• Also see: Prove that God exists

These are, even individually, vast topics. Here is an example of what has been reccomended to me as a “good” introduction to the types of problems that come up in modern philosophy:

Since at least the time of Descartes in the seventeenth century there has been a philosophical problem about our knowledge of the world around us. Put most simply, the problem is to show how we can have any knowledge of the world at all. The conclusion that we cannot, that no one knows anything about the world around us, is what I call “scepticism about the external world”, so we could also say that the problem is to show how or why scepticism about the external world is not correct. My aim is not to solve the problem but to understand it. I believe the problem has no solution; or rather that the only answer to the question as it is meant to be understood is that we can know nothing about the world around us.

But how is the question meant to be understood? It can be expressed in a few English words familiar to all of us, but I hope to show that an understanding of the special philosophical character of the question, and of the inevitability of an unsatisfactory answer to it, cannot be guaranteed by our understanding of those words alone. To see how the problem is meant to be understood we must therefore examine what is perhaps best described as its source – how the problem arises and how it acquires that special character that makes an unsatisfactory negative answer inevitable. We must try to understand the philosophical problem of our knowledge of the external world.The Problem of the External World (by Barry Stroud; local)

• Cambridge:
  • to refuse to accept something or someone as true, good, or reasonable.
  • to refuse to accept or obey something or someone; reject:
  • to decide that an agreement is no longer effective and that you will not do what it says you must do:
  • to decide that you will not pay back money that you owe:

• Oxford:
  • /rɪˌpjuːdiˈeɪʃn/ [uncountable] (formal)
  • ​the act of refusing to accept something synonym rejection (1. ex. “the world-wide repudiation of slavery in the nineteenth century”)
  • ​the act of saying officially and/or publicly that something is not true (synonyms denial, rejection)
  • the repudiation of a claim
  • ​the act of refusing to be connected with somebody any longer

• Wiktionary:
  • (vt) To reject the truth or validity of; to deny. Synonyms: deny, contradict, gainsay
  • (vt) To refuse to have anything to do with; to disown. Synonyms: disavow, forswear; see also Thesaurus:repudiate

• Wikipedia Disambiguation

Repudiation may refer to:

• Repudiation (marriage), the formal act by which a husband forcibly renounces his wife in certain cultures and religions
• Disownment, the formal act by which a parent forcibly renounces his child
• Repudiation (religion), the act of refusing and no longer accepting a philosophical or religious doctrine

All traditions in western philosophy are shaped by a series of challenges which occupied philosophers from about the seventeenth century. Philosophers in this modern period tried to come to grips with the consequences of an emerging scientific approach for our understanding of the world and our place in it.

This is a development of great concern because it represents an identifiable change, and therefore one which may be analyzed.

All of the modern philosophers, Kant, Descartes, Locke, Hume, Berkely, Leibniz, Reid and others, depend upon tracing connections between their arguments and concepts of foundational logic, science and philosophy. Concept such as a “Justified True Belief”, or “Plato's Forms”.

Therefore we may note that the present day conundrums over, for example, the role of experience in gaining knowledge of the world, the fundamental character of physical reality, the nature of the mind and our knowledge of ourselves, were not only anticipated and discussed by these thinkers, but invented by them. As is often stated, these problems did not generally exist before the 17th century (or various, Plato, et cetera). Thus we ask, how were these problems dealt with before that time? Were they simply ignored? Was there no response to a non-existant question? Or was there something of value that has been lost or forgotten?

In this work we will strike at the heart of the problem: hellenism and it's attempt to occlude the oral transmission of knowledge, and examine the nature of knowgedge and philosophy from an ancient perspective. In doing so we hope to capture a larger view of the force – one unadorned with lies, vanity, and things wherein there is no profit; It is time to grow beyond the shackles of science, philosophy and logic which have chained our souls to a limitation of what could be known as 'truth' for so long.

“My people have committed two sins: They have forsaken me, the spring of living water, and have dug their own cisterns, broken cisterns that cannot hold water.Jeremiah 2:13

One may conceive of the problem thusly; we have on one hand the 'ancient' concept of Plato's forms, and concepts like justified true belief. We have more recent concepts like the categorical imperative, and the new religious concept of presuppositionalism based on such (as CI) and interpretations of it.

Are we to assume that these problems were never addressed prior to plato? Or is it the case, ala modern medicine versus Chinese medicine, that ancient practices have been appropriated in palatable – and therefore limited ways – for a “modern” (i.e. typically Plato's Greek) audience?

This stunning proposal is just stating the conclusion before following the rabbit trail; for today we have been led to accept that the foundation of modern logic are concepts such as JTB theory, the rejection of trivialism, popcornesque back-patting over the Gettier problem and other problems (to maintain “intellectual honesty”) and a compleate lack, a dearth, of spiritual nutrition. Today's philosophy is spiritually dead – there is no life in it. This is the mind job – that you have free will but you have inevitably chosen darkness whether you are aware of it or not – and to break out of this, for most, is impossible even when you are presented with incontrovertible evidence.

