Here is a list of some of the presuppositions of science:
(1) the existence of a theory-independent, external world;
(2) the orderly nature of the external world;
(3) the knowability of the external world;
(4) the existence of truth;
(5) the laws of logic;
(6) the reliability of our cognitive and sensory faculties to serve as truth gatherers and as a source of justified true beliefs in our intellectual environment;
(7) the adequacy of language to describe the world;
(8) the existence of values used in science (e.g., "test theories fairly and report test results honestly");
(9) the uniformity of nature and induction;
(10) the existence of numbers.1
1. William Lane Craig & J.P. Moreland, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: InterVarsity Press, 2003), pp. 348.
List taken from: http://www.apologetics315.com/2011/03/ten-presuppositions-of-science.html
or here: http://www.apologetics315.com/2014/04/ten-presuppositions-of-science.html
I've adapted, added and modified the list in the following way:
Here is a list of some of the presuppositions of science:
(1) the existence of a theory-independent, external world;
(2) the orderly nature of the external world;
(3) the knowability of the external world;
(4) the existence of truth;
(5) the laws of logic;
(6) the [general] reliability of our cognitive and sensory faculties to serve as truth gatherers/identifiers and as a source of justified true beliefs in our intellectual environment;
(7) the adequacy of language to describe the world;
(8) the existence of values used in science (e.g., "test theories fairly and report test results honestly");
(9) the [presumed] uniformity of nature and [propriety of the use of the principle of] induction;
(10) causation
(11) the existence (or at least usefulness) of numbers. Given atheism, it's a strange "Happy Coincidence" that nature is so very much structured on mathematics that physicists can make predictions about the universe which are later confirmed empirically. Whereas, given the existence of God it makes perfect sense that God would create the physical world mathematically, and intellectually/rationally accessible.
As J.P. Moreland has said, "The claim that you can only know things through the methods of science is not itself something that you can know through the methods of science." He gives the example of the sentence "There are no sentences longer than three words", as a self-refuting claim.
Science has presuppositions or axioms like those above which cannot themselves be proven scientifically but must be assumed [almost like "faith"] in order for science to be done [i.e. to even begin]. These assumptions and the subscription to them make sense in theism [especially in Christianity], but the various atheistic worldviews have difficulty grounding such axioms. Most atheists live by "faith" (so to speak) when they operate with these working/operating assumptions.
William Lane Craig responding to Peter Atkins' virtual scientism
List of books that demonstrate the limits of Science as a method of acquiring knowledge:
The Philosophy of Science and Belief in God by Gordon H. Clark (highly recommended)
Mathematics: the Loss of Certainty by Morris Kline
An Enquiry Concerning Human Understanding by David Hume
The Scientific Outlook by Bertrand Russell
Unity, Identity, and Explanation in Aristotle's Metaphysics
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