Essay by an anonymous contributor* reposted from Pi Alpha
In this, the first of two posts, Pi presents reflections on ‘Pragmatism’s Conception of Truth’, a title which William James chose in 1907 for a classic paper on pragmatism.One of the most basic questions a philosopher can ask is: ‘What is truth?’ What does it mean for a thing to be ‘true’?
Truth, as a dictionary would tell you, is a property of our ideas. Their agreement (between our ideas and reality) is truth, where their disagreement is falsity. This tells us what the word ‘truth’ means in conversation, but a dictionary cannot tell us what is meant by the term ‘reality’ or the agreement of our ideas with this reality. A true idea, in the non-pragmatic sense, is an idea that accurately reflects reality. People would never believe something that they know to be false, so everyone’s beliefs are about something that they think is true. This does not really get at the heart of the problem, though, which demands what reality?
The great American philosopher (I think, the first great American philosopher) was William James. His development of the school known as pragmatism created for me America’s first original school of thought, and thus America’s first real contribution to the world of philosophy. Indeed, when James headed the Colombia philosophy department, the British philosopher Bertrand Russell, whose interests spanned the logical structure of language, said it was one of the finest schools in the world. James did not like the Cartesian idea that truth is the correct reflection of reality, but instead insisted that truth is made by us through interactions with reality, although not one stagnant reality.
Previously in Europe, the pervasive school of thought was that if your idea could be said to be true, then ‘you are where you ought to be mentally’. However, pragmatism asserts that you should take a belief to be true, then ask:
‘What concrete differences will its (an idea’s) being true make in anyone’s actual life?’This question becomes the foundation of pragmatism: what experiences with reality would be different if the belief were to be true or false? James then goes on to make his largest claim, that truth ideas are those that:
‘we can assimilate, validate, corroborate and verify’This is the practical difference that true or false ideas have to us. Indeed, this process of assimilation, validation, corroboration, and verification allow us in effect to make an idea true or false. ‘Truth happens to an idea.’ This thought is in direct response to the European schools of thought that had a stagnant reality which true ideas correspond to and false ideas do not. In effect, James is claiming that ideas become true or are made true by actual events.
The possession of a true idea is not an end in of itself, but can be seen as a tool that allows us to function towards our desires and goals. James brings up an example that I shall use for the rest of this and the next post: imagine that you are lost in the woods and starved, but you come to what appears to be a track leading in some unknown direction. If you know that it is a cow track, and that cow tracks lead to farmers’ houses, then this information is useful to you. ‘The true thought (the one that the track is in fact a cow track) is useful here because the house (at the end of the track) which is its object is useful.’ In this scenario, the track is useful because of the situation you are in, which is being in need of food. But if the situation were slightly different, the usefulness of this truth is changed as well.
Let us say that the track that we come to appears to us to be made by a goat and not by a cow , along with the knowledge that cow tracks lead to farmers’ houses and goat tracks lead to large fields. This then changes the usefulness of the path, but does not change the fact that the information that we already knew is useful to us. Back to the cow tracks scenario, let us say that it is a cow path, not a goat one. The information that goat paths lead nowhere useful is in itself useful, although not right now. James calls these extra truths.
At this point I feel I need to stop and re-clarify the example. The reason we know that goat tracks lead nowhere is because before, in a different woods, we followed a goat track and it led us nowhere, whereas previously the cow tracks did lead to a safe house. This process is the verification process, that tells us what ideas we have are true and which ones are not. However, if say we had forgotten this previous adventure, and followed the goat tracks and they led to a house, then the truth that goat tracks do not lead to houses would be false.
‘Whenever such an extra truth becomes practically relevant to one of our emergencies, it passes from cold storage to do work in the world and our belief in it grows active.’This idea of goat tracks leading nowhere, but cow tracks leading to houses, can be said to be true because it is useful, but also can be useful because it is true. Both these things say the same thing, that ‘here is an idea that gets fulfilled and can be verified. ‘True’ is the name for whatever idea starts the verification process, ‘useful’ the name for its completed function in experience.’ True ideas obtain a certain value based on their usefulness to us in situations. Pragmatism’s general notion of truth is about the way one moment in our experience with reality may lead us towards similar desired moments. We as humans, with a finite unknown amount of time here, want moments that are worthwhile having. True ideas are those that get us to our destination of worthwhile moments.
Experience is filled with regularities. One moment can (and often does) influence the next moment we have. ‘Truth, in these cases, means nothing but eventual verification.’ This verification takes place when we interact with reality from one moment to the next moment (or what I call, existence through persisting reality) and our ideas are being used to influence this persisting reality.
Back to our scenario of the cow tracks: verification takes place when we follow the tracks and actually see the house and get food and rest inside. Or the goat tracks one: the verification process takes place when we get to the end of it, and there is no house to take shelter in or give us food. Verification can be positive or negative. If the cow tracks lead to a house, it is verified positively. If it leads nowhere, it is verified negatively. On the other hand, if the goat tracks actually lead to a house, then it can be said that our previous belief was false, or that its verification was negative. We have verified that our previously held belief was false.
