Many Valued Knowledge: A study in epistemic non-absolutism

Many-Valued Knowledge: A study in epistemic non-absolutism. By Quincy Arthur [email protected] 42248112 PHIL 240: Knowledge and Reality Prof.: Dr. Adam Morton TA: Alirio Rosales Contingency as Disallowing Epistemic Absolutism: Traditionally, knowledge and understanding are thought of as being absolute. This is in the sense that either they are present, or they are absent. However, there are statements in the English language, which, in their composition and meaning, suggest a formation of knowledge that is non-absolute. Statements that have plagued philosophers with regards to the constituency of knowledge are those demarked by Edmund Gettier. A Gettier case is when a justified true belief does not constitute knowledge. Gettier’s example outlines two people applying for one. The CEO tells Smith, the first applicant, that the other applicant, Jones, will get the job offer. Furthermore, he has seen that the number of coins in Jones’ pocket consists is ten. With both of these pieces of information, Smith forms the belief that “A man with ten coins in his pocket will get the job offer.” This is a justified belief, since it is entailed by his absolutely justified belief that “Jones has ten coins in his pocket and Jones will get the job offer.” Unbeknownst to Smith, however, he himself has ten coins in his pocket, and he is the one who will get the job offer. This makes the justified belief that he has come to true, while seemingly denying its existence as a known statement. Gettier, using his example, manages to exemplify how a justified true belief (JTB) does not constitute knowledge. (Gettier 121-2) But in this case is knowledge wholly absent or is simply a weaker form of knowledge present? Stephen Hetherington seems to deny the absolute nature of knowledge, and believes that there is knowledge within Smith’s JTB, but that it is a ‘failable knowledge’: “The usual interpretation of Gettier cases says that knowledge is absent from them; I reject that interpretation. In this section I argue that knowledge is present, but that it is knowledge with a significant epistemic failing, one which makes epistemologists mistakenly think that knowledge is absent. Its failing is that it is very failable.” (Hetherington 72-3) Hetherington’s handling of Gettier cases plays into his general rejection of absolute knowledge and his counter argument of knowledge as being ‘failable’: “Knowing failably entails possibly not having that knowledge. And knowing fallibly entails knowing failably: if one’s belief that p is knowledge yet could be mistaken, then it is knowledge that could fail to exist as that knowledge. Hence, it is knowledge that might not have been that knowledge.” (Hetherington 42) The notion of knowledge not being an absolute entity ushers in a number of questions regarding potential range of knowledge capacity, and with that, an idea of degreed knowledge. In this way, Gettier cases raise interesting issues regarding the nature of knowledge. One aspect of beliefs that seems to deny their being knowledge is contingency. Contingency is a characteristic given to a proposition if it is possible, and may well be true, but it is uncertain. In terms of future contingency, the uncertainty stems from humanity’s inability to discern the future. This is outlined by Aristotle’s famous future contingent statement “There will be a sea battle tomorrow.” Whether this is true of false, it cannot be known due to the limitations of human perception. This type of contingency applies too to beliefs like “I know where my car is parked in the parking garage,” which hark back to the ‘failable knowledge’ of Gettier cases. Even if this is a JTB, based on your memory of where you parked your car, it cannot constitute knowledge. If you believe this proposition at any time other than when you are in direct perceptual contact with your car, it is contingent as to whether you know that you know where your car is parked or not. Humans’ inability to see through concrete walls is akin to our inability to see into the future. Again, perceptual restraints make our knowing this contingent. To truly know this statement, one would have to take into account, and know the truth value of, every possible thing that could have happened to one’s car between the time of parking and the moment of belief-formation; like the presence of a car thief in the garage, or you car’s dematerialising. One can say that they know this fact, but, using Hetherington’s term, this JTB would be a ‘failable knowledge’, or a ‘part-knowledge’ as this study will allude to such states. In searching for a more standardised representation of the abstract ambiguity that Hetherington alludes