It is natural to divide the world up into two categories: the objective and the subjective. Matters of fact – cases where an assertion can be either true or false – belong to the objective. And, in contrast, the subjective is a domain where everything goes, where we are free to essentially make things up as we go, and where every opinion must be given equal weight. If we look at the world through this perspective it is easy to conclude that what is really important is the objective. And thus that anything which falls short of being objective, to which the labels true and false do not apply, is unimportant, and at best a kind of entertainment. The advantage of this perspective is that it is simple, and if your interests do lie primarily with those things that are unequivocally objective (the objects of rigorous science, for example) then it is probably good enough. However, there are complexities that this simple picture hides, and sticking to it, and its associated value judgments, can lead to confusion, as anything deemed important is shoehorned into being objective.
To get started with separating the different kinds of things lumped into objectivity by the simple dualistic picture discussed above I will start with pinning down what exactly is subjective. In the strictest, most literal sense, to be subjective is to be something that a particular subject can have complete authority about. For example, whether War and Peace is an enjoyable book is subjective, in this sense, because it is up to each individual whether it is an enjoyable book for them. No one has the authority to overrule them and dictate that they did or did not enjoy it, contrary to their experience of it. Note already that, so defined, to be subjective is distinct from being arbitrary. Although there is no way to speak with authority about subjective matters from a universal standpoint, each individual can speak with authority about the subjective as they see it. In contrast, when it comes to things that are arbitrary no one can speak with authority about them.
From this understanding of subjectivity we can now take a single step towards complete objectivity. Consider shared subjectivity. What could it mean to share something that is subjective? Consider the meaning of the word “oak”. There is a way in which the meaning of the word “oak” is subjective: I experience the word as having a particular meaning, and you cannot overturn my authority about what the word means to me. However, there is also a way in which the meaning of the word is shared, and, despite variations in the way the meaning of the word is experienced, we mean “the same thing” by “oak”. In part this results from my experience of what oak means to me being partially constituted by a desire to mean the same thing as others who use the term. But, even though the meaning of the word is shared between individuals, there is still no perspective from which to make universal pronouncements about the meaning of the word “oak”. It is possible, for example, that there exists another linguistic community that associates a completely different meaning with the word. Thus there is still no universal standpoint from which to authoritatively speak about things shared in this way, although a community’s practices can be considered authoritative about the things they share. Things of this sort I am inclined to call intersubjective. Those things that can be shared from person to person, but would not themselves exist, as such, without people are almost always intersubjective. And so, along with the meaning of words, cultural ideas and values are intersubjective as well.
Another property commonly associated with objectivity is decidability. And I take decidability to be the next step towards complete objectivity. What is decidability? In this context what I mean by decidability is that given a well-formed question a single answer can be produced that everyone will agree on (or, if there is no answer, everyone will agree that there is no answer). Mathematics is decidable in this sense; you can ask “is this a valid proof from axioms A to conclusion B?” and get a definite answer. Note that this should not be confused with mathematical decidability. In some systems there may not be a finite procedure for determining whether a conclusion can be proved or disproved (or neither proved nor disproved) from the premises. I still consider such cases decidable in the sense discussed here because it isn’t the case that in such situations some people will give one answer while others will give another (assuming they haven’t made any mistakes). To go back to the question of “who can speak with authority about such things?” the answer with respect to such domains must be “everyone”, or at least potentially everyone, to the extent that they don’t make mistakes. (And note that for a domain to be properly decidable in this sense whether someone has made a mistake should itself be decidable). Another interesting consequence of decidability is that it implies that the domain can be shared. Fortunately for us this makes the “ascent” to complete objectivity linear, so far, since we don’t have to consider both domains that are decidable but not shared and domains that are decidable and shared.
Now at this point some may think that decidability is as objective as things can get. Mathematics is decidable in this sense, and many assume that it is a paradigm case of objectivity. Granted, mathematics is closer to complete objectivity than the subjective or the intersubjective. But the decidable falls short of being completely objective because of the caveat that the questions asked must be well formed. What does that mean? Well, at least in the context of mathematics, it means that the question must be asked with respect to a certain system or certain axioms. To properly answer “does 2+2 = 4?” one must assume a specific mathematical system that gives meaning to the symbols and provides rules governing their operation. This is not a fact we commonly think about because we are so used to working in particular systems by convention, but the existence of non-standard logics, geometries, and so on demonstrates that it is in fact so. In contrast, when dealing with a question about the physical world, such as “does this glass contain water?” there is no need to pin the question down with respect to a specific system or set of axioms.
