Sceptical Absolutism

A raw first draft of some thought on scepticism, a belief in an absolute objective truth and relativism. The use of logical notation is only partly so I can fuel fantasies about being a theoretical physicist, it's also because a lack of skill in writing prevents me from rendering somethings in halfway decent English.

Whilst the absolutist and relativist agree that “the world is everything that is the case”i they disagree on what they take to be “the case”. They will, naturally, often agree on specifics. Both the relativist and the absolutist are likely to hold the same opinion on the correctness of an uncontroversial statement such as “there is a blue Everton shirt in front of Eve” (call this statement “s”). Their disagreement is more abstract: over what it means for something to be “the case”, what causes it to be so, what makes s true.

Absolutism

The absolutist holds that what is the case simply is the case, utterly independent of the observer. There either is a blue Everton shirt in front of Eve or there is not. s is true just in those cases where there is a blue Everton shirt in front of Eve and false just in those cases where there is not a blue Everton shirt in front of Eve.

s entails a number of other putative facts, that there is an object that absorbs red light in front of Eve, that the object is made of cloth, that the object has a definable badge with Everton's motto “nil satis nisi optimum” and so on. Other statements, not identical to s, may have the same entailments. These same entailments may be expressed in a different language, may be expressed by speech or text, will expressed differently even if spoken in the same language in a strong Liverpool accent as opposed to in received pronunciation. “Il y a un maillot Everton en face d'Eve” and “there is a blue Everton shirt in front Eve” both entail that there is an object that absorbs red light, that the object is made of cloth and so on. Although they are different statements it can be said that they express the same proposition, from here on referred to as p.

Any two series of statements that purport to be a complete description of what is the case will either express the same or differing propositions. If the series express the same proposition then all statements that the series entail will express the same propositions. A complete description of reality in French will, if it contains the statement “il y a un maillot blue Everton en face d' Eve” entail that there is an object that absorbs red light. A complete description of reality in English will, if it contains the statement “there is a blue Everton shirt in front of Eve”, also entail that there is an object that absorbs red light. Now there either is, or is not, at a specific time and place an object that absorbs red light. If our series of statements in French is true it will correspond to that state of affairs: affirming it if it is the case, denying it if it is not the case. If both our French and our English series of statements are to be true then they must both entail the same proposition about the presence of red light absorbing objects. If they are true, and complete, descriptions of what is the case then for each aspect of what is the case they must agree with each other as well as correspond to what is the case. If they are both true they must express the same set of propositions, what is the case corresponds to just the one set of propositions: there is only one totally of what is the case. There is just the one world.


Relativism

Most relativists think this is all hopelessly vague, often circular and ultimately unproductive. The proposition seems particularly vague. A “proposition” seems to be, more or less, what a statement is if you remove all the language: and that sounds like silence. It we wish to give the concept some content we have to talk in term of what is the case rather than our method of talking about it. This makes the concept of truth sound circular, propositions are the “what is the case” about a statement that statement being true if “what is the case” corresponds to what is the case. Whether circular or not it is unproductive, to operate the concept in our lives we cannot leave the world and truth as ineffable mysteries. We need true statements and knowledge of hard facts and that necessitates that whatever is the case is determined.

This determination necessitates a framework; an “ideology”, “paradigm”, “discourse”, “world view”, “set of presuppositions” and the like. Frameworks vary, producing differing determinations of what is the case and there is no framework independent method of determining which framework is “correct”. A determination of what is the case is, thus, relative to the framework that determined that it is the case. Whilst a statement can be correct just in so far as it corresponds to what is the case it makes little sense to talk of a statement being correct per se. Eve's statement s is right relative to Eve's framework just in case Eve's framework determines that there is a blue Everton shirt in front of her and wrong just in case Eve's framework does not determine that there is a blue Everton shirt in front of her. (For ease of distinction in this paper the terms “true” and “false” will be used to denote objective truth and falsehood, the terms “right” or “wrong” will be reserved for correspondence with relatively determined facts.)

