Relations of ideas are bonds that exist between statements. The bonds that exist between relations of ideas cannot be destroyed by anything (Hume). They will remain constant irrespective of the circumstances that may come between them. The statement, 5+8=13 can show an example of relations of ideas. Nothing can change this relationship whatever the circumstances. The statement that says that all widows were once married and that one of the spouses died can illustrate another example. Nothing can change this fact whatever the circumstances. Matters of fact refer to a situation whereby a concept is presented without embellishments (Hume). With the matter of fact, the emotional aspect of the speaker or presenter is not shown or included in what is being put forth. An example here can be: He said his name matter of fact. The statement shows that there was no addition to the name of the individual. Relation of ideas falls into the category of necessary versus contingent (concerning reality) while matters of fact fall into the class of truths.
California has more people than Texas falls in the class of relations of ideas. The reason for this is that it is a known fact that many people prefer California to Texas. There are many good things in California that have attracted many people there, and nothing can change this fact. A Pentagon has more sides than a square falls in the category of matters of fact. The reason advanced here is that this is the plain truth that has not had any embellishments added to it. The fact that ‘penta’ means five shows that a pentagon has got five sides while a square has four sides. Nothing can be done on these statements so that a square becomes a figure with more sides than a pentagon. A square will remain inferior to a pentagon in regard to their number of sides. Anybody talking about a square and a pentagon will be presenting a matter of fact. A person talking about California having more people than Texas will be showing a relationship between ideas. We can, therefore, say that relations of ideas will present two ideas that are comparable while matters of fact show things as they are without any additions.
Hume, David. An enquiry concerning human understanding. Alex Catalogue, 1965.
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