CAN WE EVER REALLY PROVE SOMETHING?
Table of Contents:
Proof vs Probability
Scientific Reasoning, Proof and Falsification
Francis Bacon said that induction is an essential part of scientific reasoning. So what is induction? Induction is a way of reaching valid conclusions from the evidence. What do we mean by valid conclusions? It means that the conclusions need to logically flow from the evidence. This may seem obvious but poor science can result from invalid conclusions rather than bad evidence. In order to make sure that our conclusions are logical we need to understand how the arguments are made that lead us to the conclusion. So let’s look at how arguments are made. An example of an argument is:
All birds can fly
Geese are birds
All geese can fly
An argument has two parts:
The conclusions can be false even if the premises are trues and conclusions will be false if any of the premises are false. This is an area of science that can be misunderstood and misleading. So how do we make true conclusions from our evidence? There are two types of conclusions:
An inductive conclusion is not a proof since it contains an assumption that all the objects are the same as the observed sample, it is a conclusion from the known to the unknown. Induction is a generalisation from the specific and assumes that the laws of nature don’t vary between the two. Most of science uses inductive conclusions.
Induction does not give us certainty but gives us sufficient probability not far short of certainty. In science you may think that we would only accept a deductive proof to give us certainty. Sometimes we are able to have that certainty but most of the time we cannot definitively prove something because we have to make assumptions. Scientists are often misreported as ‘proving’ something when in fact it has been inducted using a generalisation from the examined to the unexamined. This does not mean that the science is wrong or that the work is not scientific. It means that ‘proof’ is very hard to come by and we live with an element of uncertainty while seeking evidence to give us the best knowledge we can have at that time. It is an approach that has been successfully used over the past 400 years.
The use of induction in science was questioned by the philosopher David Hume (1711-1776) in his book “An Enquiry Into Human Understanding". Hume said that, although we use induction all the time in life, it is a “brute animal” and cannot be rationally justified so we should not use it. This is ‘Hume’s problem of induction’. It says that the process of induction, which is a key element of the scientific process, does not give us justified knowledge therefore it cannot be part of the scientific process. Hume’s argument is a blow to the scientific process as laid out by Francis Bacon. This philosophical problem is still debated todajy
Hume’s problem of induction provoked Karl Popper to explore how science could only use deduction. He wrote his findings in his book "The Logic of Scientific Discovery” (1934). He believed that Hume had shown the ‘unjustifiability of induction’ and therefore science should not rely upon it. Popper developed the concept of ‘falsification’ and argued that although we may never prove a theory is true by sampling a small quantity, it is possible to prove a
Figure 2.1: Flowchart showing the deductive and inductive processes for accepting or rejecting a theory. Credit: C. Devereux and P. Farrell.
theory false by just one example of it not being true. For example, the premise 'All geese are white’ is proved false by observing one grey goose. The conclusion becomes ‘It is false that all geese are white’: a deductive proof. The logic of Popper’s argument means that scientists should be working to show that their theories are false rather than that they are true. This is not how people work though. The focus of scientist’s research is, generally, to prove that their ideas are right. Despite this shortcoming, the concept of falsification still has a role in science; a theory can be disproved using falsification and experiments should be devised to test theories based on falsification. Publishing a theory allows others to see if there are ways to falsify it.
Popper’s theory of falsification did not change the need for induction in science but it did lead him to set out criteria to distinguish between science and pseudoscience by identifying ‘good’ science as:
Probability as Science
By now, you may be sceptical about how robust scientific knowledge really is. Inductive reasoning is the basis of most scientific work but cannot give certainty. Deductive reasoning is the basis of proof but is rarely possible in science. The concept of probability can help. Even if a theory cannot be shown to be true it can be shown to be highly probable.
What is probability? It is how likely something is to occur. Flipping a coin is a random process and has an equally likely chance of landing on a head or a tail. If we flip the coin once we do not know which way it will land. If we flip the coin many times then half the time it will land on heads and half the time it will land on tails. The more we flip the coin the closer the result will be to exactly 50% heads and 50% tails. We can now put a number on the probability and we have an objective measure of the outcome of a flip of a coin. Probability can also be a subjective measure. If we say that finding alien life on Mars has a very low probability then it will mean different amounts to different people. There is no objective probability, we cannot put a number on it, we just know that it is very unlikely to occur.
Thomas Bayes was a 17th century English clergyman who pioneered probability theory and discovered the principle of conditionality; the probability of something occurring is based on whether it has occurred before. As more evidence supports a theory, there is more confidence in that theory and a scientist’s rational belief in the theory should change. A difficulty with this approach is knowing what probability to put on the theory before the evidence is collected, often this is a subjective best guess. This subjective element can be unwelcome by some scientists but it does not stop Bayes’ approach being widely used particularly in analysing the statistics of experiments and is an important part of the scientific method for many disciplines.
Using probability within scientific reasoning provides an adaptation to the scientific method:
HOW TO MAKE THEORIES AND REVOLUTIONS
Changing scientific ideas
How Do We Make Theories?
A scientific theory is an explanation that has been shown to fit the evidence, it answers the why question. Why does the World behave as we are observing it? In science, a theory and a model mean different things. The following are definitions of types of scientific explanations.
Models are used in the daily work of a scientist. In cosmology, ACDM is a model that is being built on to develop a full theory.
Now we know what a scientific theory is, the next step is to know how to develop a theory and, of course, there are theories on how to develop theories. Here are four important ideas about how to make scientific explanations.