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Philosophical argument
Not a quarrelsome dispute, but a set of statements in which one or more (premises) establish a further statement (the conclusion).
Premise
A statement that provides support for the conclusion of an argument.
Conclusion
The final statement of an argument, which the premises are meant to lead to.
Words that signal a premise
"Since," "firstly/secondly," "for," "as," "after all," "assuming that," "in view of the fact that," "follows from," "may be inferred/deduced/derived from."
Words that signal a conclusion
"Therefore," "so," "it follows that," "hence," "consequently," "suggests/proves/demonstrates that," "entails," "implies."
Why a single statement isn't an argument
It lacks both a premise and a conclusion (e.g., "People who are tired go to sleep").
Why a chronological description isn't an argument
It is a sequence of factual statements without any premise supporting a conclusion.
Why a question isn't an argument
It doesn't assert any statements meant to establish a conclusion.
Valid argument
An argument whose conclusion logically follows from its premises, regardless of whether the premises are actually true (correct form).
Sound argument
A valid argument in which all the premises are also true.
Invalid argument
An argument where the premises may be true, but the conclusion does not logically follow from them.
Unsound argument
An argument that is valid in form but contains at least one false premise.
Non-sequitur
A "conclusion" that happens to be true despite following from an invalid or unsound argument — it doesn't actually follow from the premises given.
Argument from analogy
An argument that draws a conclusion about one case because a relevantly similar case is already established; general form: X applies in case A, A is relevantly similar to B, therefore X applies in B.
Setting of the Euthyphro
Outside the court of the king-archon in Athens, immediately before Socrates' trial.
Why Socrates speaks with Euthyphro
Euthyphro is a priest who claims to know exactly what piety is.
Why Socrates is at the court
He is being charged with impiety and corrupting the youth of Athens by Meletus.
Why Euthyphro is at the court
He is charging his own father with murder.
Perception of Euthyphro
Seen by Athenians as a religious zealot; he believes justice, like piety, is objective, which is why he prosecutes his own father.
Euthyphro's 1st definition of piety
Prosecuting the wrongdoer (i.e., what he himself is doing) — Socrates rejects this as merely one example of a pious act, not a definition of piety itself.
Euthyphro's 2nd definition of piety
"What is dear to the gods is pious, what is not is impious."
Problem with the 2nd definition
The gods disagree with one another (discord among the gods) about what is just, beautiful, or good, so the same act could be both god-loved and god-hated.
Euthyphro's 3rd definition of piety
Piety is what is loved by ALL the gods; impiety is what is not loved by all the gods.
The Euthyphro Problem (dilemma)
"Is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?"
Socrates' analogy about "carried" and "loved"
A thing is carried because someone carries it (carrying causes "carriedness"); likewise, a thing is loved because the gods love it — so being loved is a state, not an essential property, of the pious thing.
Conclusion of Socrates' analogy
Being "god-loved" is only an attribute of piety, not piety's essence — piety and being god-loved are shown to be two separate things.
The sculptures of Daedalus (reference)
Socrates compares Euthyphro's shifting arguments to Daedalus's statues, which supposedly moved on their own — meaning Euthyphro's definitions won't stay fixed in place.
Euthyphro's 4th definition of piety
Piety is a part (species) of justice, just as oddness is a part of number, or shame is a part of fear.
Euthyphro's account of "part of justice"
Piety is the part of justice concerned with the care of the gods, while the rest of justice concerns the care of other people.
Euthyphro's "care of the gods" analogy #1
Comparing service to the gods to the care a horse breeder, hunter, or cattle raiser gives their animals — implying pious acts make the gods "better."
Euthyphro's "care of the gods" analogy #2
Comparing service to the gods to how slaves serve masters — piety becomes the knowledge of properly serving the gods through prayer and sacrifice.
How the dialogue ends
Euthyphro, faced with having to restart the definition of piety from scratch, claims he is in a hurry and leaves without resolving the question.