


The REAL world Wikipedia has a good discussion on truth (see http://en.wikipedia.org/wiki/Truth) and starts its article by saying this: "Truth can have a variety of meanings, such as the state of being in accord with a particular fact or reality, or being in accord with the body of real things, real events, an actuality, or having fidelity to an original, or fidelity to a standard or an ideal. The opposite of truth is falsehood, which can correspondingly take logical, factual or ethical meanings." We shall be discussing truth in the prosaic context of understanding economics and the REAL World. One truth is that all objects on this earth fall downwards towards the centre of the earth. One falsehood might be that there are fairies at the bottom of my garden. The distinction between these two statements is what science aims to demonstrate. The scientific study of something aims to show the truth of it. And there are strict guidelines on how to go about doing this. Other things that have not been subject to rigorous scientific study and logical conclusions drawn are known as belief systems. Such as the belief that there are fairies at the bottom of my garden. Actually, there are "fairies" at the bottom of my garden. I take my guests down to see my "fairies" after dinner. But we know the truth. They are not really fairies, they are glowworms! So we can get a sense of what is truth and what is falsehood. The importance of this distinction will become evident when we examine some of the "belief systems" of economists. If we believe that something is true without subjecting it to the rigors of science then we might just be believing in something not of the real world  like fairies. So, we live in the REAL world and there are REAL consequences to our actions and we will only understand REAL economics if the foundations are grounded in strict scientific analysis and solid proof. That which cannot be so proven is part of a belief system. Interesting in itself, maybe, but since it won't relate to the REAL world it is not helpful in determining what the consequences of any action will be. But scientific proof is not something locked in immutable bars of steel. It has its limitations. Sep 30, 2010, 10:00 Scientific Proof Science starts with observation and thought. We examine the REAL world carefully and determine exactly what the facts are. We carefully observe and measure. When anyone else does the same thing and gets the same result we can say that these are facts  this is the truth. Then in the REAL world we see things happening and ask ourselves, "What caused that?" When we think we know the cause of the effect we can state our hypothesis. That is, we think we know what is happening and our hypothesis is a statement of this belief. We can then look for ways to substantiate this belief. If we can "prove" the hypothesis then we can advance our thoughts to the status of theory. Once we have a theory we can test it to see if it is true. We can show it to other interested people and they can apply their tests to see if it is true. If many people test the theory over an extended period of time and it passes every test then we really can start to say, "This is true". However, if at any time someone carries out a test and shows that the theory is wrong then the theory is wrong. That is, it is not true. Even after many many experiments all showing the theory is true it still might be false as it only takes one experiment finding the theory false to prove that it is wrong. Proving a theory is true takes years and years and many tests. Even then we will always admit the possibility of error  something we may have overlooked. Proving a theory is wrong takes only one solid experiment. Then we can look at the circumstances of that experiment and decide maybe that it is wrong because the conditions of the experiment are subtly different and that the theory is true in certain circumstance but not others. We can then change the theory to encompass all conditions or have a limited theory and work on the new special case theory. A scientific theory is true until someone proves it is not. Believe me, scientists are always trying to prove that other peoples theories are not true. So we await the tests of time. We also note that science requires that we measure or count what we are observing. To do this we have standard measure. Length is measured in metres and weight in kilograms and time in seconds. The original one metre measure was supposed to be one 10,000,000th of the distance from the north pole to the equator. This was then agreed to be the distance between two marks on an iridium/platinum bar held in Paris at a temperature of zero Celsius. Subsequently it has been redefined for greater accuracy in terms of the wavelength of a certain colour of light. (See http://en.wikipedia.org/wiki/Metre#Prototype_metre_bar). Other scientific measures have been also adjusted to modern standards to produce the greatest accuracy. It is interesting to note that we have an inspectorate which carefully tests all weighing machines to ensure that we get an exact measure of tomatoes at the shop but the money we use for the purchase is not subject to the same rigor! With governments expanding money supplies by 10% to 20% per annum we can expect that its REAL value is likely to be diminishing by a similar amount. What would we think if we found the definition of a Kilogram of tomatoes was diminishing by 10% every year? I would think it was a bit of a swizz! Sep 29, 2010, 10:26 Mathematical Proof It is easy to succumb to the notion that something that is mathematically true is scientifically true in the sense discussed above. However mathematicians are not scientists. Mathematicians are not concerned about the REAL World. They work from axioms to conclusions using logical argument. This is their proof that conclusions are true. However the axioms are carefully chosen to be the minimum necessary (ie necessary and sufficient) to develop the mathematical system they are working on, they are not chosen because they relate to the REAL world. They may do, and it is surprising to find how often some esoteric fiddling of a mathematician ends up being helpful in describing the REAL world, but that is not the point. For a mathematician, the aim is to discover what is true from the given set of axioms. Change an axiom and a whole lot of other things may be true. The lesson for us here is that if we choose to use maths to describe some of the phenomena we encounter in the REAL world we had better be sure that we understand the axioms and initial conditions of any branch of maths that we choose to use. Sep 28, 2010, 12:23 True Conclusions And so we arrive at the basis for truth and a true description of the REAL World that keeps our concepts grounded in reality. The first condition is that our known facts must be subjected to scientific rigor. That is, careful observations and continual testing of our theories to ensure that they remain true. Secondly, if we are to use mathematical reasoning to develop the logical structure of our field of study we must ensure that the axioms of the mathematical system we are using are met within the conditions and observations of the phenomena we are examining. That is, we must ensure that our mathematics is suited to the problem we are solving? Sep 27, 2010, 11:22