to with his ‘failable knowledge’, there are various avenues one can go down. Symbolic logic is one avenue that can be pursued to formalise concepts when taking into account abstract and informal spaces, like this hazy ground between knowledge and ignorance. The additional truth-values used in many-valued logics can form a basis for such levels of knowledge. Alternatively, one can study the Sentience Quotient, introduced by Robert A. Freitas Jr.. While being a rather speculative formation of levels of sentience, it can provide an intuitively appealing conceptual analysis of degrees of knowledge. Both of these avenues handle contingency, and so figure nicely in the propositions that cause philosophers most trouble. Furthermore, both of these formulations support a claim to epistemic non-absolutism and represent their implicators of knowledge as being degreed, so ushering in a potential image of a degreed form of knowledge. Many-Valued Logics: Aristotle’s initial maritime quandary was an influence of his dissatisfaction with the Law of the Excluded Middle, which states that a proposition can never be true and not true (~ (p^~p)). His On Interpretation was the first known text to deal with future contingents, and ushered in the modern work to be done on many-valued logics. These are logics that subvert a notion of the existence of only two truth-values, T and F. Instead there are intermediary ones in which contingency can find some foothold and form degreed knowledge. However, before studying any many-valued logic and its associated extra values, one must first establish what the bivalent truth-values mean. This will aid in elucidating ideas about the many-valued system and its new truth-values. Logician John Woods describes them as follows: “T and F must be the right sorts of instruments with which to define the logical terms and to define the entailment relation. […]‘T’ and ‘F’ are informally read as ‘true’ and ‘false’. Of course, strictly speaking, this can’t be true. […] What T and F actually are are values of a function. The function assigns these values to sentences. Sometimes these functions are called valuations. […] It seems reasonable to say that they are formal representations of the properties of truth and falsity. […] although we don’t want our formal sentences to have content, we do want this for our connectives. So we want to give them meanings. Accordingly, we arrange things so that • ν(p) = T is the formal analogue of English sentences of the form “’p’ is true”.” (Woods) This outline intimates the lack of propositional content that logic has, and so allows for a more enlightened study of new truth-values and how they can potentially relate to knowledge. While the values included in the system represent truth, they are simply a ‘formal analogue’ holding place. Many-Valued logic comprises of a wide variety of systems, all giving varying representations of what is not truth and not falsity, and how this space can be scaled. However, to explicate the principal idea of non-absolute knowledge most easily, it makes most sense to start with the simple 3-valued logic system L3, made by Jan Łukasiewicz. With this 3-valued logic, as the name suggests, there is only one additional truth-value in the system, I. This new value has no stringent definition, but has been regarded as being a formal representation of ‘possibility’ by Łukasiewicz, ‘meaninglessness’ by Bočvar, and ‘undefinedness’ by Kleene. I in L3 is a designated value, which formally means that it is ‘truth-like’. (Woods) L3 has these valuations: L3(~): ~(T) = F ~(F) = T ~(I) = I L3(∧): ∧(T,T)=T ∧(T, I) = I ∧(T,F)=F ∧(I,T)=I ∧(I, I) = I ∧(I, F) = F ∧(F,T)=F ∧(F, I) = F ∧(F,F)=F L3(∨): ∨(T,T)=T ∨(T, I) = T ∨(T,F)=T ∨(I,T)=T ∨(I, I) = I ∨(I, F) = I ∨(F,T)=T ∨(F, I) = I ∨(F,F)=F L3(⊃): ⊃(T,T)=T ⊃(T, I) = I ⊃(T,F)=F ⊃(I,T)=T ⊃(I, I) = T ⊃(I, F) = I ⊃(F,T)=T ⊃(F, I) = T ⊃(F,F)=T (Woods) As is evident in the table of truth-valuations, I features heavily in the operation of the logical system. The results that the atomic propositions of each formal sentence yield often features this mysterious value I, which is neither truth nor falsity. I can come to represent the ambiguity which contingency throws on some propositions. Subsequently, it produces an effective model of gauging what can be T, what can be F, and what must remain I, in light of contingency in propositions like “I know where my car is parked.” This new system, also denies the Law of Excluded Middle (p ∧~p is possible when p is I). This too seems to be permitting of contingent statements. But how does this figure epistemologically? In terms of this system referring to a non-absolute representation of knowledge, one must appreciate that “A proper