Assume a situation, call it “situation1” where we would assent to s. We would assent to s because s emanates from a framework that uses the concepts of “Everton”, “shirt” and “blue”. Football clubs are a cultural construct as is the concept of “shirt”. The idea of a football club specific shirt is another cultural gift, allowing some shirts to win first prize in the lottery of shirt-dom and be Everton shirts. The blue arises as result of the human eye and brain which compartmentalises the smooth variations in wavelengths of light into distinct colours.

And none of this need be so. Were we in the early 19th century, if we had a 19th century framework, then “football” would denote a very different activity than it does today. We have to wait until 1878 before there is an Everton Football Club for the shirt to pertain to, whilst still earlier frameworks would fail to recognise a shirt. Other cultures extant today, despite the march of globalisation, would not recognise a shirt, or football, or Everton. The French “il y a un maillot blue en face d'Eve” is not entirely commensurate with the English. The French use the word “maillot” for an item of sportswear, whereas “shirt” covers both sportswear and everyday clothing. You can wear a shirt to work but not a maillot. The blueness of the shirt arises, if we accept what we are told, because it absorbs most of the visible spectrum of light reflecting only the portion we call “blue”. Were the shirt to reflect both the blue and green portions it would not be both blue and green but yellow. Now humans only see a small range of wavelengths of light, insects see more: they see ultra-violet. Where an object absorbs all light except for ultra-violet an insect will see an ultra-violet object and a human a black object. If the putative Everton shirt reflected back both blue and ultra-violet the insect would see a different colour that, because we have never seen it, we have no name for. Remaining within the bounds of human frameworks we may use Goodman's terms of grue and bleen to describe the shirt. A shirt is grue if, when examined before time t, it is green and blue if unexamined. A bleen shirt is one that is blue if examined before time t and green if unexamined.ii Or we may be speakers of one of those human languages that do no have a term that corresponds to blue. s can only be right within a very particular framework, one which there is no objective justification for privileging.

Frameworks vary, producing differing determinations of what is the case. A judgement between frameworks itself dependent on a framework. As a result although framework-f may be judged the absolute business within framework-f, outside of any framework it cannot be judged more (or less) valid than any other. The necessity of frameworks renders all frameworks equally valid.

This much, the doctrine of equal validity, is a common factor in relativism. The next step brings a divergence. Some insist that a framework is not just necessary but sufficient for establishing what is the case, the doctrine that frameworks are “equally valid and valid”. The view manifests itself in popular discourse with such ideas that there are “different ways of knowing the world”: the differing ways result in knowledge of what is the case. As they are differing ways they result in differing worlds.

An alternative take is to deny that a framework is ever sufficient. Any determination of what is the case must transcend a framework which, as the framework is necessary, is an impossibility. We are left with various “discourses” that we tale part in all with little, or no, relation to anything that might be said to be “the case”.

To bring the strands of relativism together and for ease of distinction from absolutism, the terms “true” and “false” will be used to denote objective truth and falsehood, the terms “right” or “wrong” will be reserved for correspondence with relatively determined facts.iii

Partial Refutation of Relativism

Whilst it is entirely correct that nothing that is the case can be determined it is incorrect that nothing can be determined about what is the case.

Take a situation (call this “situation2”) where the putative blue Everton shirt in front of Eve is replaced with something it would be right to call a red pair of Liverpool shorts. s has now become wrong. It becomes wrong independent of any framework: our conclusion changes, but our framework has not. We have not changed culture, developed new cognitive apparatus or undergone a sudden conversion experience. The world has changed and with it our conclusion about the world.

Neither does a person with an alternative framework, one which fails to support s when we maintain it, fail to reject s when we reject it. The framework is a necessary condition of s being right. If s is right then our framework, or the relevant part of it, holds for the observer. If our framework fails to hold for Trevor then s is not right for Trevor whether or not somebody is waving a pair of Liverpool shorts in his face. Nor does our framework need to support s being wrong. If we is presented with black Manchester United shorts, green Norwich City socks or a pint of Real Ale then s is wrong. It is not necessary to establish what it is that is in front of Eve, just that it is not a blue Everton shirt. It is not what is the case that makes s wrong but what is not the case.

