluntarily in a way one knows is wrong or bad (see also Xenophon, Memorabilia III 9.4, IV 5.6.) All voluntary wrongdoing or bad action is due to ignorance of how one ought to act and why, and to nothing else. This would be easy to understand if Socrates were using 'knowing' quite strictly, to refer to the elevated and demanding sort of knowledge described in §5 (sometimes called 'Socratic knowledge'). Someone could know an action was wrong or bad, with full 'Socratic knowledge', only if they were not just thoroughly convinced, but had a deep, fully articulated understanding, being ready with explanations to fend off objections and apparent difficulties, and prepared to show precisely why it was so. That would mean that these ideas were seated so deeply in the mind as to be ineradicable and unwaveringly present. Accordingly, a person with 'Socratic knowledge' could not come to hold even momentarily that the action in question would be the thing to do, and so they could never do it voluntarily.
However, Plato's Socrates goes further. He explains his denial of weak-willed action by saying that a person cannot voluntarily do actions which, in doing them, they even believe to be a wrong or bad thing to do (Protagoras 358c-e). He gives a much-discussed, elaborate argument to establish this stronger conclusion, starting from assumptions identifying that which is pleasant with that which is good (352a-357e). These assumptions, however, he attributes only to ordinary people, the ones who say they believe in the possibility of weak-willed action; he makes it clear to the careful reader, if not to Protagoras, that his own view is simply that pleasure is a good thing, not 'the' good (351c-e; see 354b-d). Although some scholars have thought otherwise, Socrates himself does not adopt a hedonist analysis of the good in the Protagoras or elsewhere either in Plato or Xenophon; indeed, he speaks elsewhere against hedonist views (see Hedonism). The fundamental principle underlying his argument - a principle he thinks ordinary people will accept - is that voluntary action is always 'subjectively' rational, in the sense that an agent who acts to achieve some particular sort of value always acts with the idea that what they are doing achieves more of that value than alternatives then thought by them to be available would achieve. If someone performs an overall bad action because of some (lesser) good they think they will get from it, they cannot do it while believing it is bad overall. That would mean they thought they could have got more good by refraining, and their action would violate the principle just stated. Instead, at the time they acted (despite what they may have thought before or after acting), they believed (wrongly and ignorantly) that the action would be good overall for them to do. Thus ignorance, and only ignorance, is responsible for voluntary error. Weakness of will - knowingly pursuing the worse outcome - is psychologically impossible: 'No one does wrong willingly'.
The details of this argument may not represent explicit commitments of the historical Socrates. None the less, his denial of weakness of will, understood as presented in Plato's Protagoras, was the centre of a protracted debate in later times. First Plato himself, in Republic IV, then Aristotle in Nicomachean Ethics VII, argued against Socrates' conclusion, on the ground that he had overlooked the fact that human beings have other sources of motivation that can produce voluntary actions, besides their ideas about what is good or bad, or right or wrong to do. 'Appetites' and 'spirited desires' exist also, which can lead a person to act in fulfilment of them without having to adopt the idea, in their beliefs about what is best to do, that so acting would be a good thing (see Plato §14; Aristotle §20, 22-23). The Stoics, however, and especially Chrysippus, argued vigorously and ingeniously in defence of Socrates' analysis and against the Platonic-Aristotelian assumption of alternative sources of motivation that produce voluntary action on their own (see Stoicism §19). In fact, during Hellenistic times it was the Socratic, 'unitary' psychology of action that carried the day; the Platonic-Aristotelian alternative, dominant in the 'common sense' and the philosophy of modern times, was a minority view. The issues Socrates raised about weakness of will continue to be debated today.
