My overall claim in this paper is twofold: Firstly, the activity of developing arguments in favour of the existence of the Christian God is tenable and worthwhile and, secondly, the “infinite God objection” fails to undermine the kalam cosmological argument. Concerning the former, it is often claimed that the very activity of developing arguments in favour of God’s existence is futile. I argue, however, that such theistic arguments play an important role in the philosophy of religion, natural theology, and apologetics. Concerning the latter claim, I will attempt to show how the infinite God objection fails to undermine a notable theistic argument, namely, the kalam cosmological argument. As regards this objection, the proponents of the kalam cosmological argument face a dilemma – either an actual infinity cannot exist or God’s knowledge cannot be infinite. More specifically, this objection claims that God’s omniscience entails the existence of an actual infinity with God knowing an actual infinite number of future events and mathematical truths. My solution to this problem is that (1) God’s omniscience should be understood as maximal knowledge; (2) the existence of abstract objects (such as numbers and propositions) should be denied; and (3) God’s knowledge is non-propositional in nature. / MPhil, North-West University, Potchefstroom Campus, 2014

My overall claim in this paper is twofold: Firstly, the activity of developing arguments in favour of the existence of the Christian God is tenable and worthwhile and, secondly, the “infinite God objection” fails to undermine the kalam cosmological argument. Concerning the former, it is often claimed that the very activity of developing arguments in favour of God’s existence is futile. I argue, however, that such theistic arguments play an important role in the philosophy of religion, natural theology, and apologetics. Concerning the latter claim, I will attempt to show how the infinite God objection fails to undermine a notable theistic argument, namely, the kalam cosmological argument. As regards this objection, the proponents of the kalam cosmological argument face a dilemma – either an actual infinity cannot exist or God’s knowledge cannot be infinite. More specifically, this objection claims that God’s omniscience entails the existence of an actual infinity with God knowing an actual infinite number of future events and mathematical truths. My solution to this problem is that (1) God’s omniscience should be understood as maximal knowledge; (2) the existence of abstract objects (such as numbers and propositions) should be denied; and (3) God’s knowledge is non-propositional in nature. / MPhil, North-West University, Potchefstroom Campus, 2014

Nesta dissertação, abordaremos os dois tipos de infinitos existentes: o infinito potencial e o infinito actual. Apresentaremos algumas situações, exemplos que caracterizam cada um desses dois tipos. Focaremo-nos no infinito actual, com o qual discutiremos alguns dos desafios encontrados na teoria criada por Cantor sobre este assunto. Mostraremos também sua importância e a diferença entre este e o infinito potencial. Com isso, buscamos fazer com que o professor compreenda adequadamente os fundamentos matemáticos necessários para que trabalhe, ensine e motive apropriadamente seus alunos no momento em que o infinito e conjuntos infinitos são discutidos em aula. Desta forma, buscamos esclarecer os termos usados e equívocos comuns cometidos por alunos e também professores, muitas vezes enganados ou confundidos pelo senso comum. / In this dissertation, we will discuss the two types of infinities: the potential infinity and the actual infinity. We will present some situations, examples that characterize each of these two types. We will focus on the actual infinity, with which we will discuss some of the challenges found in the theory created by Cantor on this subject. We will also show its importance and the difference between this and the potential infinity. Thus, we seek to make teachers properly understand the mathematical foundations necessary for them to work, teach and properly motivate their students at the time the infinity and infinite sets are discussed in class. In this way, we seek to clarify the terms used and common mistakes made by students and also teachers, so often misguided or confused by common sense.

Nesta dissertação, abordaremos os dois tipos de infinitos existentes: o infinito potencial e o infinito actual. Apresentaremos algumas situações, exemplos que caracterizam cada um desses dois tipos. Focaremo-nos no infinito actual, com o qual discutiremos alguns dos desafios encontrados na teoria criada por Cantor sobre este assunto. Mostraremos também sua importância e a diferença entre este e o infinito potencial. Com isso, buscamos fazer com que o professor compreenda adequadamente os fundamentos matemáticos necessários para que trabalhe, ensine e motive apropriadamente seus alunos no momento em que o infinito e conjuntos infinitos são discutidos em aula. Desta forma, buscamos esclarecer os termos usados e equívocos comuns cometidos por alunos e também professores, muitas vezes enganados ou confundidos pelo senso comum. / In this dissertation, we will discuss the two types of infinities: the potential infinity and the actual infinity. We will present some situations, examples that characterize each of these two types. We will focus on the actual infinity, with which we will discuss some of the challenges found in the theory created by Cantor on this subject. We will also show its importance and the difference between this and the potential infinity. Thus, we seek to make teachers properly understand the mathematical foundations necessary for them to work, teach and properly motivate their students at the time the infinity and infinite sets are discussed in class. In this way, we seek to clarify the terms used and common mistakes made by students and also teachers, so often misguided or confused by common sense.

No description available.