analysis of knowledge should at least be a necessary truth.” (Knowledge) When recognising the implication of truth-values in knowledge, this new truth-value seems to take into account the situations encountered earlier, which were ambiguous because of their contingency. Aligning T with absolute knowledge, and F with ignorance, where would I figure epistemologically? Acknowledging its designation, and therefore its truth-likeness, it is easy to render this value as representative of some kind of knowledge, perhaps knowledge-likeness. This rendering denies absolutist theorems of knowledge and alludes to some hinterland between knowledge and ignorance wherein lots of propositions, while void of knowledge, have knowledge-likeness. This is a step away from absolute knowledge, which is either present or absent. Now that I has been established as a possible indicator of a non-absolute knowledge, the range that many-valued logics allow for it to operate in can be studied. Stepping away from the elementary L3 there are a number of logics permitting of a more degreed and less abstract representation of what is not wholly truth or falsity. Among this number are L4, L8, and Fuzzy logic. L4 operates in a very similar way to Łukasiewicz’ L3. L4 has two additional values, I1 and I2, where I1 represents truth-likeness, and I2 represents falsity-likeness. In essence, this system is just a degree more definite than L3. L8 and Fuzzy logic are both systems that employ a more degreed representation of truth than one or two values. As one can probably infer from the name, is an 8-valued system, with truth-values numbering from 1 to 8, with each number representing a combination of Ts and Fs, with 1 being <TTT>, and 8 being <FFF>. (Woods) Fuzzy logic is a “logic in which sentences can take as a truth value any real number between 0 and 1.” (Priest 221) This permits of an even more degreed representation of the variable truth valuation, drawing truth into an infinity of alternate weight. These three logical systems exemplify how the ambiguous space formally represented by the truth-value I in L3 can be leveled in a way to measure the validity of certain truths, and how closely they tend towards absolute truth or absolute falsity. With this in mind, it is easy to see how a non-absolute knowledge too can be fitted on such a scale, with knowledge values tending towards either absolute knowledge or absolute falsity, based on the truth-values of the contributing propositions to belief statements. The Sentience Quotient: Xenopsychology is the practice of hypothesising the intelligence capabilities of potential extra-terrestrials. This can quite effectively be influential epistemologically in terms of the knowledge that advanced intelligence or sentience capabilities would allow. From the fact that Humans have a higher sentience than rocks and so have higher knowledge capabilities, one can infer that something with more sentience than humans would have more adept epistemic capabilities. Robert A. Freitas Jr. invented the Sentience Quotient in 1984 to valuate universal sentience in a way that allows for a speculation of hypothetical extra-terrestrials and their intelligent capabilities. Frietas defines the quotient thusly: “The most efficient brain will have the highest information-processing rate I, and the lowest mass M, hence the highest ratio I/M. Since very large exponents are involved, for the convenience we define the Sentience Quotient or SQ as the logarithm of I/M, that is, its order of magnitude. Of course, SQ delimits maximum potential intellect–a poorly programmed or poorly designed (or very small) high-SQ brain could still be very stupid. But all else remaining equal larger-SQ entities should be higher-quality thinkers.” (Freitas) Using this quotient, Freitas created a scale between the lowest cosmic sentience, coming to -70 on the SQ, and the greatest cosmic sentience, coming to +50 on the SQ. The quotient gives human sentience a value of +13, which is rather dwarfing. This means that there are 23 possible degrees of intelligence beyond what our physicality will allow us to achieve. This is where epistemology and contingency can make interesting reference. In the same way that we have more knowledge than a Venus flytrap, which Freitas gives a +1 value on the quotient, something with a quotient value of +35 will more than likely have a sentience level permitting of planes of knowledge beyond the grasp of our own sentience. This aligns well with our perceptual limits, which force the contingency of statements like “I know where my car is parked in the parking garage.” While a being with a sentience quotient value of +35 may not be able to see through concrete, the principle remains, there