Neo: I can't go back, can I?

Morpheus:* No, but if you could, would you really want to?

Neo isn't sure, so decides not to say anything.

Morpheus: I feel I owe you an apology. We have a rule…we never free

a mind once it reaches a certain age. It's dangerous, and

the mind has trouble letting go. I've seen it before, and I'm sorry.–The Matrix

The theory of Forms or theory of Ideas is a theory or world-view attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. It is the overlay of subjective objectivism (i.e. newtonian physics, euclidean geometry, and real-number “infinite” mathematics) over our objectively subjective world. It is in it's revealed form, the proposition of the hypothetical case as valid.

In extreme cases you will encounter this as a sort of “funnel” or “script” which people will attempt to throw at you in order to force you into a logical contradiction; ex. the A not A trap.

According to this theory, ideas, often capitalized and translated as “Ideas” or “Forms”, are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations.

Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggests that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Nonetheless the theory is considered to be a classical solution to the problem of universals.

The pre-Socratic philosophers, starting with Thales, noted that appearances change, and began to ask what the thing that changes “really” is. The answer was substance, which stands under the changes and is the actually existing thing being seen. The status of appearances now came into question. What is the form really and how is that related to substance?

A Form is aspatial (transcendent to space) and atemporal (transcendent to time). In the world of Plato, atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether.

A Form is an objective “blueprint” of perfection. The Forms are perfect and unchanging representations of objects and qualities. For example, the Form of beauty or the Form of a triangle. For the form of a triangle say there is a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form “triangle” that allows us to know the drawing on the chalkboard is a triangle, and the Form “triangle” is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, time only effects the observer and not of the triangle. It follows that the same attributes would exist for the Form of beauty and for all Forms.

Plato explains how we are always many steps away from the idea or Form. The idea of a perfect circle can have defining, speaking, writing, and drawing about particular circles that are always steps away from the actual being. The perfect circle, partly represented by a curved line, and a precise definition, cannot be drawn. Even the ratio of pi is an irrational number, that only partly helps to fully describe the perfect circle. The idea of the perfect circle is discovered, not invented.

In reality, there is something to Plato's forms. In the sense of how our brains really work, we form generalisms of objects in order to recognize them in the future. This is why people of different cultures will give you a different color of horse when you ask them to think of a horse. Taiwanese will often think of a brown horse, and Canadians (of one generation or another) are more likely to think of a black horse (because of movies like Black Stallion, or TV shows like Black Beauty). Some people may choose a white horse because their image of a horse was influenced by the movies “Zorro” and “Lord of the Rings”. The point here is that there is something to the idea of an abstract “perfect horse” by which one may judge, or in the real case recognize all other horses as being true horses or false horses.

Yet the error of plato's forms is in it's hubris. The physical world is indisputably physical – the real world is, in fact real by self-evident definition. This has suprising consequences that cause us to eventually reach a point of conclusion where we may be satisfied with a rejection of Plato's forms. In some sense this will damage the hypothetical proposition as being a valid form of argument, which is expected as with the invalidity of Forms will be seen the invalidity of the hypothetical case, and the lack of desire to use it.

A fundamental issue we take with Plato's Forms is that it indicts the real world as false or fake; i.e. reality, is not good enough for us. It essentially represents living in a fantasy world. This all comes crashing down upon analysis.

The married bachelor problem is based upon a religious philosophy problem usually stated as “If God is all-powerful (omnipotent) then he can do all things, and there is nothing he cannot do – including things which are logically impossible.” In other words, can God create a Married Bachelor? Can God create a rock so heavy that he cannot lift it? Etc.

First, this problem follows the standard secular (and false) definition of God that Plato's Forms depend on – the assumption that our form of God is the correct one – specifically, some form of God which is limited by restrictions of the physical universe or the “real world” – for example, time, space, mass, and so forth.

Thus the answer is given quickly once one is given a correct definition of God – that is, one who is not limited by the restrictions of the physical universe. Examples:

• God can create such a rock, which is too heavy for him to lift it because he has created humans (who may be considered the agents of God) and such humans cannot lift the rock.

• God can create such a rock, but God is not necessarily required to violate the laws by which he created the universe; i.e. he could in theory create such a rock (whatever that may mean), but he does not wish to do so because he chose to create the universe in this way. God is not obligated to perform every action – the principle of 'just because we can do something, doesn't mean we should.'

Examining it from the aspect of a married bachelor,

• God can create a married bachelor – If God is not limited by time, all males who marry are married bachelors.
• God can create a married bachelor – If God is not limited by space and/or law/or religion, it is possible for someone to be married and not married; ex. married in one country but not legally married in another country.
• God can create a married bachelor – If it's is God's spiritual domain to declare a marriage valid, he may declare that a marriage which exists is spiritually repudiated or annulled au contraire to our perceived reality;

fixme

square circle - resolution problem