Socrates drew to himself many of the brightest and most prominent people in Athens, securing their fascinated attention and their passionate friendship and support. His effectiveness as a philosopher, and the Socratic 'legend' itself, depended as much on the strength and interest of his personality as on the power of his mind. Plato's and Xenophon's portraits of Socrates as a person differ significantly, however. Plato's Socrates is aloof and often speaks ironically, although also with unusual and deeply held moral convictions; paradoxically, the depth and clarity of his convictions, maintained alongside the firm disclaimer to know what was true, could seem all the stronger testimony to their truth, and made them felt the more strongly as a rebuke to the superficiality of one's own way of living. In Xenophon, Socrates is also sometimes ironical and playful, especially in the Symposium, but his conversation is usually direct, even didactic, and often chummy in tone; his attitudes are for the most part conventional though earnest; and there is nothing to unsettle anyone or make them suspect hidden depths. It is much easier to believe that the Socrates of Plato's dialogues could have had such profound effects on the lives of the brightest of his contemporaries than did the character in Xenophon. That is one reason given for trusting Plato's more than Xenophon's portrait of the historical personage. But perhaps Socrates used the more kindly and genial manner and conventional approach depicted by Xenophon to draw out the best in some of his young men and his friends - ones who would have been put off by the Platonic subtleties. The historical Socrates may have been a more complex person than even Plato presents.
Plato and Xenophon both represent Socrates as strongly attracted to good-looking young men in the 'bloom' of their middle to late teens, just the period when they were also coming of age morally and intellectually. In both he speaks of himself as unusually 'erotic' by temperament and constantly 'in love'. But he explains his 'erotic' attachments in terms of his desire to converse with bright and serious young men, to question them about virtue and how best to live a human life, and to draw out what was best in their minds and characters. In Xenophon he describes his love as love for their souls, not their bodies, and he vigorously condemns sexual relations with any young man: using him that way disgraces him and harms him by encouraging a loose attitude as regards physical pleasures Symposium 8). The overheated sexuality of Plato's own accounts (Symposium and Phaedrus) of eros, sexual love, for a young man's beauty as motivating an adult male to pursue philosophical truth into an eternal realm of Forms (see Plato §12) is to be distinguished sharply from Socrates' ideas, as we can gather them from Xenophon and from Plato's own early dialogues.
Xenophon emphasizes Socrates' freedom from the strong appetites for food, drink, sex and physical comfort that dominate other people; his enkrateia or self-mastery is the first of the virtues that Xenophon claims for him (Memorabilia I 2.1). He was notorious for going barefoot even in winter and dressing always in a simple cloak. Socrates' self-mastery was at the centre of Antisthenes' portrayal, and is reflected also in several incidents reported in Plato, such as his serene dismissal of the young Alcibiades' efforts to seduce him sexually (Plato, Symposium 217b-219e), or, perhaps when engrossed in a philosophical problem, his standing in the open (during a break in the action while on military service) from morning to night, totally indifferent to everything around him (Symposium 220c-d). This 'ascetic' Socrates, especially as presented by Antisthenes - rejecting conventional comforts and conventional behaviour - became an inspiration for the 'Cynics' of later centuries (see Cynics).
Looking back on the early history of philosophy, later philosophers traced to Socrates a major turn in its development. As Cicero puts it: 'Socrates was the first to call philosophy down from the heavens... and compel it to ask questions about life and morality' (Tusculan Disputations V 10-11). Previously it had been concerned with the origins and nature of the physical world and the explanation of celestial and other natural phenomena. Modern scholarship follows the ancients' lead in referring standardly to philosophers before Socrates collectively as 'Presocratics' (see Presocratic philosophy). This includes Democritus, in fact a slightly younger contemporary of Socrates; Cicero's verdict needs adjustment, in that Democritus, independently of Socrates, also investigated questions about ethics and morality. With the sole exception of Epicureanism, which developed separately out of Democritean origins, all the major movements of Greek philosophy after Socrates had roots in his teaching and example. This obviously applies to Plato, whose philosophical development began with a thorough reworking and assimilation of Socratic moral inquiry, and through him to Aristotle and his fellow members of Plato's Academy, Speusippus and Xenocrates and others, as well as to later Platonists. Among Socrates' inner circle were also Aristippus of Cyrene, who founded the hedonist Cyrenaic school (see Aristippus the Elder; Cyrenaics), and Antisthenes, an older rival of Plato's and major teacher in Athens of philosophical dialectic. Both of these figure in Xenophon's Memorabilia (Antisthenes also in his Symposium), where they are vividly characterized in conversation with Socrates. Another Socratic, Euclides, founded the Megarian school (see Megarian school). These 'Socratic schools' developed different themes already prominent in Socrates' own investigations, and competed in the claim to be his true philosophical heirs (see Socratic schools; Dialectical School).
