Showing posts with label Philosophy. Show all posts
Showing posts with label Philosophy. Show all posts

Thursday, April 13, 2017

What is Justice?

 During Egyptian civilization, Maat or Ma'at (thought to have been pronounced *[muʔ.ʕat]), also spelled māt or mayet, was the ancient Egyptian concept of truth, balance, order, law, morality, and justice. Maat was also personified as a goddess regulating the stars, seasons, and the actions of both mortals and the deities. The deities set the order of the universe from chaos at the moment of creation. Her (ideological) counterpart was Isfet, who symbolized chaos, lies, and injustice.[2][3]
 It is an interesting question regarding Justice. Believe it or not I have held this mantra at my lips for a long time. So yes then, I raise the question of what Justice means. Philosophically this blog entry has found the right place as to the questions regarding it.

The notion of justice as a virtue began in reference to a trait of individuals, and to some extent remains so, even if today we often conceive the justice of individuals as having some (grounding) reference to social justice. But from the start, the focus on justice as a virtue faced pressures to diffuse, in two different ways. Justice as a Virtue -LeBar, Mark and Slote, Michael, "Justice as a Virtue", The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.), URL = .
 I would have attended to the first part that the suggestion would be raised as to the "trait of an individual,"  and then lost as to the many thoughts each individual could have explain as being. . But I always sought something deeper in the individual.....as acting in accordance to some moral code. So the "symbol of Justice,"  goes way back in our historical ventures so as to see that the scales can be used to weight anything against something else? More to then,  that Justice can be logically deduced by our esteem lawyers to have us conclude what? Yes, a very interesting question.

In Kant we see the completion of the distinction between justice as a virtue and justice as a norm to which a virtue may or may not correspond. While Kant has a theory (or “doctrine”) of virtue, he distinguishes that theory precisely against a counterpoised theory of justice. The two are complementary elements in the “metaphysics of morals.” Moreover, the doctrine of justice itself has two parts, roughly corresponding to the distinction present since Plato’s work, between the role of justice in the individual and the role of justice in the state. Kant calls these “private right” and “public right,” respectively. But right in either case is not how Kant at least conceives of virtue; instead, it is a “condition” that can obtain between the moral agents comprising a moral or legal community, in virtue of their principles of choice in acting (Kant 1797). Little remains here of the notion of justice as a virtue of individuals as it began with the ancient Greeks. LeBar, Mark and Slote, Michael, "Justice as a Virtue", The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.), URL = .
 So what is judgement then,  as,  having but concluded? If there is but little justice left in the individual,  then how is such a private judgement made? I must add, that the understanding here then,  is that,"the doctrine of justice itself has two parts," and that,  Justice,  once understood as virtue in the individual, does become an understanding of "Justice in the state."


René Descartes

For the Rationalist philosopher René Descartes, virtue consists in the correct reasoning that should guide our actions. Men should seek the sovereign good that Descartes, following Zeno, identifies with virtue, as this produces a solid blessedness or pleasure. For Epicurus the sovereign good was pleasure, and Descartes says that in fact this is not in contradiction with Zeno's teaching, because virtue produces a spiritual pleasure, that is better than bodily pleasure. Regarding Aristotle's opinion that happiness depends on the goods of fortune, Descartes does not deny that these goods contribute to happiness, but remarks that they are in great proportion outside one's own control, whereas one's mind is under one's complete control. https://en.wikipedia.org/wiki/Virtue#Ren.C3.A9_Descartes

 This understanding of virtue,  goes toward the foundation of first principles.

Wednesday, May 20, 2015

Are you a Platonist?

