No Justification and Infinitism
Why is justification even required? Can the proposition simply be accepted without justification? We can but this will mean that we have no rational basis to think we know that
Belief (0) Brussels is the capital of Belgium.
We may perhaps be mistaken but have no means to investigate further since our belief is based on nothing. Hence to know our beliefs, we need justification. For instance, we can refer to an atlas which lists the capitals of all the countries, resulting in
Belief (1) The atlas lists Brussels as the capital of Belgium.
How will we know though that the information in the atlas is correct? If we want to seek further justification, we can look into the credentials of the author, Smith, who produced the atlas. We do so by checking his educational certificates, leading to
Belief (2) Smith’s educational certificate proves he is qualified to produce the atlas.
We can then contact the degree-granting institution to verify he indeed graduated, leading to
Belief (3) Smith graduated from the degree-granting institution on his certificate.
If we remain unsatisfied, we can investigate the institution to see if he has been taught properly, enquire into the teachers’ qualifications and their teachers’ qualifications and so on. This leads to
Belief (4) Smith was properly taught.
Belief (5) His teachers were qualified.
Belief (6) His teachers’ teachers were qualified.
If at any point in the process, we discover a false belief, for example if he never attended the institution on his certificate, it will shake all our beliefs that preceded it. If not, we can continue the process of supporting each belief with a further belief, leading to an infinite chain of justification.[3]
This process is called infinitism. The never-ending nature of this process of justification is problematic, since if we stop at the nth belief, we do not know if we may have found a false belief in the (n+1) belief. Hence, unless we find a false belief, we can never stop investigating, leading to an infinite regress. In our case, if we had been satisfied believing Belief (2) after seeing his certificate and did not pursue our investigation further to verify Belief (3), we would not have realised he did not attend the institution. Other than the infinite amount of resource needed to investigate any belief, it seems intuitive that a belief supported by a never-ending tower of beliefs is precarious. However, this may simply be a prejudice on the part of the critics of infinitism, since many people seem to have no problems with other infinite concepts such as their belief in an infinite God or with infinite numbers. If indeed the tower of beliefs continue down infinitely, it might even be regarded as a strength of the theory. The problem is that at one point of the journey downwards, we come across a false belief, leading to the collapse of the entire tower.
Coherentism
Let us assume that in our thought experiment that
Belief (7) Smith did indeed attend and graduate from the institution.
We can then make a series of closely related beliefs:
Belief (8.1) The institution is KU Leuven (KUL).
Belief (8.2) KUL is a university.
Belief (8.3) Universities are places where students learn.
Belief (8.4) When its students complete their learning, they are granted degrees.
In addition, let the following be true in our thought experiment:
Belief (9) Smith graduated.
Belief (10) Smith worked in the mapping division of the government for 10 years before writing the atlas.
Based on these beliefs, we are satisfied that he is qualified to produce the atlas. What we have here is not an infinite tower of beliefs but a series of connected beliefs that support one another, a network or a web of beliefs. Each strand connects to multiple other strands, and the entire web forms a coherent body of beliefs. This describes the epistemological theory called coherentism.[4]
Sometimes the beliefs or parts of it could line up in a circle, for example,
Belief (11.1) Smith got the job to produce the atlas.
Belief (11.2) The atlas was published by KUL.
Belief (11.3) Smith’s father is the rector of KUL.
Belief (11.4) Smith had studied chemistry at KUL.
Provisional Belief (11.5) Because of his father’s influence, Smith managed to land an interview with the atlas-producing division of KUL.
Belief (11.1) Smith got the job to produce the atlas.
This circle of beliefs now explains how Smith landed the job of atlas-making. These new beliefs might threaten some strands of our previously coherent web of belief, such as ‘Smith’s educational certificate proves he is qualified to produce the atlas.’ We might start to wonder if our atlas is reliable after all, and hence if its statement on Brussels is true. However, other parts of the web remain intact and unshaken, such as how ‘universities are places where students learn.’ Quine proposes a process of revision to investigate the shaky beliefs, where we remedy them, reject them or momentarily suspend judgement. We then have to also revise the other beliefs supporting the remedied or rejected beliefs. This revision continues until coherence has been restored in our web.[5]
In the case of the atlas, we may discover that despite Smith’s father being the rector,
Belief (11.6) Smith did not receive any special treatment at the university.