In the third to first centuries bc, both the Stoics and their rivals the Academic sceptics claimed to be carrying forward the Socratic tradition. In both cases this was based upon a reading of Plato's dialogues and perhaps other eye-witness reconstructions of Socrates' philosophy. The Academic Arcesilaus interpreted the Platonic Socrates as a sceptical inquirer, avidly searching but never satisfied that the truth on any disputed question had been finally uncovered. He could point to much about Plato's Socrates in support: his modest but firm denial that he possessed any knowledge, and his constant practice of inquiring into the truth by examining others' opinions on the basis of ideas which they themselves accepted, without formally committing himself to these ideas even when he was the one to first suggest them. Arcesilaus, however, applied his sceptical Socratic dialectic to more than the questions of ethics and human life about which Socrates himself had argued, making it cover the whole range of philosophical topics being investigated in his day. The Stoics read the dialogues (especially the Euthydemus and Protagoras) quite differently. They found Socrates espousing a complete doctrine of ethics and the psychology of human action. He posed his questions on the basis of this doctrine, leaving the respondent (and the reader) to recover for themselves the philosophical considerations underlying it. They thus emphasized the conceptions of virtue as knowledge, of virtue as unified in wisdom, and of voluntary action as motivated always by an agent's beliefs about what is best to do, that emerged through Socrates' examination of Protagoras (see §§6-7). They thought these constituted a positive, Socratic moral philosophy, and in their own moral theory they set out to revive and strengthen it with systematic arguments and with added metaphysical and physical speculations of their own. Later Stoics regularly referred to Socrates as a genuine wise man or 'sage', perhaps the only one who ever lived. He had brought to final, systematic perfection his knowledge, along Stoic lines, of what is good and bad for human beings, and what is not, and therefore possessed all the virtues and no vices, and lived unwaveringly the best, happy life, free from emotion and all other errors about human life. It is a tribute to the complexity and enigmatic character of Socrates that he could stand simultaneously as a paragon both of sceptical, non-committal inquiry and life led on that uncommitted basis, and of dogmatic knowledge of the final truth about all things human.
The figure of Socrates has continued to fascinate and to inspire ever-new interpretations of his innermost meaning. For Montaigne, he proved that human beings can convincingly and attractively order their own lives from their own resources of mind, without direction from God or religion or tradition. In the nineteenth century Kierkegaard and Nietzsche offered extensive interpretations of him, both heavily dependent upon Hegel's absolute-idealist analysis. Hegel interpreted Socrates as a quintessentially negative thinker, aiming at making people vacillate in their superficial moral beliefs and endorse none of them wholeheartedly, thus hinting that the truth, although universal and objective, lies deep within the freedom of their own subjectivity. For Kierkegaard he represents, on the contrary, the possibility of living wholeheartedly by occupying an unarticulated position somehow beyond the negative rejection but expressed through it: 'infinite absolute negativity'. In Die Geburt der Tragödie (The Birth of Tragedy) Nietzsche treats Socrates principally as having poisoned the 'tragic' attitude that made possible the great achievements of classical culture, by insisting that life should be grounded in rational understanding and justified by 'knowledge'; but his fascinated regard for Socrates led him to return to him repeatedly in his writings. Socrates was paradigmatically a philosopher whose thought, however taken up with logic and abstract argument, is inseparable from the search for self-understanding and from a deeply felt attachment to the concerns of human life. His power to fascinate and inspire is surely not exhausted.JOHN M. COOPER


Researchers at Disney Research, Zürich, ETH Zürich, and Cornell University have invented a system to digitize facial hair and skin. Capturing facial skin and geometry is a fundamental technology for a variety of computer-based special effects for movies. Conventional face capturing is well established and widely utilized in the entertainment industry to capture a three-dimensional model of an actor's face. However, up to now, no method was capable of reconstructing facial hair or even handling it appropriately. This omission is surprising as facial hair is an important component of our popular culture.
