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lewis198
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Can 1+1 be proven? If so, then is mathematics a science?
In the usual formulation of Peano arithmetic, that is the definition of the number represented by '2'.lewis198 said:Is the Peano model based on the assumption that 1+1=2?
No, it is not. That is a theorem (although a very easy one).lewis198 said:Is the Peano model based on the assumption that 1+1=2?
I know of Principia Mathematica, but I've not actually studied it. But judging from how I hear it described, I'm quite content to stick with modern styles.arildno said:When the OP posted his question, I was thinking along the lines of Russell&Whitehead, that you know a lot more about than me, Hurkyl.
Hope my nonsense fraction was acceptably small..
HallsofIvy said:)while mathematics is based on an "Idealist" philosophy in that the "truth" of a theory depends on consistency.
An observation is the act of gathering information or data through one or more of the five senses (sight, hearing, touch, taste, and smell).
No, 1+1 is not an observation. It is a mathematical equation that represents the addition of two numbers.
1+1 is not considered an observation because it does not involve any sensory input or data collection. It is a concept that can be understood through reasoning and math.
Yes, observations can be expressed as mathematical equations if they involve measurable quantities or variables. However, not all mathematical equations represent observations.
No, not all observations lead to a conclusion. Observations are used to gather data and information, which can then be analyzed and interpreted to draw conclusions. However, sometimes observations may not provide enough information to come to a conclusion.