Briefly Answer The Following Questions In Paragraph Form

Briefly answer the following questions in paragraph form. Max word count for entire assignment is 400 words
Russell highlights two key differences between rationalists and empiricists. First, rationalists believe that some knowledge is innate or known independently of experience, while empiricists hold that all knowledge comes from sensory experience. Second, rationalists emphasize the role of reason and innate ideas in acquiring knowledge, whereas empiricists focus on observation and empirical evidence. An example of a priori knowledge, which humans possess independently of experience, is mathematical truths such as "2 + 2 = 4." In contrast, an example of a posteriori knowledge, which is gained through experience, is the observation that "the sun rises in the east." This distinction underscores the differing sources and validation methods underpinning the two philosophical approaches.
Galileo’s separation of physics from metaphysics refers to his methodological distinction between the study of the natural world and the study of ultimate reality or existence. Galileo emphasized the importance of experimental methods and mathematical analysis in understanding physical phenomena, thereby prioritizing empirical investigation over speculative metaphysical inquiries. He believed that physics should be based on observable, measurable phenomena and that its theories could ultimately be tested and verified through experiments. Meanwhile, metaphysics—dealing with questions about the nature of reality—was regarded as more speculative and less susceptible to empirical validation. By focusing on physics, Galileo helped establish a scientific approach rooted in experiment and mathematical description, distancing the study of nature from metaphysical speculation and laying groundwork for modern scientific methodology.
In "On Critical Thinking and the Nature of Logic," deduction is described as a reasoning process where conclusions necessarily follow from given premises, making it a truth-preserving form of reasoning. If the premises are true and the logical form is valid, the conclusion must also be true. Induction, on the other hand, involves reasoning from specific observations or instances to broader generalizations or theories. Unlike deduction, induction does not guarantee the truth of its conclusions, as it is based on probability and the accumulation of evidence rather than logical necessity. Consequently, deduction provides certainty, whereas induction provides probable but not certain conclusions, making both essential yet distinct methods in the pursuit of knowledge and critical thinking.
References

• Russell, B. (2009). The Problems of Philosophy. Oxford University Press.
• Galileo Galilei. (1993). The Assayer. Translated by Stillman Drake. University of Chicago Press.
• Baron, R. (2013). Critical Thinking: Better reasoning, improved decision-making. Routledge.
• Pink, M. (2004). Galileo's Scientific Writings. University of Chicago Press.
• Clarke, M. (2009). The Laws of Logic. Routledge.
• McPeck, J. E. (2016). Critical Thinking and Education. Routledge.
• Fisher, A. (2011). Critical Thinking: An Introduction. Cambridge University Press.
• Hume, D. (1739). An Enquiry Concerning Human Understanding. Oxford University Press.
• Kant, I. (1781). Critique of Pure Reason. Cambridge University Press.
• Haack, S. (1993). Evidence and Inquiry. Johns Hopkins University Press.