The system developed by the Disney Research Laboratory in Zürich constitutes a significant technical breakthrough in the field of digitizing human faces and was presented at ACM SIGGRAPH, the International Conference on Computer Graphics and Interactive Techniques. "Our method captures individual strands of facial hair and stores them separately from the actual human face. This approach allows us to 'shave' people with facial hair virtually with the computer." said Thabo Beeler, a computer scientist at Disney Research, Zürich, who is the main inventor of the technology.
The system employs several consumer-grade photo cameras to capture a face in a fraction of a second. The method then automatically detects hairs in the captured images. These hairs are being tracked and followed in the input images, much like we follow a path on a map with our fingers. A mathematical method called multi-view stereo (MVS) reconstructs them in three dimensions. The trick the researchers applied is to remove the hair strands from the input images similar to an artist painting over parts of a picture. This process makes the 3D skin surface to look as if it were digitally shaved. The system was applied to a large variety of different facial hair styles, ranging from designer stubbles all the way to wild mustaches, to demonstrate its robustness. The produced results look very compelling.
Prof. Markus Gross, director of Disney Research, Zürich, stated, "The long-term goal of our research is to make facial animation and special effects more realistic and ultimately indistinguishable from reality. This method is going to be a very important step toward this long term goal".
Explore further: Researchers develop fast, economical method for high-definition video compositing
More information: For more information, please visit the web site at www.disneyresearch.com/research/projects/cv_reconFacialHair_drz.htm


In Jena, Graph is an interface. It abstracts anything that looks like RDF - storage options, inference, other legacy data sources.
The main operations are
addition, there are a number of getters to access handlers of various features
(query, statistics, reification, bulk update, event manager) .
Having handlers, rather than directly including all the operations for each
feature reduces the size of the interface and makes it easier to provide default
implementations of each feature.
Implementing a graph rarely needs to directly implement the interface.
More usually, an implementation starts by inheriting from the class GraphBase.
A minimal (read-only) implementation just needs to implement
Wrapping legacy data often only makes sense as a read-only graph. To provide update operations, just implement the methods
which are the methods called from the base implementations of
Then for testing with JUnit, inherit
from AbstractGraphTest (override tests that don't make sense in a particular circumstance)
and provide the
getGraph operation to generate a graph instance to test.
Where the graph level is minimal and symmetric (e.g. literal as subjects, inclusion of named variables) for easy implementation, the RDF API enforces the RDF conditions and provides a wide variety of convenience operations so writing a program can be succinct, not requiring the application writer to write unnecessary boilerplate code sequences. The ontology API does the same for OWL. If you look at the javadoc, you'll see the APIs are large but the system level interface is small.
A graph is turned into a Model by calling
ModelFactory.createModelForGraph(Graph). All the key application APIs
are interface-based although it's rarely needed to do anything other that use the
standard Model-Graph bridge.
Data access to the graph all goes via find. All the read operations of application APIs, directly or indirectly, come down to calling Graph.find or a graph query handler. And the default graph query handler works by calling Graph.find, so once find is implemented everything (read-only) works. ARQ's query API, which includes a SPARQL implementation, included. It may not be the most efficient way but importantly all functionality is available and so the graph implementer can quickly get a first implementation up and running, then decide where and when to spend further development time - or whether that's needed at all.
An example of this is a prototype Jena-Mulgara bridge (work in progress as of Jan'08). This maps the Graph API to a Mulgara session object, which can be a local Mulgara database or a remote Mulgara server. The prototype is a single class together with a set of factory operations for more convenient creation of a bridge graph wrapped in all Jena's APIs.
