This is a post on the Euthyphro and also on Occam’s Razor.
The Euthyphro is a work by Plato and seems to have been a real encounter between Socrates and a man called Euthyphro. Socrates was a stonemason and one of the greatest philosophers of all time and at the time the work is set he would soon be on trial for his life. Socrates has many youthful, aristocratic followers.
We know little about Euthyphro as we only know him from this work of Plato, but we can assume he is well to do; his father has servants and slaves. We can guess that he would be in roughly the same social standing as Socrates. Clearly, he is not an aristocrat.
Euthyphro is on his way to court to prosecute his father for impiety. His father found that a servant killed a slave, so his father tied up the servant and left him in a field while he fetched help. On his return, the servant had died and it is for this act that Euthyphro intends to prosecute his father.
Socrates finds this out and discusses the nature of impiety with Euthyphro, who assumes he is an expert on this subject. Socrates poses the question, do the gods love an action because it is pious, or is an action pious because the gods love it? If it is the former then piety is external to the gods ( that is, piety is not a property of the gods) and if the latter then piety is arbitrary, that is, the definition is not fixed but subject to whim.
[Please note that I am using the strong definition of arbitrary meaning random here and not the weaker one that because of vagueness means we choose a reasonable limit. For example, there is an arbitrary speed limit on roads, which is a reasonable one, but which could be higher or lower; it is not a speed limit picked at random.]
This definition can be changed to an analogous one by substituting morality for piety (the terms are related) and the (Abrahamic) God for the (Greek) gods. This argument has been around almost as long as the Euthyphro’s (as do the gods love an action because it is moral, or is an action moral because the gods love it?). In other words: is an action moral because God approves of it or is it moral independently of God? In the former case, it is arbitrary (even if you believe God can never perform or approve of an immoral (or amoral?) act) and in the latter, God is not necessary for morality, which raises the question of where morality comes from.
I shall make an attempt at answering that question in a later post.
Turning now to Occam’s Razor. This is also known as the principle of parsimony and though it predates William of Occam by at least a millennium, it is named after this English Franciscan friar. There are a number of formulations, but, simply it is to look for the simplest explanation of a phenomenon. It is a tool and like all tools must be used with care and for suitable purposes. It is also a ‘rule of thumb’ tool, something to used as an approximation or best guess, but is a good reminder not to overcomplicate an explanation.
One of the reasons why this is a rule of thumb and not a law of logic is because of the ambiguity of what is meant by simple. A thing can be both simple and complex. Take for example a tablet computer. This is very simple in that it is one thing, that is not two things like a laptop computer, which has a separate base unit and a screen, or it is simple to use, but it is very complex in the way it works so that it can be simple to use.
Some people will claim the (Abrahamic) God is simple as it is one thing, but the close analogy is to the tablet. This should be born in mind to those who use God as the simplest explanation for any phenomenon.
Fora good summary and a different analysis of the Euthyphro see Plato’s ‘Euthyphro’ by at https://www.thoughtco.com/platos-euthyphro-2670341
For a good discussion of Occam’s Razor see https://philosophyterms.com/occams-razor/