Resisting the temptation to describe what is the case, a description that depends on a framework and is subject to relativist objections, we can designate what fails to be the case as a. We can accept that we have no idea what a is and accept that we have no idea what is the case in situation2. We must also accept both that a is a consequence of s ( s→a)iv and that a does not obtain, independent of any framework (¬a). Thus s is not just wrong, it is false. In situation2 a does not obtain, but it is entailed by s. If s were true then a would obtain, a does not obtain, thus s is false.

We can now make the confusing sentence that began this section clear. “Nothing that is the case can be determined”: we cannot say what is the case. “Incorrect that nothing can be determined about what is the case”: we can often say some of what is not the case.

If there where no objective states of affairs to which propositions may correspond no statement could be refuted solely on manipulation of what is the case. Statements can be refuted solely on manipulation of what is the case, thus there is an objective state of affairs to which propositions may correspond.


Sceptical Truth-schema
Resisting the temptation to describe what is the case, a description that depends on a framework and is subject to relativist objections, we can designate what fails to be the case as a. We can accept that we have no idea what a is and accept that we have no idea what is the case in situation2. We must also accept both that a is a consequence of s ( s→a) and that a does not obtain, independent of any framework (¬a). Thus s is not just wrong, it is false. In situation2 a does not obtain, but it is entailed by s. If s were true then a would obtain, a does not obtain, thus s is false.

Of course a is just one of a whole host of consequences of s, any one of which is sufficient to render s false. If there exists any x such that s entails x and x is false then s is false:

1.∃x [(s→x) & ¬x] → ¬s
(if there exists an x which is entailed by s and that x is false then s is false)

Now if there is an x entailed by s that is capable of being true or false then it is either true or false and thus everything entailed by s that is capable of being true or false is either true or false. If everything entailed by s were true then s would be true. To be false s must make a false claim. The falsity of s entails that there will be something false entailed by s:

2.¬s → ∃x [(s→x) & ¬x]
(if s is false then there will exist an x entailed by s that is false)

This is equivalent to:

3.∃x [(s→x)] & ¬∃x [(s→x) & ¬x] → sv
(if there exists an x, such that x is entailed by s and there exists no x such that s is is entailed by x and is false then s is true)

For good measure “3.” is equivalent to:

4.s → ¬∃x [(s→x) & ¬x]
(if s is true then there does not exist an x such that x is entailed by s and x is false)

Which combines with “3.” to give:

5.s ↔ ∃x [(s→x)] & ¬∃x [(s→x) & ¬x]
(s is true if and only if there exists an x, such that x is entailed by s and there exists no x such that s is is entailed by x and is false)

The schema holds that entailment combined with an absence of false entailments is both necessary and sufficient for the truth of a statement. The combination of necessity and sufficiency negates both the necessity of a framework and the sufficiency of a framework.

We are not entitled to conclude from the premise that a statement either entails nothing or entails something that is false that the statement is not correctly made from within a framework. There are plenty of examples of statements made perfectly in accordance with an epistemology, all the relevant data, in accordance with a preferred ideology that have predicted events that did not come to pass. A framework is not sufficient.

As for the necessity, the schema defines a logical relation between a statement and the world it purports to describe. A framework may be contingently necessary for a statement to entail, but it is not a logical necessity. Neither, as we have seen above, is a framework necessary for statement to fail to conflict with reality. Where there is contingency in failing to conflict it is a contingency of the world rather than the statement.
be false.

It has to be said, however, that the contingent need for a framework almost universally obtains. The relativist arguments against the absolutist hold for all actual statements made about the world. We cannot say anything true about the world if we use a framework, we cannot say anything about the world without a framework. It follows that we cannot say anything true about the world.