Implementing graph nodes, for IRIs and for literals is straight forward. Mulgara uses JRDF to represent these nodes and to represent triples. Mapping to and from Jena versions of the same is just the change in naming.
Blank nodes are more interesting. A blank node in Jena has an internal label (which is not a URI in disguise). When working at the lowest level of Graph, the code is manipulating things at a concrete, syntactic level.
A blank node in Mulgara has an internal id but it can change. It really is the internal node index as I found out by creating a blank node with id=1 and found it turned into rdf:type which was what was really at node slot 1. Paul has been (patiently!) explaining this to me on a Mulgara mailing list. The session interface is an interface onto the RDF data, not an interface to extend the graph details to the client. Both approaches are valid - it's just different levels of abstraction.
If the Jena application is careful about blank nodes (not assuming they are stable across transactions, and not deleting all triples involving some blank node, then creating triples involving that blank node) then it all works out. The most important case of reading data within a transaction is safe. Bulk loading is better down via the native Mulgara interfaces anyway. The Jena-Mulgara bridge enables a Jena application to access a Mulgara server through the same interfaces as any other RDF data.


News > Scientists reconstruct Red Sea parting
Researchers at the US National Center for Atmospheric Research (NCAR) have produced a computer simulation that demonstrates how the parting of the Red Sea described in the Book of Exodus could have been caused by strong winds.
The study, which is part of a larger project looking into the impact of winds on water depths, was published in the open-access journal Plos One. In it, researchers produced a reconstruction of the likely geography of the Nile Delta during the Old Testament period, which has changed considerably over the intervening centuries. The researchers have identified a stretch of the Nile where a strong east wind could conceivably have pushed the river back at a bend, opening up a walkway across the exposed mud flats and allowing the Israelites to flee the approaching Egyptians.
"The simulations match fairly closely with the account in Exodus," Carl Drews of the NCAR told the BBC. "The parting of the waters can be understood through fluid dynamics. The wind moves the water in a way that's in accordance with physical laws, creating a safe passage with water on two sides and then abruptly allowing the water to rush back in."
With the burning bush also potentially linked to freak environmental conditions, it remains to be seen how much else of the bible story can be explained by meteorology.


What are bitcoins, everybody asks. The usual answer is “they are a distributed, semi-anonymous, peer to peer, cryptographic digital currency” or something along those lines, but there is another simpler way to look at bitcoins.
Bitcoins are a tech stock – tech because they solve a technological problem and have a technological use, and stock because they can be bought and sold on open market.
Imagine a startup arrived in silicon valley one day and said they were going to create a digital currency which would succeed. A digital currency that overcomes the many limitations and fatal flaws of all its predecessors. I wonder how we could quantify it’s value in terms of VC funding, and once it reached a market cap of $300 Million, its value as an acquisition?
Let’s look at three start ups who received over $100million each in VC funding.
Dropbox has received over $250 Million in venture capital funding, for a service that essentially stores files. AirBnB, a space rental service (generally for holidays) has received $119 Million in funding. HomeAway, a vacation property booking services has raised over $500 Million.
And let’s look at a few startups that have sold for over $1billion.
Instagram, a simple photo sharing platform, sold to Facebook for $1billion. Youtube, the video sharing site we all know and love, sold to Google for $1.6billion and Doubleclick for $3billion. Yahoo bought an internet radio service for $5.7billion, geocities (now defunct) for $3.6billion, Overture Services Inc for $1.6 Billion and various others. Microsoft purchased Visio software for $1.3 Billion, NaVision for $1.3 Billion, aQuantive for $6.3 Billion, Fast Search and Transfer for $1.1 Billion, Skype for $8.5 Billion and Yammer for $1.2 Billion
In the above examples I’ve listed 12 companies that were sold for a total of $36,200,000,000. Just 12 Companies!
And let’s not even talk about the tech stocks which have floated on stock exchanges!
All of these companies have one thing in common, commerciality. Each requires a monetary transaction of some description to have been worth investing in or buying, in the first place. Now imagine a technology which facilitates the commerciality of all trade.