Thus the physical world has an extra degree of objectivity that mathematics lacks; it is completely objective. We can pin down the difference by pointing out that, with respect to the physical world, and thus questions about it, there is a single domain of objects that we all have access to. This contrasts with mathematics, where there are as many systems containing points and lines as you like, and so which one we are talking about must be pinned down precisely. But when it comes to the physical world, since there is only one domain of objects that we all are acquainted with, there is no need to pin down which objects we are talking about; our common existence in the physical world pins that down for us. Thus complete objectivity is finally defined: something is completely objective when it deals with a common set of objects we all have access to. And, as with the previous step in our “ascent”, complete objectivity implies decidability, since any question can be definitely answered by appeal to the common world of objects. Thus a hierarchy is established with complete objectivity on top (materially objective), decidability below it (formally objective), intersubjectivity below it, and subjectivity on the bottom (unless we want to include things that are arbitrary below it).
Presented in this way the hierarchy described above surely seems like a rigid ontology, such that everything we experience can be rigidly and finally thrown into one of those divisions. However, in many cases it is possible to move a question from one category to another simply by asking it in a different way. Consider the intersubjective. In its natural form “what is meant by ‘oak’?” belongs to the domain of the intersubjective. But we can rephrase that question by putting it in the form “what does culture X mean by the term ‘oak’?”. Asked in that way it falls under the domain of complete objectivity, since the culture, and the individuals that compose it, are part of that common world of objects we all have access to. Similarly, we can turn questions that fall under complete objectivity into something intersubjective. Normally when we consider a question in the domain of complete objectivity we think only about its content. When asking “are oaks trees?” we are asking about the relations between objects in that common world. However, we don’t have to approach the question in that attitude. Instead we can consider the language the question is asked using to be as important as its worldly content. Thus the question will have the same answer in our native tongue, but will be unintelligible (or possibly have a different answer) in other languages. Under this unconventional approach the question falls under the domain of the intersubjective.
Now our ability to transform questions in this way should not mislead us into thinking that everything is subjective, or intersubjective, or completely objective. Nor should we jump to the conclusion that if we can address every question, after appropriate transformations, under one domain that we no longer need the others. When we transform a question in the way described above we change its content. A question that was completely objective is about objects in the common world. Transforming it into a form that is intersubjective also transforms it into being about shared ideas, values, and language. And the content of one domain can never be wholly captured in another, because the intersubjective, for example, is essentially intersubjective and can never be captured, as is, by complete objectivity. At best some of the features of intersubjective things may find a reflection in some completely objective description. To be more precise: part of what a particular bit of intersubjectivity is is how it is experienced, subjectively, by individuals (patterns of how it is experienced). But that “how it is experienced” is necessarily shaved away by any objective treatment, leaving only facts about patterns of behavior and the use of language. Similarly, trying to understand mathematics as an obscure way of talking about how particular things interact loses the sense in which formal mathematics has the ability to be applied to anything and the sense in which the particular formal system being used is an arbitrary choice.
To conclude allow me to briefly discuss some of the benefits of this more complicated picture. Philosophically it can assist us in resolving issues that arise from taking subjectivity and objectivity to be two mutually exclusive and exhaustive categories. For example, intuitions are rejected as a guide to the objective by many. But then mathematics, and mathematical intuitions, become problematic, as it would seem to imply that mathematics is subjective. Since many take the subjective to be the domain of unsubstantiated opinions, and worthless, this may seem unacceptable. Obviously all such problems are eliminated when we have more than two categories. A second benefit of the more complicated picture is that it can help us overcome the idea that the subjective is bad and the objective is good. We can now reject the arbitrary as truly worthless, while accepting that the other levels of objectivity may have something going for them. For example, by being only decidable mathematics is a useful tool since it can theoretically be applied to anything. Similarly the subjective and intersubjective, may capture aspects of the human experience, which may be worthwhile even if we can’t build a bridge with them. Or maybe not. But at least with a more nuanced picture our options are open.