Kant, however, is correct in that we inevitably try and conceive of transcendent, which means unconditioned, objects. This generates "dialectical illusion" in the Antinomies of reason. Kant thought that some Antinomies could be resolved as "postulates of practical reason" (God, freedom, and immortality); but the arguments for the postulates are not very strong (except for freedom), and discarding them helps guard against the temptation of critics to interpret Kant in terms of a kind of Cartesian "transcendental realism" (i.e. real objects are "out there," but it is not clear how or that we know them). If phenomenal objects, as individuals, are real, then the abstract structure (fallibly) conceived by us within them is also real. Empirical realism for phenomenal objects means that an initial Kantian Conceputalism turn into a Realism for universals. See:
Meaning and the Problem of Universals, A Kant-Friesian Approach

It s always interesting for me to see what constitutes a Platonist in the world today. So I had to look at this question.  There always seems to be help when you need it most, so information in the truest sense,  is never lacking, but readily available as if taken from some construct we create of the transcendent.

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Platonism, rendered as a proper noun, is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In narrower usage, platonism, rendered as a common noun (with a lower case 'p', subject to sentence case), refers to the philosophy that affirms the existence of abstract objects, which are asserted to "exist" in a "third realm" distinct both from the sensible external world and from the internal world of consciousness, and is the opposite of nominalism (with a lower case "n").[1] Lower case "platonists" need not accept any of the doctrines of Plato.[1]

In a narrower sense, the term might indicate the doctrine of Platonic realism. The central concept of Platonism, a distinction essential to the Theory of Forms, is the distinction between the reality which is perceptible but unintelligible, and the reality which is imperceptible but intelligible. The forms are typically described in dialogues such as the Phaedo, Symposium and Republic as transcendent, perfect archetypes, of which objects in the everyday world are imperfect copies. In the Republic the highest form is identified as the Form of the Good, the source of all other forms, which could be known by reason. In the Sophist, a later work, the forms being, sameness and difference are listed among the primordial "Great Kinds". In the 3rd century BC, Arcesilaus adopted skepticism, which became a central tenet of the school until 90 BC when Antiochus added Stoic elements, rejected skepticism, and began a period known as Middle Platonism. In the 3rd century AD, Plotinus added mystical elements, establishing Neoplatonism, in which the summit of existence was the One or the Good, the source of all things; in virtue and meditation the soul had the power to elevate itself to attain union with the One. Platonism had a profound effect on Western thought, and many Platonic notions were adopted by the Christian church which understood Plato's forms as God's thoughts, while Neoplatonism became a major influence on Christian mysticism, in the West through St Augustine, Doctor of the Catholic Church whose Christian writings were heavily influenced by Plotinus' Enneads,[2] and in turn were foundations for the whole of Western Christian thought
Platonism

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Now beauty, as we said, shone bright among those visions, and in this world below we apprehend it through the clearest of our senses, clear and resplendent. For sight is the keenest of the physical senses, though wisdom is not seen by it -- how passionate would be our desire for it, if such a clear image of wisdom were granted as would come through sight -- and the same is true of the other beloved objects; but beauty alone has this privilege, to be most clearly seen and most lovely of them all. [Phaedrus, 250D, after R. Hackford, Plato's Phaedrus, Library of the Liberal Arts, 1952, p. 93, and the Loeb Classical Library, Euthryphro Apology Crito Phaedo Phaedrus, Harvard University Press, 1914-1966, p.485, boldface added]

For example, thought cannot be attributed to the One because thought implies distinction between a thinker and an object of thought (again dyad). Even the self-contemplating intelligence (the noesis of the nous) must contain duality. "Once you have uttered 'The Good,' add no further thought: by any addition, and in proportion to that addition, you introduce a deficiency." [III.8.10] Plotinus denies sentience, self-awareness or any other action (ergon) to the One [V.6.6]. Rather, if we insist on describing it further, we must call the One a sheer Dynamis or potentiality without which nothing could exist. [III.8.10] As Plotinus explains in both places and elsewhere [e.g. V.6.3], it is impossible for the One to be Being or a self-aware Creator God. At [V.6.4], Plotinus compared the One to "light", the Divine Nous (first will towards Good) to the "Sun", and lastly the Soul to the "Moon" whose light is merely a "derivative conglomeration of light from the 'Sun'". The first light could exist without any celestial body. Plotinus -

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"...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"

So what is Coxeter saying in relation to Derrida? I think this is more the central issue. On the one hand images speak to what perception is capable of, beyond normal eyesight and without concepts,  reiterated in the nature of the discussion about animals. This is what animals lack, given they do not have this conceptual ability, just that they are able to deduct, was what I was looking for as that discussion emerged and evolved.