may be an aspect of reality graspable by the sentience of more intelligent creatures than ourselves, which we will never access due to limitations. The idea of their being aspects of reality which we cannot ever perceive due to the relationship between the information-processing rate of our brain and its mass ushers in a reality about which we will never have absolute knowledge. How can our knowledge of something be absolutely and necessarily true if we cannot perceive the entire frame of reality? The degreed nature of the Sentience Quotient intimates a degreed leveling of sentience, which entails a degreed leveling of knowledge too. This way in which possible sentience is scaled here is akin to the way in which L8 scales truth between absolute truth and absolute falsity. The Sentience Quotient seems to scale sentience in a way that quantifies absolute ignorance, at -70, and absolute universal knowledge, at +50. The intermediary degrees represent ‘part-knowledge’ or some degree of perception of the surrounding reality. In this way, the Sentience Quotient too can come to represent the existence of non-absolute knowledge, as well as a degreed interpretation of such. Closing Notes: The call started by Gettier cases, then, has seemingly been responded to by two non-epistemic formulations: many-valued logics, and the sentience quotient. The study of many-valued logics, like the one designed by Łukasiewicz, outlined how a formal semantics of logic can be permitting of non-absolute truth. This, in turn, permits of non-absolute knowledge, through the implication of truth in epistemology. Similarly, Freitas’ Sentience Quotient gives an interpretation of non-absolute knowledge through its formulation of a measurement of non-absolute sentience or perception, which too is crucially implicated in knowledge and belief formation. Evidently, then, they support Hetherington’s notion of knowledge as not being absolute, mainly due to the existence of contingent sentences and Gettier cases. There are, however, limitations upon this argument. With regards to many-valued logics, the designation of I could pose some issues. Designation is a property that is applied to truth-values in aid of the technical virtuosity of the logical system. In so doing, the conceptual adequacy of a pursuit of a many-valued representation of entailment is somewhat abandoned for mathematical fluidity. Conceptually, I is not truth-like exclusively, so much as both truth and falsity-like. It is an intermediate between T and F, and Woods claims that “perhaps a better candidate for I is ‘approximate truth’.” This interpretation, while straying from the stringency that a logical system demands, still allows for the support of non-absolute knowledge given. With regards to the Sentience Quotient, there are limitations here too. First published in 1984, the Quotient can be regarded as being rather outdated in the field of xenopsychology, and its interpretation of the scales of sentience could be suspect. Another method of comparing interspecies intelligence is Nikolai Kardashev’s Kardashev Scale, which, while introduced in 1964 is constantly being updated and improved upon. This scale takes energy consumption into account and is more focused on civilisations, so is not as appropriate for this study of the nature of knowledge. Many avenues of further enquiry for this study could be pursued. A close analysis of the nature of a number of many-valued logics could be done, which may shed more light on the nature of non-absolute knowledge via the nature of non-absolute truth. The way in which species fit onto the very quantified Sentience Quotient could be a way in which to glean more information about the nature of interspecies knowledge based on sentience. Works Cited: Freitas Jr., Robert A.. “Xenopsychology,” Analog Science Fiction/Science Fact. Vol. 104, April 1984: n. pag. Web. 10 April 2013. Gettier, Edmund. “Is Justified True Belief Knowledge?” Analysis. Vol. 23, 1963: pp 121-123. Transcribed into hypertext by Andrew Chrucky, Sept. 13, 1997. Web. 17 April 2013. Hetherington, Stephen. Good Knowledge, Bad Knowledge. Oxford: Oxford University Press, 2001. Print. Ichikawa, Jonathan Jenkins and Steup, Matthias, "The Analysis of Knowledge", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), (Ed.) Edward N. Zalta. n.d. Web. 10 April 2013. Priest, Graham. An Introduction to Non-Classical Logic: From If to Is. 2nd Ed. Cambridge: Cambridge University Press, 2008. Print. Woods, John. “Many-Valued Logic.” Phil. 323. Non-Classical Logics. U of British Columbia. 24 February 2013. Woods, John. “Semantical Considerations on Many Valued Logics.” Phil. 323. Non-Classical Logics. U of British Columbia. 4 March 2013. Class notes.