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But what about Russel's type system(s)? Were they just an addition he proposed that never went anywhere, or are they used much like certain programming language
by kruhft 9y ago
But what about Russel's type system(s)? Were they just an addition he proposed that never went anywhere, or are they used much like certain programming languages have types and others don't, depending upon the preference of the user? Or are types just 'too hard/restricting' for general mathematics?
- danharaj 9y agoRussel and Whitehead's type system never gained significant traction. It's primarily of historical interest. Once mathematicians became convinced that ZF set theory over first order logic was plausibly consistent and expressive enough, such foundational issues became less important to the typical mathematician. Lately there's been a resurgence in foundations because of what new foundations like Homotopy Type Theory bring to the table. Funny how something as basic as equality can be revisited time and time again for thousands of years!
- pmoriarty 9y ago"Once mathematicians became convinced that ZF set theory over first order logic was plausibly consistent and expressive enough, such foundational issues became less important to the typical mathematician." Was this decision ever explicitly expressed and agreed on by mathematicians at the time, or was it just implicitly adopted?
- danharaj 9y agoA bit of both over the years.