Peirce’s Cable, Quine’s Web, and Neurath’s Boat
Descartes was inspired by Euclid’s geometric proofs, which demonstrated their claims to truth through incremental steps each with a simple justification in a long chain of reasoning. He likened himself to an architect needing “to demolish everything completely and start again right from the foundations,” and he sought then to build an edifice of knowledge upon such metaphysical first principles using Euclidean chains of reasoning.
Letting the “foundation” metaphor alone for now, Peirce pointed out a key problem with the chain metaphor for knowledge. If Descartes had come up with a “long chain of reasoning” which could, by its end convince us that, say, making a cup of coffee is what we ought to do about now, that conclusion would be as weak as the weakest link of reasoning that aided in the construction of the chain. Even with a rock solid foundation on which to base our beliefs, in Descartes architectural model for knowledge, the strength of our foundation is no more important than the strength of each individual link in a chain of reasoning. Rather than model philosophy on mathematics, Peirce recommended that,
“Philosophy
ought to imitate the successful sciences in its methods, so far as to
proceed only from tangible premises which can be subjected to careful
scrutiny, and to trust rather to the multitude and variety of its
arguments than to the conclusiveness of any one. Its reasoning should
not form a chain which is no stronger than its weakest link, but a cable
whose fibers may be ever so slender, provided they are sufficiently
numerous and intimately connected.”
Even
better than having one convincing line of thought that leads to a
conclusion is the possibility of generating multiple such lines of
reasoning to support it. What is emphasized in Peirce’s cable metaphor
is the importance of all the inferential connections between fibers or
beliefs that don’t necessarily all follow in a single sequence of
deductions but rather wrap around one another in mutual support.
The problem with Descartes’ chain metaphor is that the strength of
the chain fails as easily as a single link can break. And we know that
they can
break since we’ve all made deductions that we thought were rock solid
in the past but were later shown to have serious flaws. Quite heavy
links may be found to weigh on the support of a single loop of hair,
while a cable can endure the failure of a few fibers so long as there
are enough other fibers remaining. It is the interconnectivity of
propositions rather than a single sequence of deductions that makes a
cable of beliefs strong.
Peirce’s cable could be seen as a hemp rope where no single fiber
could extend along the entire length, yet, pulling as hard as we might,
it won’t come apart. No single belief imagined as a fiber in such a
cable or rope is any more a core or foundational belief without which
the whole structure would collapse. W. V. O. Quine saw this sort of
interconnectedness and mutual support for our systems of belief as a
web. Perhaps we can even mix metaphors and think of the structure of our
beliefs as a web of ropes or cables rather than a web of distinct
fibers. In any case, we can imagine reweaving parts of such a web while
the greater structure remains intact. With enough reweaving, it is
possible to imagine that after a time the entire web no longer has any
of the same fibers as it did before. It could in principle be completely
rewoven without needing a “doubt everything” clearing away of all past
knowledge; yet, at no time would the majority of beliefs in the web have
gone unsupported by other strands. Our existing beliefs are all the
foundation we need to extend and improve our webs of belief without any
limits on the degree to which our beliefs could be improved.
While cables, ropes, and webs are excellent antidotes to chains and
the myth of core beliefs, my favorite antidote to foundationalism—the
thought that we need a rock solid foundation to claim any knowledge
which often takes the form of a Platonic essence—is Neurath’s boat.
While Descartes modeled his philosophical method on mathematics,
following Peirce, Otto Neurath also took science to be the proper model
for philosophical thinking. As Quine explained, rather than clearing
away all but a single bedrock belief or two upon which to build a system
of thought,
"Neurath
has likened science to a boat which, if we are to rebuild it, we must
rebuild plank by plank while staying afloat in it. The philosopher and
the scientist are in the same boat. Our boat stays afloat because at
each alteration we keep the bulk of it intact as a going concern."
It
doesn’t merely stay afloat. In fact, as contemporary philosopher of
religion and self-described pragmatist Jefferey Stout put it, Neurath’s
boat
“can
travel the open seas, trade with foreign places, and send parties in
search of virgin timber. Its crew can take unimagined treasures on
board, plunder shipwrecks for usable gear, and invent an engine to pull
weight once pulled by oar.”
Presumably
at that point, we could ditch the oars. Note that there is no analogue
to doing so in the chain metaphor. Every link is integral to a line of
reasoning, whereas in attaining greater understanding of, say, the atom,
it may be useful at some point in our educations to think of it as a
round particle and later to drop that notion in favor of the
Rutherford-Bohr “planetary” model, later a cloud model, and later still
some better not yet imagined conception that we perhaps could have never
created without such scaffolding. What this ship cannot do is sail into
dry dock for a complete overhaul. In Neurath’s words,
"We
are like sailors who on the open sea must reconstruct their ship but
are never able to start afresh from the bottom. Where a beam is taken
away a new one must at once be put there, and for this the rest of the
ship is used as support. In this way, by using the old beams and
driftwood the ship can be shaped entirely anew, but only by gradual
reconstruction."
Just
as the web of beliefs can be rewoven, the ship can be rebuilt, but we
can only do it from aboard the ship. Such is the human condition. This
rebuilding is the process of criticizing and revising our beliefs. While
we can’t call all of our beliefs into question at once—where would we
stand to do that?—there is no belief we have that cannot be subjected to
such criticism. The complete overhaul (question everything!)
of knowledge that Descartes wanted to do is not possible in this
analogy, and it isn’t possible in practice either. Though many people
hoped at one time that all our knowledge could be erected as a tower on
top of solid ground, such a model does not agree with how knowledge
functions in practice. And just what is it, a pragmatist wonders, that
we wanted to be able to do in that tower that can’t be done in Neurath’s
boat?
Peirce’s Cable, Quine’s Web, and Neurath’s Boat are metaphors better suited to how knowledge acquisition functions than are Descartes’ foundation and chain metaphors. The position that Descartes imagined himself to be in deducing his existence was never the position we were actually in. We always already have beliefs. What we need to do is decide which ones to keep, which ones to drop, which ones to change, and which ones to add in an ongoing process that seems very little indeed like clearing a plot of land to erect a building from the ground up. There is no single belief such that if it needed to be updated in light of new experience it would cause the entire tower of knowledge to collapse. The reweaving of a web or the repairs and alterations on a boat while at sea seem much more to the point.