Part 1: What is reasoning? And, how does it lead to knowledge?
What is reasoning? A possible answer: reasoning is the mental processing of information. But, not all mental processing of information counts as reasoning. The transformation of the electrical impulses sent down the optic nerve to the brain into a mental image is an example of mental processing of information. But it is surely not an example of reasoning. Does only the mental processing of propositional information (information that comes in the form of statements) counts as reasoning? What about spatial reasoning?
What is an inference? Drawing an inference involves deriving a conclusion from a premise or set of premises. Premise = a statement that supports/acts as a basis form/provides evidence for another statement. Conclusion = a statement that is supported by one or more premises. The process of drawing inferences is very important in understanding how reasoning can lead to knowledge – i.e., how reasoning can count as a “way of knowing”.
Two kinds of inference Deductive inferences – when successful: if the premises are true, then the conclusion has to be true. Example 1: (Premise 1) Steve is a bachelor. (Conclusion) Steve is not married to Sally. Example 2: (Premise 1) All ravens are black (Premise 2) X is a raven (Conclusion) X is black
Two kinds of inference Non-deductive inferences – Even when successful, the truth of the premises makes the conclusion likely, but not certain. Example 1: (Premise 1) The window of my car is broken, and my laptop – which I left on the back seat – is missing. (Premise 2) The best available explanation of this state of affairs is that someone has broken into my car and stolen my laptop. (Conclusion) Someone has broken into my car and stolen my laptop. Example 2: (Premise 1) Most ravens are black. (Premise 2) X is a raven. (Conclusion) X is black.
Part 2: The relationship between reason and experience
Scientific Reasoning Natural science is considered to be an area of knowledge in which reason (a way of knowing) and experience (another way of knowing) come together. But how does this work?
Inductive reasoning/inference When philosophers first started thinking about scientific reasoning, they took the process to be inductive. What is inductive reasoning? Reasoning from particular observations/experiences to general conclusions about the world. Examples: All tigers observed so far have been stripy. Therefore, all tigers are stripy. The sun has always been observed to rise in the eastern sky. Therefore, the sun rises in the eastern sky every morning (including tomorrow morning). The fallibility of induction Inductive reasoning is a form of non-deductive reasoning. The mere fact that all X’s so far observed have been Y does not make it certain the all X’s are Y: All swans observed by Europeans up until the 18 th century were white!
Inductive reasoning/inference Hume’s problem of induction. The sun has always risen in the east in the morning. Therefore, the sun will rise in the east tomorrow morning. But, how do we know that inductive reasoning is reliable? Surely we are not justified in making a particular inductive inference unless we are justified in believing that induction, more generally, is a reliable process of reasoning. We know that induction is reliable because induction has always proved reliable in the past. Uh oh, we are using inductive reasoning to justify the use of inductive reasoning! This is like trying to find out if Bob is a reliable witness by asking Bob himself.
Hypothetico-Deductive Reasoning What is it? This is where you: (1) Come up with a hypothesis/theory (2) Work out what the empirical consequences of the theory will be. (3) Conduct experiments/observations and see if the results match those predicted by the theory. Example: Einstein’s relativity theory entails – amongst other things - that nothing can travel faster than the speed of light. If we fail to observe anything travelling faster than the speed of light – or doing anything else that contradicts the theory – then the theory stands. If we do observe some event that the theory says is impossible, the theory falls.
Hypothetico-Deductive Reasoning Advantages of the hypothetico-deductive approach: Gets us around the problem of induction We don’t need to assume that the future will be like the past. If a theory makes a prediction and the prediction is not borne out, then the theory is proven false, and that is that. Disadvantages: Only allows for falsification, never for absolute verification. The fact that the predictions generated by a theory have come true so far does not mean that this will continue for ever. E.g. – Scientists have not yet made a reliable observation of an object travelling faster than the speed of light, but such an observation might be made at some time in the future.
A priori reasoning: pure reason A priori reasoning involves reasoning to conclusions in a way that does not involve any reliance on experience. The example of mathematical reasoning: Most mathematical reasoning involves the drawing of inferences from mathematical axioms or principles. But how are the principles themselves supported/justified? By experience? Surely not. Because to understand them is to see that they simply must be true? This answer actually seems more plausible.
Knowledge without reasoning? Sometimes it looks as though we can gain knowledge is a way that doesn’t rely on other knowledge. In fact, it seems like this must be the case: if all knowledge relies on other knowledge for support, then the chains of support will go on forever. Self-evidence in logic and mathematics Do you need a reason to accept that 1 + 1 = 2? If you know what “1 + 1 = 2” means, then you know that it is true, right? Basic empirical beliefs What about beliefs about the contents of experience? E.g. “I have a pain in my leg” or “I see something red”
Discussion questions for this week What is reasoning, and how does it differ from other kinds of mental processing of information? What is an inference? What is the difference between deductive and non-deductive inference? Can you come up with some examples of each? What reasons do we have to prefer the hypothetic-deductive account of scientific reasoning to the inductive account? Can there be reasoning without experience, or knowledge without reasoning?
Journal entry due week 1, Term 2, and reading. What is the difference between deductive and non- deductive inference? Come up with two examples of each. Reading for the start of term 2: Nicholas Alchin, Theory of Knowledge, pp. 72-91