We might however wish to reject the belief that Smith was qualified to produce the atlas since he studied chemistry. However, we also discover that
Belief (12) His work in the government’s mapping division gave him a thorough training in map-making, qualifying him as an expert map-maker.
In this way, our web of belief has been further developed and stabilised. The fact that our web of beliefs is revisable to take in new facts and to reject or fix newly falsified beliefs and their associated beliefs is a strength of coherentism. However, just because our beliefs are coherent does not make it true.[6]
Man had believed that the earth was the centre of the universe since antiquity until it was challenged in the Middle Ages by Copernicus. A coherent web of belief was built around this geocentric model of the universe and it worked well. This points to a weakness of coherentism: the body of beliefs coherentism encompasses may work well, but it may be untrue and hence does not justify knowledge. However, as new discoveries surface, the web is resilient enough to be revised. For example, the motions of the planets seem not to follow circular orbits, and Ptolemaic innovations such as epicycles were introduced to the web of beliefs to account for the eccentricities. With the benefit of hindsight, the adjustments became too cumbersome and the web became increasingly incoherent. Copernicus’s hypothesis of a heliocentric universe became a landmark breakthrough which thoroughly simplified the mechanics of the universe. However, his discovery was so fundamental that it struck at the core of the web, practically tearing the web apart. His discovery changed the way man understood his place in this world, his religious beliefs and the very structure of the universe. Much of the existing beliefs in the web had to be revised. This is because a foundational belief in that web of belief is the belief that the earth is at the centre of the universe.[7]
Foundationalism
If we only had a solid foundation on which we could base all our beliefs, we would escape the weakness of coherentism. Indeed, foundationalism is considered the most plausible theory of how we can justify our beliefs to have knowledge, explaining its popularity through the ages.[8] According to Pritchard, classical foundationalism “argues that knowledge is structured in such a way that chains of justification end with special self-justifying foundational beliefs which do not stand in need of any further support.”[9] Aristotle describes how his predecessors attempted to find the “principles of all things.”[10] He himself proposes a candidate principle in his Metaphysics: the principle of non-contradiction, which he believes is indubitable. It cannot be demonstrated since it is foundational – Aristotle writes: “it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there will still be no demonstration).”[11]
The quest for foundational principles did not stop there. Descartes almost 2,000 years later launched a new epoch in philosophy with his method of radical doubt. In doubting literally everything, he realised that there must be a doubter doing the doubting, hence “cogito ergo sum (I think therefore I am).”[12] From this indubitable principle and other principles he reasoned to be likewise indubitable, such as the existence of a perfect God,[13] he managed to restore the veracity of everything. In this way, foundationalism is like an inverted pyramid, where a vast number of beliefs are supported by a few foundational principles. This in itself is not a problem. After all, from Euclid’s five foundational axioms of geometry, all of Euclidean geometry can be derived. A problem is how it is not quite clear how we can get from cogito ergo sum to more mundane beliefs such as ‘Jack is eating his lunch at 1230pm today,’ short of accepting that we live in a deterministic world. Hence, according to Pritchard, foundational beliefs do not seem able to support ‘everyday’ beliefs.[14] Perhaps a way foundational beliefs can do so would be for fallible beliefs from sense-experience to also qualify as foundational. Aristotle had argued for this with the concept of proper sensibles and Quine with observation sentences, which delineate observable objects and events in such a way that they would be agreed to by witnesses.[15] However, since such beliefs are not infallible, it is unclear whys they are foundational.
Another problem troubling foundationalism is that Gödel has proved that in a system, not all truths can be derived from the system’s axioms. Hence taking self-evident steps from self-evident truths would not be able to deliver a system that contains all knowledge.[16] This suggests that the truths that cannot be derived from the axioms cannot be justified through foundationalism, but yet they still require justification under the JTB criterion for knowledge.
