Musings on Gettier and the definition of knowledge

This article first appeared on Scientia Salon

Philosophers have traditionally defined “knowledge” as a belief that is both true and justified, a definition that sufficed until, 50 years ago, Edmund Gettier pointed out that the conditions could be fulfilled by accident, in ways that didn’t amount to what we would intuitively regard as “knowledge”.

Gettier pointed to scenarios such as:

“Smith has applied for a job, but, it is claimed, has a justified belief that “Jones will get the job”. He also has a justified belief that “Jones has 10 coins in his pocket”. Smith therefore (justifiably) concludes that “the man who will get the job has 10 coins in his pocket”. In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that “the man who will get the job has 10 coins in his pocket” was justified and true. But it does not appear to be knowledge.”

Since Gettier’s paper many attempts have been made to patch up the “justified true belief” definition, often by adding extra conditions aimed at ruling out being right accidentally, though none of the proposed solutions has gained general acceptance and most have been shown not to work. [1]

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The roots of empiricism: Hume’s fork, and the divide between knowledge “by observation” and “by reason”

Scientia Salon recently published my article advocating that mathematics is best regarded as a part of science. In reply to “scientism week”, Massimo Pigliucci wrote an article criticising “the return of radical empiricism”. The collision of “scientism week” with “anti-scientism week” generated a lot of energy and comments!

Massimo Pigliucci’s article is well worth reading, being a clear exposition of the relevant ideas. He traces the issues back to Hume’s famous fork, in which Hume declares that:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact and real existence.


The “relations of ideas” category is taken to include mathematics and logic, where knowledge is “discoverable by the mere operation of thought”, while the “matters of fact” category contains science, where knowledge derives from empirical data.

Kant rejected Hume’s empiricism and sought to establish the primacy of reason. He adopted the term “a priori” for knowledge that does not derive from experience, in contrast toa posteriori” knowledge which does. A related concept is that of “analytic” statements, which follow from the definitions of the terms, contrasting with “synthetic” statements that describe how the world is.

This notion of a fundamental epistemological divide holds today, and is at the heart of resistance to the idea that mathematics, logic and science are a unified whole.

In reading Pigliucci’s article I agree with much of what he says, but, to me, he seems to miss the main arguments for the essential unity of the different domains of knowledge. I will thus outline how I see the roots of empiricism, and then consider the supposed divide between knowledge “from reasoning” versus knowledge “from observation”. Continue reading

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Eric Pickles and Britain as a “Christian Nation”

On Baroness Warsi’s resignation from the UK government, David Cameron would have done best to drop the “Minister of Faith” role that he had created for her, but instead handed it over to Eric Pickles. Pickles, we recall, is another minister who thinks that Christians should still have special privileges in the UK. Informing us that Britain is a “Christian nation” and that atheists should “get over it”, he gloated that he has “stopped an attempt by militant atheists to ban councils having prayers at the start of meetings”.

As ever, anyone who believes in church–state separation and a secular, religiously neutral government is a “militant”, while handing ever more state schools over to be run by churches, awarding them an exemption from the Equality Act, thus allowing them to discriminate against non-religious families, and passing laws violating religious liberty by requiring school kids to worship the Christian god, is merely defending “traditional British values”.

Thus The Telegraph, defending compulsory religion in schools, against the wishes of the majority of parents, and school governors (and indeed the Church of England!), states that “There can be few things in life less harmful than the gentle Christian values learnt by children during school assemblies” and that “the British values of which we hear so much are based on ancient Judeo-Christian beliefs and the teachings of the Bible”. Continue reading

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A scientific response to the Brain in a Vat

Scientia Salon is an enjoyable webzine discussing philosophical matters, which recently addressed an old conundrum: how do we know we are not a brain in a vat? As I see it, this question is straightforwardly answered by the usual scientific method, so here I’ll summarise the argument that I advanced in the Scientia Salon discussion.

The Matrix-style scenario, which dates back to the skepticism of Descartes, supposes that we are a brain kept alive in a vat, being fed with a stream of inputs generated by an Evil Genius. Everything that we experience as sense data is not real, but is artificially simulated and fed to us. Since, ex hypothesi, our stream of experiences is identical to that in the “real world” explanation, we cannot know for sure whether or not we are such a brain in a vat.

How to respond? First, the whole point of science is to make sense of our “stream of experiences”. We do that by looking for regularities and patterns in those experiences, and we develop those into descriptions and explanations of the world (I’ll use the term “world” here for the sum of those experiences, regardless of whether they derive from our contact with a real world, or from a simulated world being fed to us). Continue reading

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Applying falsifiability in science

Falsifiability. as famously espoused by Karl Popper, is accepted as a key aspect of science. When a theory is being developed, however, it can be unclear how the theory might be tested, and theoretical science must be given license to pursue ideas that cannot be tested within our current technological capabilities. String theory is an example of this, though ultimately it cannot be accepted as a physical explanation without experimental support.

Further, experimental science is fallible, and thus we do not immediately reject a theory when contradicted by one experimental result, rather the process involves the interplay between experiment and theory. As Arthur Eddington quipped: “No experiment should be believed until it has been confirmed by theory”.

Sean Carroll recently called for the concept of falsifiability to be “retired”, saying that:

The falsifiability criterion gestures toward something true and important about science, but it is a blunt instrument in a situation that calls for subtlety and precision.

Meanwhile, Leonard Susskind has remarked that:

Throughout my long experience as a scientist I have heard un-falsifiability hurled at so many important ideas that I am inclined to think that no idea can have great merit unless it has drawn this criticism.

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The Religious Freedom Restoration Act establishes religious privilege

In the United States, the Supreme Court tells us, corporations have the status of “people” and thus have attendant constitutional rights including freedom of religion. That allows corporations to decline to participate in aspects of Obamacare if it considers that doing so would be against the corporation’s religious beliefs.

This landmark “Hobby Lobby” ruling followed predictable lines, with five Catholic judges out-voting the Court’s four moderates. Much of the commentary has focused on the doctrine of awarding personhood to corporations. An equally important issue, however, is the role of the 1993 Religious Freedom Restoration Act, whose effects are seen for the first time.

That Act would have been better named the Religious Privilege Establishment Act. It requires that the:

“Government shall not substantially burden a person’s exercise of religion even if the burden results from a rule of general applicability”, with allowed exceptions only where the burden “furthers a compelling governmental interest”, and in addition “is the least restrictive means of furthering that compelling governmental interest”.

This privileges the religious since it grants greater import and status to a religious motivation for doing or not doing something than to a secular motivation for the same thing. Through this promotion of religious belief it is a law “respecting an establishment of religion” and thus it violates the First Amendment. Continue reading

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A “conscience clause” would negate equality under the law

The suggestion of a “conscience clause” opt-out from equality legislation has been floated by no less a person than Lady Hale, Deputy President of Britain’s Supreme Court, and the most senior female judge in the land. The idea is that if treating people equally goes against your conscience then you get to play the “conscience” trump card entitling you to treat people unequally.

Unsurprisingly, some Christians have welcomed the suggestion, which they see as preserving their “religious freedom” against what they see as the encroachment of equality legislation.

“It is obvious that there is a growing conflict between religious freedoms and equalities legislation, and that a new balance has to be struck” opines The Telegraph. So, for example, the Christian hoteliers who famously turned away a same-sex couple, and lost the resulting court case, could in future be indulged by a clause that makes “special provisions or exceptions for particular beliefs”. Continue reading

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