1Whether it is Possible to Know Something
1.1Arguments Contra
1.11 As Georgias of Leontini (483 B. C.) says we cannot know something since:
(1) | Suppose there is nothing; then there is no knowledge because to know means to know something. |
(2) | Suppose there is something; then it could not be known. For if there is knowledge of being, then what is thought must be and not-being could not be thought at all; in which case there could be no error, which is absurd.1 |
Thus it seems doubtful whether it is possible to know something.
1.12 To know something about real things means to judge them as they are in reality. As Sextus Empiricus says, it is impossible to judge things as they really are.
The Mode based upon relativity as we have already said is that whereby the object has such and such an appearance in relation to the subject judging and to the concomitant percepts, but as to its real nature, we suspend judgement.2
Therefore it seems doubtful whether it is possible to know something about real things.
1.13 An assertion can be called knowledge only if the assertion is true. As Sextus Empiricus says, if someone claims that his assertion is true he ought to give a proof for the truth of his assertion. And then again a proof for this proof and so on.
The Mode based upon regress ad infinitum is that whereby we assert that the thing adduced as a proof of the matter proposed, needs a further proof, and this again another, and so on ad infinitum so that the consequence is suspension, as we posses no starting point for our argument.3
This leads to an infinite regress without terminus. Thus the original claim cannot be proven to be true, and consequently an assertion cannot be called knowledge.
1.2Arguments Pro
1.21 “Bodily Awareness” is one type of direct, immediate knowledge.
...the body is originally constituted in a double way: first it is a physical thing ... secondly I find on it, and I sense ‘on’ it and ‘in’ it: warmth on the back of the hand, coldness in the feet, sensations of touch in the fingertips.4
‘My body’ is the body of which, when I am conscious, I have self-conscious knowledge.5
Therefore it is possible to know something.
1.22 To be able to calculate with the help of the multiplication table implies to have knowledge within a small part of finite number theory. Every educated child manages to calculate with the calculation table. Therefore it is possible to know something.
1.3Proposed Answer
The statement “it is possible to know something” can have different meanings. For a more accurate analysis, we shall understand “something” as some state of affairs, which can be represented by some statement or proposition p. Then to know something can be understood as to know that p is the case or to know that p is true. Under this interpretation, the statement “it is possible to know something” can have three meanings which differ in strength:
1.3.1Three Meanings, Different in Stength
(1) | It is possible that someone (i. e. some human being) has knowledge concerning some proposition p (i. e. knows that some proposition p is true or that the respective state of affairs obtains). Symbolically: ♢(∃x∈H, ∃p) xKp |
(2) | It is possible that everyone (i. e. every human being) has knowledge concerning some (or other) proposition p. Symbolically: ♢(∀x∈H, ∃p) xKp |
(3) | It is possible that there is some proposition p such that everyone has knowledge concerning p (i. e. knows that p is true or that the respective state of affairs obtains). Symbolically: ♢(∃p, ∀x∈H) xKp |
In the arguments contra, the possibility to know something is denied. This means that these arguments claim the negation of (1) or (2) or (3). The respective negations are the following:
(1’) | It is not possible that someone has knowledge concerning some proposition. Symbolically: ¬♢(∃x∈H, ∃p) xKp |
(2’) | It is not possible that everyone has knowledge concerning some (or other) proposition. Symbolically: ¬♢(∀x∈H, ∃p) xKp |
(3’) | It is not possible that concerning some proposition p, everyone has knowledge of p. Symbolically: ¬♢(∃p, ∀x∈H) xKp |
Statement (1) is the weakest claim concerning human knowledge and consequently claim (1’) is the strongest kind of skepticism concerning human knowledge. Such a claim can be refuted by a single example of human knowledge possessed by a single person as the self-conscious knowledge (“bodily awareness”) of the own body or as a calculation according to the multiplication table. On a higher level (1) also claims that there is expert-knowledge, some selected (by education and training) people know some specific things. To deny this, i. e. to claim (1’) is certainly absurd. We need experts all the time (physicians, technicians, pilots, bus drivers, chemists, peasants, ...). Statement (2) is stronger than (1) claiming that it is possible that everyone has some knowledge in some domain or other. If someone denies this possibility, i. e. if he claims (2’) then he denies that all people have knowledge in some domain. It is clearly absurd to deny this since very simple things like self-conscious knowledge or E1–E4 below everyone will know. Statement (3) is even stronger than (2) claiming that it is possible that there are some propositions with respect to which everyone has knowledge. A statement of the form “it is possible that p” is proved if one can give an example for an actual instance of p, since if p is the case, then possible p holds. Several kinds of such examples can be given which justify statement (3). Some famous ones from the philosophical tradition are these:
1.3.2Famous Examples E 1–E 5
E 1 | “If there is only one sun then there are not two.”; “Either the world is finite, or the world is infinite.”6 |
E 2 | “If he doubts he knows that he doubts ... if he doubts he knows that he does not know.”7 |
E 3 | “Si enim fallor, sum.” Since he who does not exist cannot err. Therefore I am if I err.8 |
E 4 | “Cogito ergo sum.” I think, therefore I am.9 |
Examples E 2 – E 4 are concerned with self-reflecting knowledge. E 1 is concerned with knowledge of simple logical propositions. In this respect Aristotle has proposed his principle of non-contradiction as the most general and the most basic logical principle which implies and justifies statement (3) above: “Let this, then, suffice to show that the most indisputable of all beliefs is this:
E 5 Contradictory statements are not at the same time true.”10
The principle E 5 is the most tolerant formulation of the principle of non-contradiction which is invariant w. r. t different types of systems of logic like classical two-valued logic, intuitionistic logic, minimal logic, different types of many-valued logic.11
E 1–E 5 refute the claim that knowledge is not possible, expressed in different strength by (1’), (2’) and (3’). By this, they justify the statements (1) and (2) and (3).
1.4Answers to the Objections
1.41 (To 1.11:) There are at least three possibilities to interpret Gorgias’ claims. First, he did not take them serious himself, but, as a Sophist, wanted just to provoke. Second, he took them serious because he gave some arguments of defence, although these arguments contain untenable premises like “being can neither be one nor be many.”12 Third, he wanted to stress the fallibility of human knowledge. In this case, he starts with the experience that there is error in human thinking. Moreover, if knowledge is not compatible with that kind of error we have to give up knowledge. “What is thought must be, and not-being could not be thought of at all” is not a literal quotation from the fragments but seems to be a reasonable interpretation. If correct, it shows that Gorgias did not differentiate between being and being so, and not between existing and non-existing objects to which our thoughts are directed.13 It is correct that thinking is intentionally directed to some object. However, such objects may exist (in space-time like Venus or independent of space-time like the prime number between 5 and 11) or not exist (in space-time like a perpetuum mobile or independent of space-time like the prime number between 31 and 37). Thus there can be error concerning the existence or non-existence (being or not-being). However, errors occur much more frequently concerning being so or not being so, i. e. concerning the question whether t...