Philosophy

According to Hume, Relations of Ideas refer to every affirmation, which is either intuitively or demonstratively certain. Relations of Ideas are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. This however is not true when talking about Matters of Fact. A proposition like That the sun will not rise to-morrow is almost in the same level as the proposition That the sun will rise to-morrow. Both cannot be ascertained by a mere operation of thought. Propositions of this type can only be affirmed or rejectedrefuted through experience.
What two elements are held in common between the idea of cause and effect and the experience of cause and effect What one element is present in the idea but seems to be missing from the experience of cause and effect

Two elements are held in common between the idea of cause of effect and the experience of cause and effect. First, both have the element of a posteriori judgment because causes and effects are discoverable, not by reason, but by experience. Second, that both are results of custom. The connection that we see between cause and effect (be it an idea or in the process of experience) is a result mostly of custom. Hume explains that it is that principle alone, which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past. Without the influence of custom, we should be entirely ignorant of every matter of fact, beyond what is immediately present to the memory and senses. One element however is present in the idea and not in the experience, that is the element of an a priori judgment with all probability. As a Relation of Idea, causality can be judged a prior through the calculation of chance and probability. As a Matter of Fact, judgment is exclusively a posteriori.

Sketch Humes resolution of the problem of liberty and necessity.
Hume delves on the problem of liberty and necessity by explaining the problem of human freedom. He explained that the connection we see between cause and effect, and necessity in general, sprang from the uniformity of our experiences. According to Hume, without any similitude to whatever had been seen before, we should never, in that case, have attained the least idea of necessity. Necessity, explained by many as the product of the human will, is found by Hume as the product of the constant conjunction of objects, and the consequent inference of the mind from one to another, and finding, that these two circumstances are universally allowed to have place in voluntary actions. The uniformityregularity of human behavior means that it is being caused and therefore necessary. Seeing this connection between causality, necessity and behavior, Hume believed that freedom have no room in the actual sense even if humanity freely wills. This is because freedomliberty appears to be a behavior which has no cause at all. Hence, liberty does not exist because it is not necessary (in Humes terms).

When are we justified in believing the account of a miracle
Hume rejected miracles as farce and proclaimed that upon the whole, then, it appears, that no testimony for any kind of miracle has ever amounted to a probability, much less to a proof. He also added that no human testimony can have such force as to prove a miracle, and make it a just foundation for any such system of religion. There was however a note Hume left that we can be justified in believing the account of a miracle and that is though hard to prove using reason, miracles are products of faith. Mere reason is insufficient to convince us of its veracity And whoever is moved by Faith to assent to it, is conscious of a continued miracle in his own person, which subverts all the principles of his understanding, and gives him a determination to believe what is most contrary to custom and experience.

What is the source in our experience of the idea of necessary connection
In order to explain the idea of necessary connection, Hume first explains the idea of power. He postulated that that our idea of power is not copied from any sentiment or consciousness of power within ourselves and that we got the idea of power from custom. This is the same thing when it comes to necessary connection. According to Hume, this connection, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression, from which we form the idea of power or necessary connection. The source therefore in our experience of the necessary connection is custom. When we say, therefore, that one object is connected with another, we mean only, that they have acquired a connection in our thought, and give rise to this inference, by which they become proofs of each others existence A conclusion, which is somewhat extraordinary but which seems founded on sufficient evidence.

What does Hume argue rational human beings should believe about an afterlife
The concept of an afterlife surely does not fit Humes system. In the last portions of his Inquiry, he suggested that rational human beings should only accept two truly knowable things and these are truths derived from mathematics and facts derived from our experiences. Hume proclaimed When we run over libraries, persuaded of these principles, what havoc must we make If we take in our hand any volume of divinity or school metaphysics, for instance let us ask, Does it contain any abstract reasoning concerning quantity or number No. Does it contain any experimental reasoning concerning matter of fact and existence No. Commit it then to the flames For it can contain nothing but sophistry and illusion. There is no afterlife as far as mathematics and concrete experience goesany rational being knows that.