Mathematical a priori Statements

 

Mathematical a priori Statements 

    A triangle having three sides and angles equaling 180 degrees is an analytic a priori since the predicate of 3 sides and 180 degrees are in the word triangle. The equation, 2+2=4, would be a synthetic a priori because the concept of four is not present in two. 
    In the case of a triangle having three sides and angles equaling 180 degrees, the concept of a triangle already contains within it the idea of having three sides and angles adding up to 180 degrees. All three-sided polygon has 180 degrees and all triangles are three-sided polygons by definition. Therefore, the truth of this statement is considered analytic a priori, as it is true by definition and can be known independently of experience unless it can be proven otherwise. 
    On the other hand, in the case of 2+2=4, the concept of four is not contained within the concept of two. Rather, the truth of this statement is established through logical deduction and requires the use of concepts that are not contained within the original terms. Therefore, this statement is considered synthetic a priori, as it involves combining concepts in a novel way and can be known independently of experience. 
    It could be argued that 2+2=4 is also analytic a priori since the concept of four is already contained within the concepts of two and addition together. However, while this may be true, the concept of addition itself is not contained within the concept of two. This involves combining concepts in a way that goes beyond the definitions of the individual terms. 
    A rebuttal to this may state that it is true that the concept of four is not explicitly contained within the concept of two, it can still be considered analytic a priori because the concept of addition, which is necessary to arrive at the answer of four. However, since the concept of addition is also required, this would make it synthetic because addition is not an innate quality of two. Although two can be added to itself to produce the result of four, this relationship is not inherent in the concept of two itself. The concept of addition is a separate concept that must be introduced in order to arrive at the truth of the statement 2+2=4. Therefore, mathematics can be both synthetic and analytic a priori.

Comments

Post a Comment

Popular posts from this blog

Refutation of the Ashariyyah Aqidah

Image
Refutation of the Ashariyyah Aqidah   Aqidah:   Ash’ari beliefs:   1. Divine timelessness i.e. that Allah سُبْحَانَهُ وَتَعَالَىٰ does not perform new sequential actions Himself. 2. Allah سُبْحَانَهُ وَتَعَالَىٰ acts without motive or wisdom behind His acts as they believe if Allah was acting to fulfill a purpose then He would have been previously imperfect as He would be in need of something. 3. Metaphorical interpretations of Allah’s actions and attributes in order to avoid anthropomorphism. 4. Occasionalism i.e. the belief that God is the only true cause and that what we perceive as causes and effects in the world are merely occasions for God’s direct intervention. They deny that created entities have any intrinsic causal power or secondary causation. In other words, God creates the cause and the effect at each moment independent of the material 5. objects that seem to be involved. 6. Morality is arbitrarily based on Allah’s سُبْحَانَهُ وَتَعَالَىٰ will i.e. absolu
Read more

Overview of Athari Metaphysics

Image
Overview of Athari Metaphysics Metaphysics, the study of the fundamental nature of reality and existence, presents significant challenges and complexities. Within the realm of metaphysics, the Athari, a school of thought in Sunni Islam, perspective offers a unique approach to understanding the attributes and actions ascribed to Allah, or God. This overview explores the fundamental principles of their (and also my) metaphysics, including the distinction between the different types of predications when describing God’s attributes. It also considers the role of rational arguments alongside textual proofs for the existence of God and questions the concept of Divine Simplicity. Additionally, the overview delves into the uncreated nature of the Quran and the understanding of God's actions within His essence. By examining Athari metaphysics, we gain insights into the nuanced interpretation of divine attributes and deepen our understanding of God’s unknowable essence. The Athari view d
Read more

Challenging the Trinity: Indexicals and the Leftow Dilemma

Image
Challenging the Trinity: Indexicals and the Leftow Dilemma     The Doctrine of the Trinity stands as a central tenet of Christian belief, positing the existence of three distinct persons—Father, Son, and Holy Spirit—within the divine unity of God. However, a nuanced examination reveals intriguing challenges that will be discussed in detail. This blog post will present two more arguments against the Doctrine of the Trinity. I have already discussed the Logical Problem of the Trinity (LPT) and how the Trinity contradicts Divine Simplicity elsewhere on my blog.   The Argument from Indexicals:   Indexical: A linguistic expression whose reference can change based on the context. Examples of indexicals include I, he, she, here, that, etc. If Person A says I am happy and Person B utters the same sentence, even though the sentence is the same, Person A is saying it while person B is saying it. In the orthodox conception of the doctrine of the Trinity, there is only one mind or one will in the
Read more