Knowledge and facts

Knowledge and reality
June 2, 2020
Coincidence, determinism and free will
June 13, 2020

In Knowledge and Truth, I wrote that knowledge is supposed to refer to facts. But what are facts?

Possible meanings of “fact”

In ordinary language, the word fact has a strong connotation of truth. Sentences like “it is a fact that p” or “p is true” seem to mean the same – p stands for a proposition.  But “p is true because p is a fact” is not the same as “p is a fact because p  is true.” Reducing the meaning of the predicate “true” to the meaning of “fact” – or the other way around – will inevitably lead to circular reasoning. An even more serious caveat is that the notion of truth is mind-dependent: truth is meaning. This implies that if we define “fact” using the notion of “truth”, we either exclude the possibility of mind-independent facts or we are forced to accept Hilary Putnam’s famous, but temporary position that “Meaning ain’t just in the head”, meaning is shown directly by reality. Finally, “true” is one of only two possibilities to evaluate propositions, while propositions may express facts, beliefs, qualifications, theories, feelings, nonsense or even nothing at all.

Let’s look for plausible referents of the word “fact”. “Fact” may either refer to an aspect of reality, or to a mental representation of an aspect of reality, or to a worded representation of an aspect of reality. In these three denotations of “fact”, the key distinctions are between existence and non-existence, between belief and disbelief and between objective and not-objective wordings respectively.“Existence” is used in the sense of actual, present existence, of “being the case now”, to distinguish it from modal or eternalist notions of existence. “Belief” is used in the restricted sense of “believing something to actually be the case”, to distinguish it from belief as qualification or theory.  “Objective” is “expressed in object language”, that is, in a language not expressing any meaning.

Are propositions reducible to facts or the other way around? A fact could be something that is actually the case, and believed to actually be the case, and worded in object language, but combining these conditions is counterintuitive: aren’t facts just facts, whether or not we believe them or succeed to formulate them objectively? This route I shall further refer to as the reality-belief-language route. Under this option, knowledge cannot contain facts but only refer to facts, forcing us to elaborate on the relation between knowledge and facts. Another possibility is to go the other way around, a move in early 20th-century philosophy, known as the linguistic turn: a fact is a true proposition representing a belief of something that is actually the case, the language-belief-reality-route. At first sight, this route is unsatisfactory also, because it would imply that a fact is an objectively formulated true belief, reducing “fact” to “true”, a move I hoped to avoid.

The reality-belief-language route

During the larger part of metaphysical tradition, facts have been characterized either as substances with properties – snow is white – or relations between existents – there’s snow on the lawn. Under this existents-and-properties-based notion of facts, the inner structure of facts needs to be explained, because existents and properties are different metaphysical categories, so how do they relate? As we saw in The Metaphysics of Truth, white may be considered as a universal property that can be instantiated simultaneously in different places – something that substances are incapable of – or as a particular, the whiteness of this here snow. Many more positions have been taken across philosophical history. The status of facts is in need of explanation also. “Snow is white” might be universally true, but “There’s snow on the lawn” is a particular truth, true here and now. Should we distinguish between types of facts, and does this influence their ‘factuality’?

Shamik Dasgupta

But the main problem is to take objects or relations as facts to then explain how knowledge of them relates to reality.  Shamik Dasgupta gives the example of a conference occurring. What does it take for something to count as a conference, or how is the conference-as-fact grounded? On the classical notion, this would require summing up all of the essential features of conferences, or of a number of underlying facts to ground the single fact that what is the case is a conference, at the risk of course, of encountering new complexities, in their turn in need of grounding.