Conclusion
While each of the three theories of justification has been illustrated with shapes, such as a tower for infinitism, a web for coherentism and an inverted pyramid for foundationalism, we should not be misled into thinking that one theory gives more stable results than the others. In philosophy, even statements which seem obvious, such as ‘every effect has a cause,’ has been challenged effectively, in this case by Hume who rejects causation in favour of conjunction.[17] In the sciences, the principle of conservation of mass and the principle of conservation of energy, both thought inviolable, had to be reformulated as the principle of conservation of mass-energy after Einstein published his theory of relativity. What is thought indubitable today may require modification or abandonment tomorrow. As Quine writes: “No statement is immune to revision.”[18] Foundationalism is hence a difficult theory to maintain since it requires infallible truths which have been shown to be not so infallible after all. Coherentism, on the other hand, retains its strength for being able to absorb new beliefs and revise or reject falsified ones.
By considering the dialectic between coherentism and foundationalism, the solution to the problem of justification might be a synthesis of the two. The ideal theory for the justification of knowledge is a combination of foundationalism and coherentism. The proposed web of belief will be composed of indubitable foundational beliefs at its centre, with its radials and outer rings comprising non-foundational true beliefs coherent with the foundational beliefs, forming a coherent web with a core of solid foundational beliefs. Scientific and philosophical research can then continue to discover new beliefs or challenge existing ones, foundational or otherwise, and the combinatorial web will adjust accordingly giving knowledge a flexible yet well-grounded coherent web of belief. Bibliography
Aristotle. Metaphysics. Translated by William David Ross. Oxford: Clarendon, 1970.
Demey, Lorenz. “Lecture Slides for Theory of Knowledge.” 2019.
Descartes, René. “Meditations on First Philosophy.” In The Philosophical Works of Descartes, translated by Elizabeth S. Haldane. Cambridge: Cambridge University Press, 1911.
Hume, David. A Treatise of Human Nature. Edited by L. A. Selby-Bigge and P. H Nidditch. Oxford: Oxford University Press, 1978.
Kuhn, Thomas S. The Structure of Scientific Revolutions. 4th ed. Chicago: University of Chicago Press, 2012.
Pritchard, Duncan. What Is This Thing Called Knowledge? Third edition. London: Routledge, 2014.
Quine, W. V. “Two Dogmas of Empiricism.” In From a Logical Point of View: 9 Logico-Philosophical Essays. Cambridge: Harvard University Press, 1953.
Quine, W. V., and J. S. Ullian. The Web of Belief. Second edition. New York: McGraw Hill, Inc., 1978.
[1] Duncan Pritchard, What Is This Thing Called Knowledge?, third edition (London: Routledge, 2014), 23, 31.
[2] Lorenz Demey, “Lecture Slides for Theory of Knowledge,” (2019), Chapter 4.
[3] Pritchard, Thing Called Knowledge, 32–34.
[4] Ibid., 35.
[5] W. V. Quine and J. S. Ullian, The Web of Belief, second edition (New York: McGraw Hill, Inc., 1978), 16–18.
[6] Pritchard, Thing Called Knowledge, 35–36.
[7] For a detailed account, read Thomas S. Kuhn, The Structure of Scientific Revolutions, 4th ed. (Chicago: University of Chicago Press, 2012).
[8] Demey, “Lecture Slides for Theory of Knowledge,” chapter 4.
[9] Pritchard, Thing Called Knowledge, 36.
[10] Aristotle, Metaphysics, trans. William David Ross (Oxford: Clarendon, 1970), book A, part 3.
[11] Aristotle, book G, part 4.
[12] René Descartes, “Meditations on First Philosophy,” in The Philosophical Works of Descartes, trans. Elizabeth S. Haldane (Cambridge: Cambridge University Press, 1911), Meditation I.
[13] Ibid., Meditation III.
[14] Pritchard, Thing Called Knowledge, 38.
[15] Quine and Ullian, Web of Belief, 21.
[16] Ibid., 65.
[17] David Hume, A Treatise of Human Nature, ed. L. A. Selby-Bigge and P. H Nidditch (Oxford: Oxford University Press, 1978), 649.
[18] W. V. Quine, “Two Dogmas of Empiricism,” in From a Logical Point of View: 9 Logico-Philosophical Essays (Cambridge: Harvard University Press, 1953), 43.
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