Thought
As an Evangelical, Poythress advocates the complete, divine authority of the Bible. As a Calvinist, he places great emphasis the sovereignty of God and adopts the Neo-Calvinist theme that Jesus is Lord over every sphere of human existence, not just private or religious life. He makes use of Biblical theology in the tradition of Geerhardus Vos, and builds on Meredith G. Kline's work in Images of the Spirit to argue that "imaging" is a pattern in the Bible beyond man and woman being made in the image of God. He has a decidedly positive view of the Old Testament Law, though he rejects theonomy and Christian Reconstructionism, and he also rejects the hermeneutics of dispensationalism in favor of traditionally Reformed covenant theology. In Christian eschatology, he advocates an Augustinian amillennial perspective (compare the summary of Christian eschatological differences).
He is an advocate of Cornelius Van Til's presuppositional apologetics, particularly the ideas that epistemology and ontology must find their ultimate grounding in the Trinity. He has also sought to work out presuppositionalism's central claim that there is no neutrality in the area of science and mathematics. In a manner akin to Augustine's view that truth is divine, Poythress views scientific law as a form of the word of God. In 1976, Poythress broke new ground with a chapter on "A Biblical View of Mathematics," while in a 1983 article, he argued that mathematics is the rhyme of the universe.
A central idea in Poythress' thought has concerned the validity of multiple perspectives, or multiperspectivalism, a project that he shares with his teacher and collaborator John Frame. In Poythress's seminal work Philosophy, Science, and the Sovereignty of God, he explored how the scientific concepts of wave, particle and field can be used analogically to demonstrate different ways of looking at things. He argued that such a triadic structure is a "a means of avoiding unhealthy dualism", and he continued on this line of thought in Symphonic Theology, where he applied multiperspectivalism to theology.
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