Why the Quest for Certain Knowledge Fails
In the past, I’ve mentioned that the attempts over history to find an utterly unshakeable basis for human knowledge have failed, but I’ve not dealt in enough details as to why…
I will not attempt to demonstrate this claim’s ultimate grounding — that would be impossible without assuming the very thing it aims to demonstrate. It would also miss the point…
…that final grounding for useful working knowledge is, I am convinced, impossible by any means currently known outside of pure logic and mathematics and their conventions, theorems, and axioms.
I am equally convinced that it is unnecessary.
I am confident that there is no such grounding without question-begging or circularity, even with formal reasoning as useful and internally consistent as any given system of it may be.
This applies to any item of knowledge up to and including the conclusions and claims of deductive reasoning, long considered the queen of the logics and the pinnacle of rationality, until the 20th century held to be the ultimate model to which all argumentation should aspire.
Also, it has long been a dogma of the Roman Catholic Church that the existence of God may be demostrated by unaided reason, the basis of much questionable and spurious argument by Christian apologists and others who try to use reason as the mere handmaiden of faith.
I’m confident that this particular dogma is mistaken, for it involves erroneous assumptions about the nature and proper role of the very logic it attempts to elevate.
There is the Problem of induction, of course, and I won’t dispute this.
Inductive reasoning assumes the regularity of nature, that the future can be predicted on the basis of the past — that the future will be like the past because it has so far always been so — that induction will work because it always has.
This is using induction to justify itself, clearly circular, but this is not really a problem if we bite the bullet and use it anyway as long as long as it continues to do useful work in furthering our understanding of the world.
Regarding contingent matters of fact, those we’ve discovered and will very likely continue to, this is both reliable and effective in adding to our knowledge, even without formal grounding on first principles.
But induction makes no claims at anything but pragmatic justification, no claims of absolute logical self-evidence.
To paraphrase Richard Dawkins, “It works, bitches.” And until it no longer works, or something better comes along, we are fully warrented, even if without metaphysical certitude, in continuing to use it.
Deductive reasoning is not without its problems either, for its property of logical validity is not a substitute for truth, and there is a sense in which it too is fundamentally circular and question begging.
It’s certainty is conditional, and still fallible. We must test such arguments for formal or semantic validity and even that does not guarantee the truth of our statements.
All that validity does is preserve whatever truth is already in the premises through to the conclusion of an argument.
What truth we start with, we end up with…
If the premises are true, and the logic valid, then the truth of the conclusion is automatic — within the formal system used, and different logics have different uses — and the conclusion thus follows as true.
I’ll grant that. But that’s as far as it goes. Such conventions may work, but they could be otherwise.
Deductive reasoning suffers from the fact that we do not always start from true premises in our arguments, though it would be nice if we did.
It also suffers from the fact that in only preserving the truth of the premises, it cannot tell us anything new.
The conclusion can never go beyond what the premises say. Formal reasoning can only rearrange what information is already contained in the premises, not lead us to novel claims.
Statements may be abstract, even counterfactual. They need have no real-world referrent. Just plug in whatever term or statement is needed into a variable, and stipulate our constants and logical operators.
We continue to use the axioms and conventions of logic and mathematics, not because they really are self-evidently, necessarily true, but because they work, and therefore remain the rules of the game.
Other systems of geometry, and other systems of logic exist, and these use different axioms that could be otherwise.
Note the differences between Euclidean geometry and other, perfectly self-consistent types of non-Euclidean geometry, where the angles of a triangle do not necessarily add up to 180 degrees, and in which the shortest path between two points may be a geodesic curve, not a straight line.
Such alternative systems can be just as accurately descriptive of parts of the world as the standard ones, and other systems of formal reasoning, such as Quantum logic, Three-valued logic, Modal logics, and Fuzzy logic, all just as effective and useful despite each using different rules.
Even the concept of validity is limited, and we know that it is, as a look at the Paradoxes of entailment will show.
A tautology or contradiction may be trivially valid by the formal definition, however inadequate or unconvincing as argument, despite either being necessarily true or false, in all possible situations.
Validity as a concept is useful despite its limits. Even without ensuring that we work from true premises, it is useful to all those with even a passing concern for truth.
Clearly, we need the Law of Noncontradition and validity as rules in logic, even with limits.
So despite the flaws of validity, we do not yet know of an alternative definition that produces a useful, consistent logic. We must make due with what we have so far as we know no other way.
Not so with inductive reasoning, which while not being truth preserving or strictly valid, as admittedly important that is, allows us to go beyond the premises and discover new things, even with only a degree of probability, even without certain justification on first principles. The premises of induction are gained by observation and experimentation, but not only that, through all our experience of the world.
I don’t claim that the natural sciences are the only way of understanding the world, merely that they are one of the best we have at uncovering the secrets of nature. We need the social sciences as well, for a balanced view of reality, ourselves as well as the world, culture as well as nature.
I do claim, though, that the best way to see if an idea is useful is to try it out, to test it and see if it works or not. Science does this remarkably well, as our powerful technologies show, even without final certitude in it’s own grounding, and even if that were the case.
This is why ideas that cannot be tested, either verified if particular claims or falsified if general claims, are not useful and why such ideas are not scientific, much less actually knowable.
This is why my view is that much of classical theology and metaphysics are fundamentally flawed, untestable even in principle, and so nonsense. Problems that cannot by their very nature be solved are not real problems.
All human claims to knowledge, even supernatural claims, are first gained through the senses, including our initial knowledge of religious teachings, via sight and hearing, via secondhand experience, reading from and listening to others tell us about these things.
Sensory experience, firsthand or secondhand, in some form, appears to constitute the vast bulk of our learning.
Any further knowledge, insight, or understanding we have later, including our private, personal experiences, are colored by and gained after our fundamental learning via our senses.
I’m convinced that the best foundation for our knowledge rests on experience, made using whatever means are at hand, the strength of our premises resting on their closeness to how things really are, and our reasoning the best currently available.
In building a cogent, solid, reliable, however imperfect but perfectible foundation for our knowledge, I know of no other way, without invoking the evident chimera of absolute understanding as a better standard for human knowledge.
Posted on Wednesday, 0:49, May 29, 2013, in Logic & Philosophy, Musings & Ponderings and tagged Logic, Logic and Foundations, Math, Modal logic, Problem of induction, Reason, Validity. Bookmark the permalink. 1 Comment.