Potentially good idea: eliminating the a priori/a posteriori distinction

This is going to be one of those posts where I propose an unorthodox and highly radical idea and I give a completely insufficient and non-robust defense of it. I think I attempted something similar with moral realism in one of my previous posts before. This time, it's on the a priori/a posteriori distinction.

Typically the a priori/a posteriori distinction is understood as applying to propositions: an a priori proposition is one where its truth is knowable independent of (or prior to) experience. Philosophers usually point to propositions in geometry and mathematics, such as 'the internal angle of a triangle is equivalent to the angle of a straight line' or '2 is the positive square root of 4' for examples of a priori propositions. 

Conversely, an a posteriori proposition is one where its truth is knowable in virtue of experience. The proposition that 'Black swans exist in Australia' is an example of an a posteriori proposition, as one can only find out whether this proposition is true by visiting Australia and checking if there really are black swans in Australia. Claims made in the natural sciences are generally a posteriori.*

Now, this distinction may seem pretty unproblematic at first, for it's pretty obvious what most propositions fall under which category under the distinction. This distinction is also uncontroversial (for what I know), as it is so often used in arguments even in contemporary philosophy. But as long as the definitions of a priori and a posteriori I stated above are used, I think the distinction is problematic because it is based on the notion of experience.

Why is the notion of experience a problem? The reason why I think it causes problems for the distinction is our uncertainty of what experience refers to when we ask the question of 'what is experience'. Let's look at two possible definitions of the word:

1. Experience refers to what is felt, seen, heard, tasted or smelled, i.e. information available to the five senses)
2. Experience refers to whatever that is made available to the consciousness.

In general, the use of the distinction inclines towards the understanding of experience as in (1). With (1), however, you can get some pretty awkward results. Firstly, if experience is whatever that is available to the five senses, and assuming that the five senses are the only inputs to a person's experience, wouldn't it follow that all propositions are a posteriori? (Otherwise, where would the new data for the proposition come from?) Think about geometry: how do we come to have a concept of circle, or a line? Aren't they initially abstracted from the things we perceive with our five senses in the world? If there is no such thing as an a priori input, then what does the distinction mean at all?

The sun (left) and a circle (right): is it not a better explanation to say that the circle is abstracted from a natural object like the sun, then to say that we are born innate with the concept of a circle? (Left photo taken from Oia, Santorini)

Perhaps - as an immediate reaction - you're thinking about something like this: no, it's not like that; this understanding of the mind is too simplistic. Instead, one should think of the mind as having the five inputs but these five inputs are constrained by the structure of the mind. In other words, (under this view) there is no pure untainted inputs that we can get from our experience; the structure of mind make our percepts a certain way. For instance, without the mental structure that allows us to categorise things, we would not be able to individuate between things and hold the concept of a circle as an object. Without the innate principles of logical inference, we cannot infer that if P & Q is true, then P is true. In that case, you may argue that there are actually six senses: smell, vision, hearing, touch, taste and the innate structure of the mind which constrains and structures these senses. While the very last sense may seem very different from the rest, it is nonetheless an input because it contributes to our total knowledge. To end this rejoinder: if we do have six different types of input, then the a priori/a posteriori is still meaningful under definition (1). 

My second problem is this: if I am to take the view of the mind made by this rejoinder, then ultimately I will have to resort to definition (2). If every input into our mind from the five senses are cross-influenced by the sixth input into our mind, then in what sense does it mean when we say that we can classify the truth of propositions into ones knowable independent of experience and ones knowable in virtue of experience? If the innate mental structure input is part our experience, what does it mean to distinguish between a priori and a posteriori?

Picture according to definition (2) of experience

At first glance, I think my argument would most likely be rebutted by analysing the word knowable in the definition. Does that really improve the situation? I'll get to this in another post. 

*For a more detailed introduction on the distinction, I'd recommend David Papineau's (2012) book Philosophical Devices, Chapter 4.3. For now, my brief explication should be sufficient.

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Beyond Logic

Before I was introduced to the world of academic philosophy, I used to entertain the following idea quite often: there are always things in this world that we don't know about or cannot understand, given our limited capacities. From that, I skipped carelessly to the conclusion: anything is possible. For how can you say for sure that a certain phenomenon (e.g. that ghosts exist) is impossible, when it could just be a case where you failed to know enough?

When I began venturing into 'professional' philosophy, the answer to my question seemed immediately obvious: logic. Anything is possible, except for that which is forbidden by logic. For example, a ball cannot be black or white all over, we can never draw a square circle, and a triangle can never have four sides.

I admit that I wasn't a rigorous thinker. I couldn't think of examples such as these at the time. But for some reason, I was not 'psychologically' convinced. For instance, I would hesitate if someone asked me to bet me and my family's life (say for a million dollars) that it is impossible to draw a square circle, or that it is impossible to find a married bachelor. I wouldn't take that action. If it is as William James says - that belief is measured by action - then you can certainly come to the absurd conclusion that I don't believe in logic.

You may say that it is irrational not to place such a bet, or that I suffer from an extreme inferiority complex with respect to my intellect. After all, it does seem more of a psychological issue that I am so unconfident in my ability to reason. But let me just push this a little further:

Why can't we have ideas or existing things which are beyond what logic permits? What makes us always right? If it is possible for us to get a mathematical proof wrong, why is it not possible for us to get the more basic bits wrong? In other words, why must we have certain things which are necessary?

To solve this problem, I find it useful to see logic as as a model.

If logic, like mathematics, is a tool to model the universe around us, then the results it generates are fallible. Just like how classical macroeconomics models have failed to predict stagflation, logic - as a model - can fail to predict about facts of the universe. And when logic (as a language) fails, we get paradoxes, such as the Liar Paradox*. So maybe within logic, there are things which are necessary, and not everything is possible. But we shouldn't expect that if something is forbidden by logic, it cannot exist in any form in real life. (there's this famous demonstration where someone 'showed' that a triangle can have three right angles by drawing it on a non-Euclidean space - e.g. a basketball)

I certainly don't mean that we should be expecting to be able to find a married bachelor anytime soon. But I'm still sceptical as meanings of the words 'bachelor' and 'married' can shift in real life. Also, it needs to be said that all reasoning (including my train-of-thought as I write this entry) is captured by logic - if not logic, then grammar, or syntax. Anything illogical is very likely going to be meaningless, since logic plays a very important part in our thoughts (not everything illogical is meaningless - just think of how comedy often makes use of logical contradictions).

Hence, it's not crazy to be sceptical about whether logic tells us everything about possibility and necessity. But if we reject logic altogether, none of what I've just written should make hold any force since it relies on reasoning.

*'This sentence is false.' - as Tarski has shown, this paradox remains as long as we use our natural language which contains self-referring terms.

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