0:00 The Biblical Christian Foundation For Math …A Degree Of Skepticism
1:28 People Will Say, “Surely Worldview Considerations (Religious Considerations) Don’t Have Any Impact Upon Mathematics.”
2:10 A Worldview Defined: A Network Of Presuppositions In Terms Of Which Everything In Human Experience Is Interpreted, And By Which All Human Reasoning Is Guided
2:56 People In General Believe That Their Worldview (Philosophical & Religious) Cannot Possibly Have An Affect Upon The Truths Of Mathematics …GLB, Questions This Line Of Thinking, And Begins To Layout His Argument, Showing That Without The Christian GOD No One Can Account For Their Doing Mathematics
3:35 Academic Curriculum: The Deceptive Appearance Of Widespread Agreement Across All Religious Lines
5:05 History Documents The Effects Of Worldview Outlooks On Mathematics & Science …The Pythagoreans, Emmanuel Levinas, Immanuel Kant, Euclidean Geometry, Riemannian Geometry
6:26 Mathematics Is Affected By Your Philosophy Because You’re Asking, What Is Real; How Do We Know What’s Real; And How We Should Live Our Lives?
6:37 Metaphysics’ Relevance To Mathematics
7:13 Epistemology’s Relevance To Mathematics And Theology …Mathematics Is NOT NEUTRAL TO WORLDVIEWS (PHILOSOPIES, OR RELIGIOUS COMMITMENT)
7:59 Historic Mathematical Disagreements Based On Philosophical Commitments: e.g. Intuitionism (The Law Of Excluded Middle)
10:57 Mathematicians’ Problem With The Ideas Of Zero & Infinity
12:21 Is Zero Real?
14:16 Resolving The Problematic Issues With Zero & Infinity Require Something More Than Math
14:40 GLB Warns Against Being Satisfied With Just Jumping Through The Mathematical Hoops & Ignoring All The Weighty Subject Matter Associated To It
16:54 GLB Gives Some Down To Earth Questions Having To Do With Math And Whether Math Is Possible …
17:05 Is It True That Religion Is Totally Irrelevant To Mathematics? GLB Proposes Some Relgious POVs With Regard To Mathematics…
17:17 e.g. #1: Radical Monism (holds there is only one reality) The Relgious Expression Of Monism Is Eastern Hinduism (Maya) …Paul Deussen Quote from The Philosophy of the Upanishads …Atman (no second from the universal soul)
18:53 If Everything Is ONE, Then You Cannot Do Mathematics…The Truths Of Arithmetic Are All Illusory & Invalidated Except In A Worldview Which Acknowledges An Ultimate Metaphysical Plurality
19:45 e.g. #2:Radical Pluralism, Ancient Greek Philosopher Democritus
20:22 e.g. #3:The Nominalist (only particulars exist)
21:37 e.g. #4:Using Tokens For Particular Experiences …No One Has Experienced The Number 2.
24:15 The Fallout Of The Nominalist POV
24:54 Now We Have A Real Problem …Worldviews Collide
25:50 In Order To Do Math, One Has Got To Have Resolved The Metaphysical Question, OF THE ONE & THE MANY. …IS REALITY ONE OR IS IT MANY?
26:01 With Any Science We Have The Right To Ask, With What Is It Concerned? And How Do We Justify Its Truths?
26:41 What Is The Object Of Mathematical Study?
27:32 What Are Numbers? Do They Exist? …Mental Constructs?
28:08 “Everybody Knows What Math Is About.”
28:31 How Are Mathematical Truths Justified?…There Are Three Schools Of Thought: #1 A priori (Derived by logic, without observed facts) (Antonym: A posteriori: Derived from observed facts)
30:06 Now Let’s Ask Ourselves Whether Math Is Proven In An A priori Way. …If You Say Yes They Are, GLB Lists The Problems With That.
31:52 #2:The Problem Of The A posteriori Approach To Verify The Truths Of Math
33:52 #3:Linguistic Stipulation Or Convention
34:44 When All Is Said And Done, You Cannot Account For Math Unless You Solve Some Pretty Sticky Philosophical Problems
35:09 Remember: People Do Math. Math Is An Activity. It Is Not An Abstract Person Free Entity. And The Question Is Going To Arise, WHAT ETHICAL STANDARDS WILL GOVERN THE DOING OF MATH?
36:37 RECAP
37:02 Make The Distinction Between The Ability To Do Something, And The Ability To Explain What You Are Doing (Between Practice & Theory)
38:27 The Unbeliever And Non-Christians Cannot Account For Math, But Can Christians Account For The Doing Of Math?
39:21 The Ethical Question Of Math With Regard To The Christian Worldview
39:49 The Ontological & Metaphysical Aspects Of Math With Regard Of The Christian Worldview …THE NUMERICAL REALITY OF GOD
41:31 The Christian Worldview Answers How We Know The Truths Of Math, And Can Justify Them Both A priori & A posteriori
42:15 Conclusion …Only The Christian Worldview Can Account For The Math That We All Practice For Our Day To Day Affairs
The Christian Worldview Answers How We Know The Truths Of Math, And Can Justify Them Both A priori & A posteriori
