UNIVERSAL DEFINITIONS AND GENERAL AXIOMS

The desire to search and to find standard universal definitions for things and the need to believe that they are regular and objective truths which really exist eternally and abstractly and at times concretely as part of reality has haunted philosophers for two and a half millennia.
The need for universal definitions of the abstract and concrete qualities, states and conditions of things such as justice, beauty, love, fear and so on are usually part of any in depth thinking about the qualities, states and conditions of the things we experience in regard to whether they are universally intuited and felt or not. Some universal definitions for things require an abstract and a concrete analysis, such as universal definitions for beauty, whereas the quality and condition of some things are mostly abstract in definition.
The analytical process of actually searching for universal definitions from particular cases at hand is one of induction and requires that the thinker syllogize in inductive questioning concerning the quality and conditions of the things in question, for example, what is considered to have a beauty is not only pleasant to our minds, but is also something which is pleasant to our feelings and our senses also and this is because symmetry and proportion are aspects of what is pleasant to our senses in objects. Now the things which we think that are pleasant to our feelings and emotions usually involve how people and things behave and operate in nature and how they make us feel in the sense that they give us a pleasant feeling that is noticeable to us. A static work of art when observed can also give us a pleasant feeling in our being and in our emotions generally. When I mention that the conditions of a thing play a part in an assessment of its universal definition I mean to say, for example, that a damaged work of art is not as beautiful as an undamaged one or that justice has to be applied to actual situations rather than just being purely universal and abstract. Universal definitions and general axioms can only be arrived at by using induction. There are philosophers and scientific minded thinkers who view induction as a problem and claim that induction is a non-demonstrative method of inference therefore it is not justified or valid and any proposition, theory or inference based on it can be deemed false or worthless for the reasons mentioned. This so-called problem of induction exists only in logical procedures and their inability to assess processes in reality that cannot be demonstrated or proven outright. The validity of an inductive inference should be considered as being relative to the situation at hand and should also be dependent on the other forms and methods of reasoning at one's disposal for any given inductive assessment of a phenomenon or fact. Induction should not be viewed and applied as a rigid and regular method of reasoning to all situations and this is because philosophers and thinkers generally use many methods and forms of reasoning and logic simply to figure out one particular thing.
An example of the relative aspects of inductive inference and their dependence on other methods of reasoning for their validity can be shown by the following examples: All observed swans are white, therefore all swans are white, it is obvious that if one comes across a black swan this inference will be disproved but the problem with this pseudo inference is that it is based on what John Locke called a secondary quality because colour is not a real stable property of objects themselves and are variable and therefore it should never have been used for an inductive inference of this kind. Take for example, the claims of the inductive theories of evolution and also quantum physics as examples of induction which provide evidence that is hard to doubt and disprove as facts because they are backed up by evidence. Opposition to any inductive theory or inference can be crushed and neutralized if these theories and inferences have evidence to back them up, what would be the point of saying that these theories are false because they are non-demonstrative and therefore not justified if they have evidence to back them up. Also when one thinks of quantum theory it is not possible to imagine matter consisting of anything except molecules, atoms and particles in wave form, etc, what else is matter going to consist of instead of these things? Induction when it involves self-evident truths whether these truths happen to be empirical, universal, abstract or concrete or a combination of the two is what are known as legitimate conclusions and inferences and are valid unless proven otherwise.
The whole point about logic is that it can give valid reasons for things rather than being a tool to explain and demonstrate all things which cannot be demonstrated by using logic, an example of this inability of logic to demonstrate processes in reality is the claim of the theory of evolution that human beings and apes have a common ancestor; now how can logic and its premises demonstrate this? It cannot and the reason for this is because logic is out of its depth in this instance. Even though the theory of evolution is an inductive theory it does not need logic to validate itself in a demonstration and this is because it has the DNA research as well as all the other evidence in existence that can and does validate its authenticity and this is because non-demonstrative logic is only needed to explain the reasons of how and why things are so. Sherlock Holmes the fictional character or any detective in a real life situation would use deduction to solve crimes in a non-demonstrative sense also because they are not able to show you the actual crimes occurring but only in how they seemed to occur and how and why they happened due to evidence and apparent motives and this is not much different to inductive theories that have evidence or are self-evident but cannot be actually demonstrated.
A common argument that is used by people who doubt the validity of induction is that it is presumptuous to assume that the sun will rise tomorrow (i.e. the earth continues to spin on its axis and orbit the sun) because it has always done so as far as we know during our life. What these skeptical people who view induction as a problem fail to realize is that it is a valid enough conclusion to think that the sun will rise tomorrow due to our scientific knowledge and evidence. Also if something prevents the sun from rising tomorrow it will be due to another reason that will not have a thing to do with our original inductive conclusion. The universal and the particular, the potential and the actual are all aspects of reality which must be analyzed in a rigorous manner if universal definitions and general axioms are to be reached and found. Justice is in a sense an extension of the harmony and balance that can be found in nature but is perceived as necessary because it is impossible for a community of advanced forms of biological life to be happy without it.