If there is a Platonic Ideal Form then there must be an ideal representation of such a form. According to logocentrism, this ideal representation is the logos.

Think of what the Good means again here that it cannot decay into anything else when it is recognized, and that any other wording degrades. If you can draw from experience then in a way one is able to understand this. I had mention an archetype as a medium toward which one could meet the good, and in that find that the archetype itself, contain in the good, allows this insight to be shared. The whole scene is the transmission of the idea, can become the ideal in life. This is an immediate realization of the form of the good. It needs no further clarification......at the deepest levels you recognize it. You know, and you know it as a truth.

Understanding the foundations of Mathematics is important.

So I relay an instance where one is able to access the good.......also in having mentioned that abstraction can lead to the good. This distinction may have been settle in regard to the way in which Coxeter sees and Derrida sees, in regards to the word, or how Coxeter sees geometrically.

This is a crucial point in my view that such work could see the pattern in the form of the good. This is as to say, and has been said, that such freedom in realization is to know that the fifth postulate changed the course of geometrical understandings. This set the future for how such geometries would become significant in pushing not only Einstein forward, but all that had followed him, by what Grossman learned of Riemann. What Riemann learned from Gauss.

See: Prof. Dan Shechtman 2011 Nobel Prize Chemistry Interview with ATS


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See Also:

Monday, May 04, 2015

Distilliation, as Deductive Logic

I mean the deductive logic while being objective according to being logical, to get to that point of knowing, was a exploration into the way deductive logic was being used. I think deductive logic is before Aristotelian from what I understand and to get to that point is critical.

 As Plato tells it, the beautiful orderliness of the universe is not only the manifestation of Intellect; it is also the model for rational souls to understand and to emulate. Such understanding and emulation restores those souls to their original state of excellence, a state that was lost in their embodiment. There is, then, an explicit ethical and religious dimension to the discourse. Plato's Timaeus -Zeyl, Donald, "Plato's Timaeus", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.),

Belief and Intent are very important here as the person comes to a position of judgment. I do not need to talk about the person, their qualities as a human being other then to know that people in general what ever their profession make judgements, and these become the intent, even if they wish to connect in that moment. Why Judgement is so important as a finality to making a decision about things. This in that moment as to recognizing the intent, betrays the pursuit of what is wanted to be known, so there is this to consider.

The link to Ian I remember. Sort of brings up another point I wish to reveal in consideration of that moment. This I connected to synchronicity a long time ago, as I read Jung. As TC mentions intent is very important, and freewill in this life as the person "is" an able function while we are here. This moment is directly connected to logic and deja vu. The moment, is a parallel recognition of something forward in time, as to a recognition of the course you are following in that moment, and why you recognize it. It confirms, that you are following the correct path.

I mentioned the Park , to show that this has been with me for almost 50 years now so as to decipher the way in which I as individual could connect to the data as information from in the Larger Consciousness System( LCS.) That experience was located in the dream environment, so such a construct of images of people what ever their religion could call this philosopher a God, or, what ever their religion may be, was a time of respect in the encounter.

The point was this connection to the LCS was a method that I was able to recognize, and consequent information reveal an understanding of the point I had been referring too, after all these years. I had time then to perfect that method. While living I had no access to teachers, so I had to find the teacher in me to connect for the answers. Why I would profess that people have this ability in them to be the teacher and student at once. Why, I want to drive people to this point. It s a small moment of enlightenment if you will that had intrigue my life ever since.

Now people talk about magic, and I understand that there is this possibility that they will see something that will not follow all the rules we have come to know of in science, so this is why I engage science. Why I followed the development of quantum gravity. Go ahead quote and use any knowledgeable person you would like and you cannot change the experience( I am referring to an objective experience). A person of that ilk will know something about science that not everyone else knows. My perspective with regard to materialism was well formed before TC came along. The mystery of what is not know of consciousness, as we learn to recognize, will eventually become an ability of its use.

