In this video, I talk about the foundational principles of logic and its relationship with the philosophy of science. I share some basic understandings of deduction, induction, and abduction, and how these forms of logical inference are applied in scientific reasoning.
- Deduction: Deduction is a form of logical inference where if all premises are true, the conclusion must also be true. Deduction is often used in formal sciences like mathematics and theology. I mention the importance of the structure of an argument, differentiating between ‘validity’ and ‘soundness’. A valid argument has a correct structure, while a sound argument is both valid and has true premises.
- Induction: Unlike deduction, induction deals with probabilities. In empirical sciences, induction is often used to make general conclusions based on specific observations. However, I talk about the ‘problem of induction’, which questions the logical necessity of our inductive conclusions. While empirical sciences can’t provide absolute truth, they are ‘true enough’ to match our sense experience and help in technological advancements.
- Abduction: This is inference to the best explanation. In science, when data can lead to multiple explanations, abduction helps in choosing the most plausible one. I use an example of a doctor diagnosing a common cold based on symptoms, illustrating how abduction is used in practical scenarios.
- Paradoxes and Limitations: I also touche upon the existence of paradoxes in logical reasoning, indicating the limitations of our rational faculties. Reality is ultimately beyond what we can understand through rationality alone.
- Hidden Premises: I emphasise the need to be aware of hidden premises or presuppositions in logical arguments. These are statements that are not explicitly stated but are crucial for the argument’s validity.
Mentioned in this episode:
- Validity vs Soundness by IEP.
- Categorical Syllogism by Brittanica.
- Lecture on Conditionals, Modus Ponens, and Modus Tollens by RCP Philosophy. Warning: It’s long.
- The Problem of Induction by SEP. If you enjoy technical details.
- Highlight on Original Antigenic Sin by The Rockefeller University.
- Logical Paradoxes by Encyclopedia.com.
- Abduction by SEP. Nothing to do with kidnapping.
- Stephen Strange is not a cocaine addict in Earth-616. This is where many MCU movies take place, as strongly implied in Doctor Strange in the Multiverse of Madness.
In this video, I talk about the the intricate relationship between mathematics and other sciences. I start by distinguishing between empirical sciences, which focus on natural objects, and formal sciences like mathematics that study abstract constructs such as numbers.
I highlight the importance of formal sciences in providing a holistic understanding of life and science. For example, Mathematics is a versatile formal science with applications ranging from probability and statistics to blockchain technology.
I explore the role of theorems and axioms, foundational truths that are accepted without proof, in shaping mathematical understanding. These axioms are not just confined to mathematics but extend to the philosophy of science and can even inform discussions about science and religion, particularly in Islamic contexts.
I then discuss how mathematical models influence philosophical and political decisions, with examples from the COVID-19 pandemic and ethical considerations in AI for medical diagnoses. I ask for a more humble approach to science and rational systems, acknowledging their limitations.
Mentioned in this episode:
- How many ways are there to prove the Pythagorean theorem? by Betty Fei
- The paradox at the heart of mathematics: Gödel’s Incompleteness Theorem by Marcus du Sautoy
- Axiom by Britannica