Truth, proof and certainty

Knowledge and belief

We all have beliefs. Beliefs are the conclusions we come to, the things we think are right about big things (like God, or right and wrong), small things (like where I think I left my drink at a party) and even trivially obvious things (such as I have a head).

We all know things too. Sometimes we think we know things, but we are wrong (i.e. our beliefs are mistaken); sometimes our beliefs are correct and we do indeed know. But we don’t always know which of our beliefs are right and wrong.

There are several types of knowledge – there are propositions (sentences) that may be true and thus represent knowledge. There is also knowledge that isn’t necessarily expressed in propositions – like knowing how to do something like swim, or knowing how it feels to be you.

Philosophers define propositional knowledge as beliefs that are true, and that we are justified in thinking are true – i.e. we have good reason to think they are true. (There are some problems with this definition, but it is mostly true for propositions.)

How we know things

There are many ways we can be justified in thinking something is true, or at least probably true.

• Some things can be proven by logic or mathematics.
• Some things we can just ‘see’ by intuition. A designer may just know what is the best colour in a situation; a mathematician may be able to see a mathematical statement is true before she can prove it; and most of us deep down know that some things are morally right and others morally wrong without being able to prove it.
• Some things we learn by observation, through our five senses. This includes ordinary every day events such as we can see it is raining, but is also the basis of scientific experiment. Mostly this knowledge can be verified by others.
• We can know things about ourselves (e.g. ‘I am feeling pain’ or ‘I like the colour yellow’) by personal experience that may not be verified by others.
• There are some things we may never be able to know by ourselves, but we can learn by authority – from someone who does know (for example a medical diagnosis).

Each way of knowing may be appropriate in certain situations and not in others.

Proof and certainty

Most of us want our important beliefs to be true, but how can we tell if a proposition is true? Do we have to be certain to know something is true, or is ‘probably true’ enough?

• The only things we can actually prove beyond doubt are mathematics and logic, where truths can sometimes be established by ‘cast iron’ proofs.
• Most things we observe we can only know to be probably true at best – we can always be mistaken for a variety of reasons. Science is in this category. Science has a good record of discovery, but most scientific knowledge is provisional and can always be shown to be wrong, or in need of modification, by further information. For example, Newton’s laws of motion ‘work’ for most situations, but we now know them to require modification if velocities approach that of light.
• Much science is based on statistics, and is thus ‘known’ within 95% confidence limits or similar – for example, medical testing of new drugs. Many scientific conclusions (e.g. climate change predictions) are based on models that are statistically accurate, but not certain.
• Some science is even less certain. When studying the past (e.g. the beginning and evolution of life, or the beginning of our universe in the big bang), scientists do not have opportunity to measure or observe directly, and have to rely on indirect methods that are less certain. ( see note 1, below)
• Historians, who also study the past, have similar limitations on their knowledge – they cannot observe the events directly and many of the written reports may now be lost. Historical knowledge is thus also subject to change as new information is gained.
• As well as the inherent uncertainties in all the above, people make mistakes and have biases. Much of our knowledge comes from reading or the media which may be biased or in error.
• Much of life is even less certain. We make decisions on relationships, jobs, values, etc, based on information that is often uncertain and unstructured, but also (rightly) based on less tangible matters such as trust, feelings and attitudes.

Three interesting conclusions arise from all this.

1. If we only know what we can prove with certainty, then we can ‘know’ very little, even in science. It is most sensible to consider knowledge to be a matter of probability, not certainty.
2. If there are many different ways of knowing, it is important to know which way is appropriate in each situation. For example, some people claim that the only true knowledge is scientific knowledge, but this is not a self consistent view (for that statement in itself is not scientific) and it ignores much of what we know.
3. If we want to know about God, we will need to choose appropriate methods (if we can determine what they are).

Evidence and interpretation

Most ways of knowing require evidence, but not all evidence is the same. Science generally requires repeatable and statistical evidence to a defined degree of confidence, law courts require evidence ‘beyond reasonable doubt’, while history and philosophy generally require the most reasonable explanation. In life, we often have to make decisions with limited information and a tight timeframe, especially in emergencies, and so have to settle for what seems best at the time.

But mere facts are not sufficient to justify belief – the facts must be interpreted by reason to show how they support a belief. And different people may interpret the same facts differently, perhaps out of bias, or different assumptions or simply different assessments of the importance of different facts.

So justified belief is a complex area which this discussion only barely outlines. It should not be surprising that people come to different beliefs on many important matters.

Can we have knowledge of God?

If God exists, it is unlikely he would be obervable, measurable or known directly because, by definition, God lives outside our space-time universe. But we should in principle be able to observe his actions in the world or in our own consciousness. For example:

• Scientists cannot observe the beginning of the big bang or the beginning of life, but can look for signs of what happened back then, and postulate possible causes. Theists generally consider that logical arguments based on the same scientific information lead to the conclusions that God is the cause and designer.
• Historians likewise cannot observe the events they study, but look to evidence in texts, archaeology and artefacts to ascertain what occurred. Similarly, christians believe that the events recorded in the gospels provide historical evidence for the life of Jesus, and thus for the existence of God.
• Much of what we know comes from personal experience. We human beings are conscious of ourselves. It feels like we are capable of making choices (i.e. we are not just robots controlled by our brain chemistry). We are capable of thinking rationally, and of loving. And we generally have a sense of justice and believe some things are truly right and wrong. Theists believe that all of these human experiences are signs that we are created by God, and could not occur if we weren’t created by God.
• Most theists also believe that God is capable of revealing himself to them and that their experience of life includes experience of God. Non-theists often use their experience of life to argue that God doesn’t exist.
• Some people claim to have been miraculously healed. These experiences can in principle be verified, and there is good medical documentation for a very few of them.

It is not the purpose here to discuss whether these claims are valid or not. (For my take on them, see Why believe?.) The point here is that these approaches can in principle justify belief so that it can be called true knowledge. The discussion on whether the claims are true should be on this basis.

Thus I suggest that we can reasonably hope to have justified belief (one way or the other) about God, using a variety of ways of knowing. Only a person who wanted to disprove God’s existence would insist that scientific evidence is the only way to know the truth about God’s existence.

note 1:

W. Ford Doolittle, Biochemistry Professor, Dalhousie University, Canada said:

Questions about the past – whether in cosmology, geology, paleontology, archaeology, or human cultural and political history – are different. We cannot do experiments in the past, so any attempt to reconstruct it must be based on indirect and inferential methods.

Evolutionary biologists who seek to reconstruct life’s history have three such inferential methods: (1) comparisons of the properties of living species; (2) study of relics, such as biological and chemical fossils, or apparently primitive features retained by modern cells; and (3) feasibility experiments.