 Sir Isaac Newton studied Optics.

Newtonian science became a central issue in the assault waged by the philosophes in the Age of Enlightenment against a natural philosophy based on the authority of ancient Greek or Roman naturalists or on deductive reasoning from first principles (the method advocated by French philosopher René Descartes), rather than on the application of mathematical reasoning to experience or experiment. Voltaire popularised Newtonian science, including the content of the both the Principia and the Opticks, in his Elements de la philosophie de Newton (1738), and after about 1750 the combination of the experimental methods exemplified by the Opticks and the mathematical methods exemplified by the Principia were established as a unified and comprehensive model of Newtonian science. Some of the primary adepts in this new philosophy were such prominent figures as Benjamin Franklin, Antoine-Laurent Lavoisier, and James Black. Reception

I find "incubation" a good term with regard to intent. Distillation, an apt term to decipher the context of one's life experience, and of the understanding emotion. Emotion, as if used in a olfactory sense, provide for the impetus for memory to be placed in existence as data. I associated the collective unconscious as a permeation of a fabric of reality as all that exists as data, as information. Water would not be understood without understand the emotive quality that one might assign to it. How fluid as a substance that flows through the body as a distillation as memory would leave nothing but the hard fact of ones experience..Ouspensky,  was good and finding that point in between the moments.

Sir Isaac Newton studied Chymstry.
After purchasing and studying Newton's alchemical works in 1942, economist John Maynard Keynes, for example, opined that "Newton was not the first of the age of reason, he was the last of the magicians". Isaac Newton's occult studies

So in a sense, I may have given a glimpse of the man known as Sir Isaac Newton, as being in such a question as to understand his biology, to see that the use of distillation, was a form of deductive logic. I had come to recognize it did not lessen the ability of Sir Issac Newton to be shown as a suspected illogical side to him while he wrote his Optics, but a better understanding by him of the matters that course through him, and as matters in the earth.


Biology of Quantum Mechanics
Austrian-born physicist and theoretical biologist Erwin Schrödinger, one of the founders of quantum theory in physics, also became one of the first scientists to suggest a study of quantum biology in his 1944 book What Is Life?. Quantum biology

Before computers came along, we existed, and so did libraries as data banks of information, but still the cataloged data as that kind of information did not speak to what could be gained from using intent to find answers, so it had to be found somewhere.

Wednesday, April 29, 2015

Truth, as it Descends from Heaven




 https://youtu.be/P-TODM8oO9c?t=6m3s

Well most know I am a layman looking at the methods of your arguments and understanding the Traditional versus the Modern, is a understanding of the move from Aristotelian to Boole,  as a historical sense of use of mechanics.

https://youtu.be/xSKIpyHttsk?t=7m59s

I had come to know about Plato's recognition of the pyramids in Egypt, as a pattern used in the Aristotelian Square of Opposition......Aristotle had to have learn this method, as an opposition too, Plato's point of views about God in Heaven, without suggesting that the way in which things flow downward.

The Inductive-Deductive Method of Aristotelian Science
Aristotelian intuition supplies the first principles (archai) of human knowledge: concepts, universal propositions, definitions, the laws of logic, the primary principles of the specialized science, and even moral concepts such as the various virtues.  This is why, according to Aristotle, intuition must be viewed as infallible.  We cannot claim that the first principles of human intelligence are dubious and then turn around and use those principles to make authoritative claims about the possibility (or impossibility) of knowledge.  If we begin to doubt intuition, that is, human intelligence at its most fundamental level of operation, we will have to doubt everything else that is built upon this universal foundation: science, philosophy, knowledge, logic, inference, and so forth.  Aristotle never tries to prove first principles.  He acknowledges that when it comes to the origins of human thought, there is a point when one must simply stop asking questions.  As he points out, any attempt at absolute proof would lead to an infinite regress.  In his own words: “It is impossible that there should be demonstration of absolutely everything; there would be an infinite regress, so that there would still be no demonstration.” (Metaphysics, 1006a6ff, Ross.)  Aristotle does make arguments, for example, that meaningful speech presupposes a logical axiom like the principle of non-contradiction, but that is not, strictly speaking, a proof of the principle. See: Aristotle: Logic

I will  assign image symbology, as logica, grammatical, and rhetorica, to a triangle, the Square represents Earth. It is thoughts which fill my head that the liberal arts is defined when you look at the pattern, as the square of opposition, and that the peak is man's pinnacle and reach for God, and as modeled in the pyramid under this ancient schooling method.