On the turning point

Ludwig Wittgenstein’s Tractatus Logicus-Philosophicus merits the turning point between the two routes mentioned.  According to the Tractatus, the world does not consist of things, but of facts. Wittgenstein calls them Sachverhalte, alternately with Tatsachen (facts) and Sachlagen (the ways things are). The German sich verhalten does not only mean to relate; it has a very strong connotation of behavior. Therefore, Sachverhalt expresses how Sachen (things) behave. In a Sachverhalt like “Snow is white”, snow is not seen as an existent having the property of being white or being capable of satisfying the functor “… is white”. “Snow” and “white” are just two Sachen, which behave such as to link into a fact completely according to their logical, internal properties or simply put, possibilities. This idea was a decisive blow to all metaphysical poppycock about properties, such as the universalism-nominalism controversy or the discussion about essential and accidental properties.

Facts lead to thoughts, which can be expressed in propositions. Wittgenstein then claims that these thoughts and propositions mirror atomic facts because they take the same form – a position he would revise later. Atomic propositions are then linked together into complex propositions in a logical way. The total of these propositions constitutes reality. To the early Wittgenstein, knowledge is identical to reality, and the discussions about the question if propositions are shaped by reality or the other way around are futile, since the early Wittgenstein takes their isomorphic structure as an axiom. According to the famous final sentence of the Tractatus, everything beyond the realm of knowledge is nonsense.

The language-belief-reality route

Since the Tractatus made clear that facts only become apparent once they are formulated in propositions, others began to approach the connection between facts and propositions from the other end. To define the criteria for a language for the description of facts, Alfred Tarski distinguished between object language – to describe facts– and metalanguage, the language we use to talk about the facts thus described. Tarski chose to not take ”true” and “false” as primitives since this would have committed him to ” p is a fact because p is true.” With Tarski, truth is not a material condition – of correspondence between expression, belief, and reality – but a formal condition. He insisted on correct definitions of “true” and “false” that could vary according to the formal logic of the language used. His most important example was not a natural language, but the language of logical calculus, yet his theory applies to all languages. The object language is capable of endlessly linking together propositions using simple logical operators like and, or, not. The metalanguage is supposed to contain all concepts and methods for mathematical-logical proof, the precise meanings of all primitive signs of the language – such as logical operators –, a grammar for defining new expressions, and the rule that clear vocabulary will be used, consisting of words meaning what you would expect them to mean, as in Tarski’s famous example of his truth condition, Condition T : “ ’Snow is white’  is true if, and only if  snow is white.” Or: “ ‘p’ is true if and only if p ”

If we employ Tarski’s system to define knowledge, we see that individual mental representations of facts are irrelevant, and so is justification of belief in specific facts if based on mental states. Truth is context-dependent, because for different contexts different logical-mathematical languages may be used, each containing their language-specific definition of truth. Only logical validity is universal. Condition T compels to binary judgments on truth, so, it leaves no room for graded assessment of the meaning of propositions. If binary judgment of a proposition is impossible, it needs to be reformulated or split up, until it is able to satisfy the principle of non-contradiction.

Propositions are either true or false and if not, they are false.

So, Tarski proceeds directly from formally correct expressions to logical validity. With Tarski, facts are not existents sui generis, but formal constructs. Facts have to be established and to pass logical tests: knowledge is what is formally true.

Knowledge and facts

We saw that if facts are ‘only’ aspects of reality, knowledge cannot contain facts, let alone consist of facts, but only refer to facts. This reference is problematic because correspondence between propositions and facts cannot be proven: it has to be accepted as an axiom, to be believed, see Knowledge and Reality. To put it less indulgently: correspondence is a dogma. With facts as formal constructs expressed in object language, facts can be the core of knowledge. Apart from accounting for the method by which the facts were assembled and formulated, knowledge will also contain formal judgments on truth-value as well as the underpinnings of these judgments.

But it is naïve to believe that knowledge can be just facts and accounting for facts. To go from knowledge to belief – on the language-belief-reality route –, facts have to be selected, ordered, highlighted, and will be modeled into explanations and predictions and assessed for relevance, usefulness, and satisfaction. It is therefore impossible to go from facts to knowledge and retain objectivity.

In theory, knowledge could consist of nothing but facts, but already the arrangement of these will express meaning: facts cannot be presented in a sender-independent way, and neither can knowledge be understood objectively.

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