8. Which of the following, if true, would best serve to challenge Ogburn and Thomas's belief that the discovery of calculus is an example of the 'phenomenon' mentioned in the first sentence?
Answer: C
Finding a previously unknown letter between Newton and Leibniz discussing calculus that predated its commonly assumed discovery challenges Ogburn and Thomas's belief.
This discovery would indicate that Newton and Leibniz were not independently discovering calculus in isolation, but rather collaborating or communicating about it beforehand, thereby undermining the notion of simultaneous discovery as an inevitable phenomenon.
A) Uncovering the existence of a journal that Newton kept while working with calculus
While this option could provide insights into Newton's thought process and development of calculus, it would not challenge the idea of simultaneous discovery. A journal would likely document Newton's independent work rather than imply a lack of inevitability in the discovery itself.
B) Learning that scientists other than Newton and Leibniz had also made substantial progress on calculus
This option suggests that multiple individuals were working on similar ideas, reinforcing rather than challenging the concept of simultaneous discovery. It supports the idea that calculus was in the intellectual climate, rather than contradicting the inevitability suggested by Ogburn and Thomas.
C) Finding a previously unknown letter between Newton and Leibniz discussing calculus that predated its commonly assumed discovery
This finding would directly challenge Ogburn and Thomas's belief by suggesting that the discovery of calculus was not purely independent but rather involved prior communication between the two mathematicians. It implies that their discoveries were influenced by each other, thus questioning the notion of inevitability.
D) Identifying a minor error in Newton's original mathematical calculations
While identifying a minor error may affect the perception of Newton's contributions, it does not challenge the concept of simultaneous discovery itself. The error does not negate the fact that both Newton and Leibniz arrived at the concept of calculus around the same time.
Conclusion
The correct answer, option C, effectively challenges Ogburn and Thomas's assertion by introducing evidence of communication between Newton and Leibniz, suggesting that their discoveries were not merely coincidental. All other options either reinforce the idea of simultaneous discovery or do not provide sufficient evidence to dispute the inevitability of the phenomenon as proposed by Ogburn and Thomas.