 The pyramid was a scheme for which those things which will become self evident, that after seeing infinite regress, allows views of Gods heaven to descend into the mind of man.

The Quadrivium is made up of the four triangles together with the trivium, seeks man as to perfecting. Each of the four triangles, represents aspects of perfecting when it comes to the understanding of the proponents of the Quadrivium.

The Quadrivium is made up of the four triangles together with the trivium, seeks man as to perfecting. The Quadrivium speak to a cyclical process as well as the developing the student toward logic, grammatical, and rhetoric.

This all belongs to Plato's Academy, but Aristotle took that pattern to the logic application, as the square of opposition, this, when Aristotle formed his own school.



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Parsons, Terence, "The Traditional Square of Opposition", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), URL = .



All S are P, No S is P
All s is P is contrary to the claim NO S is P.
-----------------------
A contrary can be true as well as false.
Contraries can both be false. Contraries can't both be true.

The A and E forms entail each other's negations

Subcontrary

Some S are P, Some S are not P

--------------------------------------------
Sub contraries can't both be false. Sub contraries can both be true.

The negation of the I form entails the (unnegated) E form, and vice versa.


Contradiction-

All S are P, Some S are not P,
Some S are P, No S are P
-----------------------------------
For contradictions -Two propositions are contradictory if they cannot both be true and they cannot both be false.

Contradictory means there is exactly one truth value and if one proposition is true the other MUST be false. If one is false the other MUST be true. The propositions can't both be true and the propositions can't both be false.

The A and O forms entail each other's negations, as do the E and I forms. The negation of the A form entails the (unnegated) O form, and vice versa; likewise for the E and I forms.


Super alteration-

Every S is P, implies Some S are P
No S is P, implies Some S are not P
--------------------------------------------
The two propositions can be true.


Sub alteration-

All S are P, Some S are P
No S are P, Some S are not P
----------------------------------
A proposition is a subaltern of another if it must be true

The A form entails the I form, and the E form entails the O form.

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 Yes....I tried to get some clarity here regard such a start, and as a Universal. I have come to recognize, that such an association as may be given as to the statement of I am, of God, as something "inside the square of opposition" as it arose from the early understandings in relation to Aristotle and Plato. This, I have come to know of them, as expressions of the School run by Plato, and Raphael's setting of Aristotle and Plato together under the arch in that painting called Plato's Academy.

My distinction of intuition may be at odds with the classical description of the Aristotelian view, as to being infallible, while my own views were an assumption under the idea that such regressive moments, were when we had come to a point where infinite regress can no longer be applied, that such a step was necessary as to receiving the idea.

With regard to the advancement of science then, and under boole, the square of opposition changed as to being the undermined logic, as a product of the Aristotelian school. Mathematics then underwent a change in the modern sense as to giving up, the Platonism understanding of the Academy of the times.

While setting up for the idea, here I was seeking to have an idea as to descend into mind, was to me like inserting into an open space between the neurological function, as a gap. I was pushing discreteness to find that place in consciousness. Consciousness as a Derivative of Reductionism?

Can animals reason, yes they can, but do "ideas" settle into the neurological gaps as they do in humans? One would have to say yes as to the expressive state of animals as being part of God's creatures? Then, only to the degrees with which reason can be applied to animals, that such an idea may or may not be, evidential in the evolution of that animal? One may then understand "the idea of a stick being used"  by a monkey in the termite hill, as to arriving from somewhere?