The current market cap of Bitcoins is around $300 Million. If bitcoins are a more commercial, more versatile and more readily traded tech stock (and they are), I don’t think it’s far fetched for bitcoin as a tech stock to be worth more than instagram. In that case their value should increase by 330%.
In fact I don’t think its far fetched to suggest bitcoins are a more commercial, readily traded, versatile and also sustainable tech stock than all of the above combined, in which case they are under valued by 11900%. ie. They should be trading at $3284 per bitcoin.
In my mind it goes even further. Apple is a company that simply sells computers, phones and software, and its value peaked at around $650 Billion. I think this is a realistic market cap for Bitcoins to hit within 10 years, at a value per coin of $55,000 each.
Imagine again for a second that the general public could have invested and the ground level with each of the above companies, ala kick starter. With bitcoins they can, and what’s more, this investment is more secure, more liquid, and more useful than any of the aforementioned investments could ever have been.
Bitcoins aren’t just a digital currency, they are a tech stock


This page lists climate science and climate impact claims that have either not been proven, or have had the claim modified, moved, or expanded to protect the claimant from having to admit the original claim was wrong.
This will always be a work in progress. New items will be added as they are examined and will include:
- The claim itself – what was stated as factual or predicted? A clear unambiguous statement, such as “50 million climate refugees by 2010″
- Proof of the original claim – website, documents, photos, audio, video that clearly and unambiguously show the claim being made sometime in the past.
- A test of the of the claim, and the results – website, documents, photos, audio, video that clearly and unambiguously show the claim not coming true or not meeting the claim.
- Proof of change in the claim (if applicable) – often, when the claim fails to materialize, goalposts get moved, such as we saw with the “50 million climate refugees” story that was originally set with a due date of 2010, is now set for the year 2020.
The Claim: 50 million climate refugees will be produced by climate change by the year 2010. Especially hard hit will be river delta areas, and low lying islands in the Caribbean and Pacific. The UN 62nd General assembly in July 2008 said: …it had been estimated that there would be between 50 million and 200 million environmental migrants by 2010.
The Test: Did population go down in these areas during that period, indicating climate refugees were on the move? The answer, no.
The Proof: Population actually gained in some Caribbean Island for which 2010 census figures were available. Then when challenged on these figures, the UN tried to hide the original claim from view. See: The UN “disappears” 50 million climate refugees, then botches the disappearing attempt
The Change in claim: Now it is claimed that it will be 10 years into the future, and there will be 50 million refugees by the year 2020.


The Search for Certainty: A Philosophical Account of Foundations of Mathematics. Marcus Giaquinto. xii + 286 pp. Oxford University Press, 2002. $45.
David Hilbert (1862–1943) was arguably the leading mathematician of his time. In struggles over how mathematics was to accommodate new understandings of the infinite, the Dutch mathematician L. E. J. Brouwer was his most fervent opponent. When Hilbert's favorite student, Hermann Weyl, went over to the enemy, saying "Brouwer, that is the revolution," Hilbert was incensed. In a passionate address delivered in 1922, he proclaimed:
Weyl and Brouwer . . . seek to provide a foundation for mathematics by pitching overboard whatever discomforts them and declaring an embargo. . . . But this would mean dismembering and mutilating our science, and, should we follow such reformers, we would run the risk of losing a large part of our most valued treasures. Weyl and Brouwer outlaw the general notion of irrational number, of function, even of number-theoretic function, Cantor's [ordinal] numbers of higher number classes, etc. The theorem that among infinitely many natural numbers there is always a least, and even the logical law of the excluded middle, e.g., in the assertion that either there are only finitely many prime numbers or there are infinitely many: these are examples of forbidden theorems and modes of inference. I believe that impotent as Kronecker was to abolish irrational numbers . . ., no less impotent will their efforts prove today. No! Brouwer's [program] is not as Weyl thinks, the revolution, but only a repetition of an attempted putsch with old methods, that in its day was undertaken with greater verve yet failed utterly. Especially today, when the state power is thoroughly armed and fortified by the work of Frege, Dedekind, and Cantor, these efforts are foredoomed to failure.
