An attempt at solving the Gettier Problem

An attempt at solving the Gettier Problem Xinyuan Gu 2016.12 This article attempts to find a solution to the Gettier Problem. Below is “necessary conditions to know p” summarized in a MIT online course “Minds and Machines” slide:1 1)p is true 2)S believes p 3)S's belief is justified Through various counterexamples, we know that the conditions above are not sufficient for knowledge. The question is how to fix it. For any S who wants his or her belief to be true, S has to seek for evidence to support the belief. Or, reversely, evidence convince S to believe that proposition p is true. That is, possibly, a process of searching for propositions other than p to form a practical or solid argument. Based on such possibility, I shall analyze two existing examples. Smith Case in the original Gettier paper:2 How did Smith reach the conclusion that “the man who will get the job has ten coins in his pocket”? Argument 1: Premise 1: the president of the company said that Jones would get the job. (which is true) Conclusion 1: Jones will get the job. Argument 2: Premise 2: I(Smith) counted the coins in Jones’s pocket myself. (which is true) Conclusion 2: Jones has ten coins in his pocket. Argument 3: Premise 3: Jones will get the job. Premise 4: Jones has ten coins in his pocket. Conclusion 3: The man who will get the job has ten coins in his pocket.(which happens to be true) In fact, 1)Smith will get the job; 2)Smith has ten coins in his pocket(a fact unknown to Smith). So the facts form Argument 4 as below: Premise 3’: Smith will get the job. (which is true, and refutes premise 3 in argument 3 as false) Premise 4’: Smith has ten coins in his pocket. (which is unknown to Smith and is true, yet premise 4 in argument 3 stays true) Conclusion 3’: The man who will get the job has ten coins in his pocket. (which is superficially identical to the conclusion in argument 3)

Smith case could be represented in Figure 1. as below:

Despite the superficial identity of Conclusion 3 in Argument 3 and Conclusion 3’ in Argument 4, the reasoning route from Argument 1&2 to Argument 3 is unreliable. This is because 1) fatal failure marked as “×1” in figure 1. Conclusion 1, though is reasonable in daily life, contradicts with what actually happened; 2) fatal failure marked as “×2” in figure 1. Since Conclusion 1 is false, “The man” in Conclusion 1 should not be linked to “The man” in Conclusion 2. Starts-with-S Case in Williamson paper:3 I shall save the analysis above and move to this example. For our S “Larry” in the starts-with-S case, here is the argument 1: Premise 1: The capital of California is San Francisco.(which is false) Premise 2(hidden): “San Francisco” starts with ‘S’.(which is true) Conclusion 1: The capital of California starts with ‘S’. (which happens to be true, despite that the argument is unsound) In fact, for someone who really knows, the reasoning, namely argument 2 should be as below: Premise 1’: The capital of California is Sacramento.(which is true, and refutes premise 1 in argument 1 as false) Premise 2’ (hidden): “Sacramento” starts with ‘S’.(which is true) Conclusion 1’: The capital of California starts with ‘S’. (which is superficially identical to the conclusion in argument 1) Starts-with-S case could be represented in Figure 2. as below:

Despite the superficial identity of Conclusion 1 in Argument 1 and Conclusion 1’ in Argument 2, the reasoning in Argument 1 is unreliable. This is because “Premise 1 in Argument 1 is false” is a fatal failure, marked as “×” in figure 2. Proposal Now I am ready to propose that: For S, to reach a proposition p which counts as knowledge, it is necessary to establish an argument X which chooses p as the conclusion. Consider figure 3. a representation of the proposal:

The figure above could be defined as a TREE. To reach proposition p, S needs at least one layer of argument, and that will form Argument X. Argument X requires at least one premise. It is fine for Argument X to have multiple premises, and it is fine for every premise in Argument X to be terminal conclusions in minor arguments that lead to Argument X(exampled in figure 3. as the upper-left Branch of the TREE). In Gettier paper Smith Case, argument 3 is Argument X; argument 1 and argument 2 are both Branches. In Williamson paper Starts-with-S Case, argument 1 is Argument X as the minimal layer. Proposition p is knowledge iff: 1) p is true 2) S believes p 3) S establishes a justification TREE for p 4) there is no fatal failure in S’s justification TREE for p Note that “fatal failure” is arguable, especially in practical settings.

References 1. Lecture 16 Slides, MIT online course “Minds and Machines” Entrance for PDF file: https://courses.edx.org/courses/course-v1:MITx+24.09x+3T2015/info

2. Gettier Paper Entrance for PDF file: Part 3 - Minds and Brains > Lecture 16: Belief > Knowledge and Internalism: Gettier Cases 3. Williamson paper Entrance for PDF file: https://courses.edx.org/courses/course-v1:MITx+24.09x+3T2015/info Part 3. Reading materials Met the Gettier Problem in: Week 2, The University of Edinburgh Online course “Introduction to Philosophy” https://www.coursera.org/learn/philosophy/home/welcome Part 3, MIT online course “Minds and Machines” https://courses.edx.org/courses/course-v1:MITx+24.09x+3T2015/info An online course that also helped: The University of Melbourne “Logic: Language and Information 1” (currently inaccessible) Misunderstandings my fault~