THE ALGEBRA OF BEING—A SIGNIFICANT BUT PLAYFUL ANALOGY
BETWEEN ALGEBRA AND ONTOLOGY
The following shows one aspect of the significance of being via an analogy between the use of being and a very simple example of the algebraic approach in mathematics. The essential point is that in using the term being we name the unknown. Although the analogy is simple and playful, the point is of immense significance but no further aspects of the analogy are implied |
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Problem solving A first example. Ten oranges plus two dollars is worth twenty five dollars. What is the cost of an orange? |
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Direct guessing |
Algebra |
Make a first guess that one orange costs $2.50 Then, ten oranges plus two dollars is $27.00 So an orange clearly costs a little less than $2.50. Then, ten oranges plus two dollars is $26.00 So an orange clearly costs a little less than $2.40. Then, ten oranges plus two dollars is $25.00 So one answer is that an orange costs $2.30 |
Let x = the cost of an orange in dollars. Then: 10x + $2 = $25, or 10x = $25 - $2 = $23, or x = $23 ¸ 10 = $2.30 I.e. one answer is x1 = $2.30 Suppose there is another answer x2 Then 10 x1 + $2 = $25 (1) 10 x2 + $2 = $25 (2) Subtract (2) from (1) to get 10(x1 - x2) = $0, or x1 - x2 = $0, or x1 = x2, so there is precisely one answer
In the algebraic approach, guesswork is reduced and the power of the approach allows us to answer general questions such as how many solutions are there. The problem is admittedly trivial. With harder problems, guesswork is not entirely eliminated. Therefore the algebraic approach provides compact symbolization and consequent efficiency of thought and method, a fine balance between method and guess, and the ability to write problems as abstract (replace the numbers by constant letters a, b, c…) and so address classes of problems rather than single problems. In the algebraic method (1) essential difficulty may be faced without distraction by difficulty that is an artifact of symbolization but, further, (2) effective symbolization may be seen as part of processes of solution |
Metaphysics A second example. Of what is the Universe made? |
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Direct guessing |
Algebra |
A first guess. It’s made of mind. This guess results in millennia of grand schemes of thought that appear to have ended in failure Thinkers conclude on the basis of examples that no grand schemes are possible and we must revert to small local schemes or piecemeal analysis. Of course this conclusion has not been demonstrated. It seems reasonable but what has been shown is that certain schemes failed for one reason or another and the reason failure may teach us something which includes that discovering a scheme for the Universe may be difficult. Most schemes consist of a paradigm and an implementation. If the scheme is in error either paradigm or implementation may be inadequate but it is often concluded that both are in error. Thinkers who are careful with regard to thinking about the world but often not so careful in thinking about their thought. In fact they may often be very prejudiced in thinking about their thought as in the phrases ‘absurdity of idealism—i.e., of taking the Universe to be mental,’ ‘absurdity of materialism,’ and so on. Is idealism absurd? Only on certain accounts of what mind is! |
Make no guesses. It’s what it is (being) This approach is roughly, no paradigm but all implementation This cuts the Gordian Knot of substance and cleans the Aegean Stables of the myriad half-attempts at metaphysics via substance claims… and leads to immense positive advance It allows for and implements Universal though not merely posited schemes that have immense consequences but are not grand in their formulation… and small local schemes and sub-schemes Of course there is guessing (hypotheses) in the development but no absolute commitment to any particular guess And it is natural that the approach from being should have learned much from the ‘substance’ approach (opposite) as well as from thinkers who emphasized an approach from being |
Further guesses. It’s made of matter, of fact, of instances of qualities, of sentences, of propositions, of relations, of interactions, of processes, of atoms, of fields… resulting in more debate, much expression of certainty in the modern era of the material character of the Universe that is motivated by common sense and the ascent of science but has far from accounted for numerous difficulties Despite the certainty of scholars, contention and debate and irresolution abound |