A decade later Hilbert's own program for the foundations of mathematics lay in tatters, destroyed in an investigation by the young logician Kurt Gödel, which had initially been undertaken in an effort to contribute to that very program. Today, passions have cooled, and working mathematicians show little interest in foundational matters. The infinitary set theoretic methods that occasioned such controversy are casually absorbed in passing by the beginning graduate student and used unhesitatingly.
Like a military historian surveying the battlefield long after all the bodies have been cleared away, Marcus Giaquinto coolly revisits the controversies in The Search for Certainty. It all began with a necessary effort by mathematicians to put their house in order. Although the methods of the calculus had proved highly successful, their underlying logic had been in grave need of clarification. Calculus worked with numbers and functions, but no coherent theory of the so-called "real" numbers had been developed, and the notion of function had been stretched in the direction of a frightening arbitrariness. Richard Dedekind's elegant characterization of the real numbers in terms of "cuts" had a distinctly set-theoretic flavor, and Georg Cantor's new push into the "actual" infinite expanded the boundaries of the subject matter of mathematics into what Hilbert later characterized as "Cantor's paradise." But Cantor's infinite was plagued by paradox. The kernel of at least one of these paradoxes could manifest itself in what seemed like everyday reasoning, as Bertrand Russell showed in his famous paradox: If we consider the set S of all those sets that are not members of themselves, then S is a member of itself if and only if it is not a member of itself. This was particularly bad news for Gottlob Frege, whose ambitious logical system for the foundations of mathematics proved vulnerable to Russell's paradox and was thus seen to be inconsistent.
The highly influential but rather baroque three-volume Principia Mathematica was Bertrand Russell's effort (with coauthor Alfred North Whitehead) to revive Frege's wrecked program. Paradoxes such as Russell's were to be avoided by slicing up the universe of mathematical discourse into discrete successive "types," with set membership permitted only between adjacent types.
Meanwhile, Ernst Zermelo, who never accepted the stringent syntactic demands of formal logical systems, proposed a set of axioms for set theory. By the 1920s, it was realized that Zermelo's axioms provided the basis of a formal system rivaling that of Principia. In an important paper appearing in 1930, Zermelo proposed what came to be called the iterative notion of set, in which a hierarchy of sets is built from some initial collection of things by iterating indefinitely the operation of forming the set of all subsets of a given set. He observed that his axioms could be construed as being about just this notion. A few years later, in an address on the foundations of mathematics, Kurt Gödel emphasized that rather than being seen as a rival to Principia, when viewed from the perspective of the iterative notion of set Zermelo's system could be seen as the result of eliminating unnecessary complications and artificial restrictions from the Whitehead-Russell system. By the 1940s and '50s, set-theoretic methods had become a crucial part of the mathematician's toolbox.
Back in the 1920s, when passions were aflame, Hilbert developed an ingenious strategy by which he intended to overcome his opponents. He would establish the legitimacy of methods that Brouwer and Weyl considered dubious by encapsulating those methods in formal systems whose consistency would then be proved using only methods of which they approved. In a revolutionary paper in 1931, the young Gödel demonstrated not only that consistency could not be proved using only these restrictive methods, but also that the same negative conclusion held even if the entire panoply of methods encapsulated in the systems in question was brought to bear. After Gödel, the foundations of mathematics were seen as inevitably open-ended, with more and more propositions becoming provable as ever more powerful methods were employed. Gödel liked to emphasize that these more powerful methods could be thought of as being essentially a matter of venturing sufficiently far out in the iterative hierarchy of sets.
Giaquinto has provided a careful and judicious discussion and analysis of these matters, supplying needed technical background for readers who are not mathematicians. Although foundational questions have ceased to be of much importance to most mathematicians, controversies among specialists continue. Readers of this book will be well prepared to follow the current literature on foundations of mathematics.