As soon as a mathematical formula is applied to a situation in the world outside the mathematician’s mind, it ceases to be certain. In Polanyi’s summary, only statements that can be doubted make contact with reality. In other words, the mark of an indubitable statement is that it makes no contact with reality. If we are to make contact with reality, we must have the courage to make statements that can be doubted. There can be no knowing of reality without the courage to affirm what can be doubted and to act on the affirmation.
– Lesslie Newbigin Proper Confidence
To continue on with my last post on Polanyi, Newbigin has something to say as well. I just recently started reading Proper Confidence for the second time, it had been so long I’d forgotten most of it. It primarily deals with (as the subtitle gives away) “faith, doubt and certainty in christian discipleship”. Basically this means he writes a lot about Polanyi. If you want an nice easy overview of Polanyi’s thought without actually having to read Polanyi, you can’t go wrong with Proper Confidence.
In the quote I found last time, Polanyi was asserting the personal component to mathematical knowing. Here however, Newbigin is saying that certainty is only found at the expense of contact with reality. Pure mathematics existing solely in the mental realm can make statements that are absolutely certain…and yet have nothing to say about reality (that is, the reality that exists outside of the mind).
Newbigin’s eventual conclusion is that we must embrace doubt in our thinking. Not the paralyzing doubt that rejects any hope of knowing, but a kind of critical realism that recognizes the limits of certainty. This middle ground between the unthinking certainty of fundamentalism and paralyzing nihilistic doubt is appealing.