Question

In this video ( ?v=TrnteM9E2tI&t=6633s) about mathematics in the Wolfram Physics Project, Stephen Wolfram says at minute 1:49:37 something that seems contradictory: He begins by apparently saying that the human observer determines what is true in mathematics and denies that, as Hilbert said, you can have axioms of all types (you can have axioms that talk about chairs and tables just as you can have axioms about integers) and that it is not true that there is a platonic object associated with whatever arbitrary thing that we can think of. But then, just after that, he says that this platonic object would be the ruliad, and in other writings, such as this ( /) he precisely says that all formal systems that we can think of would be platonic objects that would exist. So this seems a bit contradictory to me: He first explains, apparently, that observers like us determine what axioms are true and what axioms are not and that there are no platonic objects associated with abstract things we can think of, but then he says that all axioms are equally valid and exist in the ruliad as some kind of platonic elements... Perhaps I did not understand something and someone can clarify this a bit? a) Contextual Interpretation

b) Evolution of Ideas
c) Multiple Layers of Explanation
d) Interplay of Human Observation and Platonic Existence

Answer 1

The student is asking about a contradiction in Stephen Wolfram's statements regarding the role of human observers and the existence of platonic objects in mathematics. This can be understood by considering the contextual interpretation of Wolfram's ideas, the evolution of his thoughts, and the interplay between human observation and platonic existence.

Step-by-step explanation:

In this question, the student is pointing out what seems to be a contradiction in Stephen Wolfram's statements regarding the role of human observers and the existence of platonic objects in mathematics. On one hand, Wolfram suggests that human observers determine what axioms are true and denies the existence of platonic objects associated with abstract concepts. But on the other hand, he also states that all axioms are equally valid and exist as platonic objects. This contradiction can be understood through a contextual interpretation of Wolfram's ideas, the evolution of his thoughts, and the interplay between human observation and platonic existence.

Wolfram's understanding of mathematics is complex and has evolved over time. It is important to consider the context in which he makes these statements and the specific arguments he is addressing. In some writings, Wolfram does refer to formal systems like the set of all possible axioms as platonic objects. However, in the video mentioned, he may be emphasizing the role of human observation in determining what axioms are considered true and valid, while still acknowledging the existence of these platonic objects.

Overall, it is necessary to take into account multiple layers of explanation and the interplay between human observation and platonic existence in order to understand the apparent contradiction in Wolfram's statements. It is also important to note that the field of mathematics is complex and subject to ongoing debates and discussions among mathematicians.