False Lemmas in more detail • Gettier gets us to agree that 1) ‘…it is possible for a person to be justified in believing a proposition that is in fact false. ‘ 2) ‘for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P…then S is justified in believing Q.

A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.

Logically Necessary and Sufficient Conditions for Knowledge A logically necessary condition for something to be the case is one without which the thing could not possibly be the case; and a logically sufficient condition for something to be the case is one given which the thing absolutely must be the case.

Knowledge and Opinion in Plato’s Meno. Knowledge is a mental faculty/power that allows us to apprehend “being” (i.e., reality). Opinion is subject to error, but knowledge is not.

As the object of knowledge the Form is “seen” with the “mind’s eye” (the faculty of nous) in analogy to the way in which opinions take as their objects the beautiful physical objects “seen” with the body’s eyes. Thus Forms are the objects of knowledge while physical objects are objects of opinions.

The highest object of knowledge, according to Plato’s Socrates, is goodness, sometimes translated as “the Good.” (Rep.

For Plato, forms, such as beauty, are more real than any objects that imitate them. Though the forms are timeless and unchanging, physical things are in a constant change of existence. Where forms are unqualified perfection, physical things are qualified and conditioned.

Plato’s ideal state was a republic with three categories of citizens: artisans, auxiliaries, and philosopher-kings, each of whom possessed distinct natures and capacities. Those proclivities, moreover, reflected a particular combination of elements within one’s tripartite soul, composed of appetite, spirit, and reason.

Plato’s main contributions are in philosophy, mathematics and science. However, it is not as easy as one might expect to discover Plato’s philosophical views. The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote about 30 dialogues written in the form of conversations.

Plato is considered by many to be the most important philosopher who ever lived. He is known as the father of idealism in philosophy. His ideas were elitist, with the philosopher king the ideal ruler. Plato is perhaps best known to college students for his parable of a cave, which appears in Plato’s Republic.

It offers what many scholars believe is a fairly reliable account of what the Athenian philosopher Socrates (469 BCE – 399 BCE) said in court on the day that he was tried and condemned to death on charges of impiety and corrupting the youth.

His writings explored justice, beauty and equality, and also contained discussions in aesthetics, political philosophy, theology, cosmology, epistemology and the philosophy of language. Plato founded the Academy in Athens, one of the first institutions of higher learning in the Western world.