* This post is adapted from Pi Alpha, the first embodiment of Pi. In the transition to Pi Beta, the name of the author was unfortunately lost. His identity would be a welcome addition - if anyone can help.
7 comments:
I have two problems with this.
1. Pragmatism relies on feedback. We don't have the luxury of feedback before it really matters.
2. Pragmatism is not grounded anywhere. It receives the feedback it is looking for.
Having said this, this post is a first class summary of 'America’s first real contribution to the world of philosophy'. I look forward to the second part.
'Anon' wins the prize for our essay passing the 250k mark - a cheque is on its way to me in lieu of an actual recipient. That
is the pragmatic solution, I feel.
“James then goes on to make his largest claim, that truth ideas are those that ‘we can assimilate, validate, corroborate and verify.’ This is the practical difference that true or false ideas have to us. Indeed, this process of assimilation, validation, corroboration, and verification allow us in effect to make an idea true or false.”
So, what is the state of an idea before it is ‘validated, corroborated, and verified’? Take, for example, Fermat’s last theorem, first conjectured in 1637 in the form of scribbles in margins, remaining neither proved nor disproved for three and a half centuries. That is, to put this point about Fermat’s theorem in James’ terms, an idea that remained neither validated, corroborated, nor verified for all those years.
At least, neither validated corroborated, nor verified until the mathematician Andrew Wiles finally came up with the proof in the mid-1990s, almost 360 years later. Whereupon, according to what I understand James’ ground rules to be, one may then declare that Fermat’s last theorem reached the tipping point of garnering the designation ‘true’.
But this is my question: per James’ philosophy of pragmatism, what was the status of the theorem between the moment that Fermat came up with the idea in 1637 and the moment Wiles solved (proved) it in the mid-1990s? Is there some other ‘category’ of reality — a suspended state between conjecture and proof — that carries its own unique name, given that presumably neither ‘true’ nor ‘false’ knowingly applied to the theorem for 360 years?
This is an astute observation. In fact even Wiles had an incomplete proof for two years. And while not much hinges on Fermat, there is no shortage of ideas we really do depend on.
An imaginary situation. A peal of thunder rolls across the city. ‘It’s related to the heat,’ I say. ‘Oh? How so?’ asks a friend. ‘It’s always like that,’ I reply. Another friend offers, ‘Heat rises. Clouds form. Charges separate. That makes lightning—and thunder.’ My own answer now looks foolishly simple. Besides, what did I mean, when I said that thunder is related to the heat? How much did I really know?
Casting this in terms of Hume's 'things and relations': in a best case, when we talk about the relations between things, this merely represents a kind of shorthand for something about which we are not being explicit. In a worst case, it represents ignorance. I may be completely ignorant, for example, of what connects the heat with the thunder, although I might be right about the relation itself.
This would surely be true of Fermat's last theorem. Not that I have solved anything here, but it might just cast some light on the 'suspended state'.
I stumbled upon this, in Pi's own Philosophical Morsels: 'I have had my results for some time, but I do not yet know how I am to arrive at them.' –Carl Friedrich Gauss.
In the context of the ‘truth’ of Fermat’s last theorem, I can envision the ‘suspended reality’ I referred to above — that is, the period between Fermat’s conjecture and Wiles’s proof three and a half centuries later — in at least two ways. (Though I don’t doubt there are many other possibilities.)
One take is that the mathematics involved in getting from one state (conjecture) to the other (proved) was always present — fundamental to reality — but just needed to be ‘discovered’. Reminding me, that is, of the famous ‘is mathematics discovered or invented?’ question, with Wiles in the role of discoverer. (Gauss’s remark might be interpreted in this manner, I suggest, even if he didn’t explicitly think in those terms.)
The second take is the suspended reality proposed by quantum theory’s explanation that all possible micro-level realities are probabilistically caught up mathematically as ‘wave functions’ in ‘superposition’, until measurement causes wave-function collapse and one reality. Perhaps I’m being overly simplistic, but I see ‘superposition’ as similar to the appearance of ‘suspended reality’ in the intervening period between Fermat’s conjecture and Wiles’s proof (‘measurement’).
All that aside, this essay about James’s pragmatism made for an interesting read, opening doors onto all sorts of ‘what if’ speculation.
Isn't the thing about Fermat's theorem not that there is a way to prove it, but that there is an elegantly simple way to do so? He seemed to be speaking as one who had a mathematical proof but was hiding it - playing with it. But if you have a mathematical proof, and particularly if you have one that is elegantly simple so unlikely to be wrong, then surely the status of the theorem is 'proved', if not publicly so.
ps
I like that quote of Thomas'!
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