Sunday, March 01, 2015

Justice

Plato prove that justice does not depend upon a chance, convention or upon external force. It is the right condition of the human soul by the very nature of man when seen in the fullness of his environment. It is in this way that Plato condemned the position taken by Glaucon that justice is something which is external. According to Plato, it is internal as it resides in the human soul. "It is now regarded as an inward grace and its understanding is shown to involve a study of the inner man." It is, therefore, natural and no artificial. It is therefore, not born of fear of the weak but of the longing of the human soul to do a duty according to its nature.

Plato's Concept Of Justice: An Analysis Bold was added by me for emphasis.
The element of the syllogism? The Syntax. Any thoughts here then as to semantics, as to what then resides in the human being?

What about merit as to what is to be defined as the gold person, is really about the values a person has? Even though Plato define them as philosophers, I think as if by a natural inclination, we have learnt to judge accordingly, as an understanding of a position with which we assume things to be. To me this may be insightful as to the nature of the individual, that by such introspection learns to understand these character positions.

So I am thinking this is indeed built into an individual, just lost to inspection as to the natures of our characters?


Socratic questioning (or Socratic maieutics)[1] is disciplined questioning that can be used to pursue thought in many directions and for many purposes, including: to explore complex ideas, to get to the truth of things, to open up issues and problems, to uncover assumptions, to analyze concepts, to distinguish what we know from what we don't know, to follow out logical implications of thought or to control the discussion. The key to distinguishing Socratic questioning from questioning per se is that Socratic questioning is systematic, disciplined, deep and usually focuses on fundamental concepts, principles, theories, issues or problems.

Socratic questioning is referred to in teaching, and has gained currency as a concept in education particularly in the past two decades.[citation needed] Teachers, students or indeed anyone interested in probing thinking at a deep level can and should construct Socratic questions and engage in these questions.[2] Socratic questioning and its variants has also been extensively used in psychotherapy.
So in reference to what has survived for so many years what is the conceptual law of justice while the idea could have deeper implications to it? How did you come to know what you know, or don't know. So the method for determination? Nicomachean Ethics?


In the larger context of society, what is good governance, as to imply that Descision making, is a critical part of understanding such governance? In a just society, we come to understand the merits of the individual as we would expect good governance to rule, and as such good governance by the individual, becomes good governance of the country


ABSTRACT
Recently the terms "governance" and "good governance" are being increasingly used in development literature. Bad governance is being increasingly regarded as one of the root causes of all evil within our societies. Major donors and international financial institutions are increasingly basing their aid and loans on the condition that reforms that ensure "good governance" are undertaken.

This article tries to explain, as simply as possible, what "governance" and "good governance" means. What is Good Governance?

 In historical context below the question of philosophical arguments. While talking about immortality with regard to Plato, how does this affect judgement in relation to how we may perceive justice.


Opposites Argument 70a–72e. Whatever has an opposite comes to be from its opposite; the cold from the warm, the weaker from the stronger, the sleeping from the waking. Between every pair of opposites there must always be two processes of transformation, e.g. cooling down and warming up, falling asleep and waking up. Living and dead are evidently opposites, and one of the processes between them, namely dying, is evident to us. We may infer that there is a second process by which living things and stuff come from dead things or stuff. This conclusion is taken (by a palpable equivocation on ‘the dead’) to mean that ‘the souls of the dead must be somewhere whence they can come back again’. An appendix argues that if the process from life to death were not matched by a process from death to life, then the original stock of living things would have been exhausted in the infinite past.

Recollection Argument 73a–77e. Our ability to give the right answers in abstract discussions shows that we possess a kind of knowledge (of the Forms, as it happens) that we must have acquired before birth. It follows that ‘our souls existed apart from the body before they took on human form’. That they continue to exist after we die is said to follow by combining this proof with the Opposites Argument outlined above. (On this and the related argument of Plato’s Meno 81 ff. see Innateness in ancient philosophy.)

Resemblance Argument 78b–84b Forms and particulars differ systematically: Forms are invisible, unchanging, uniform and eternal, where particulars are visible, changeable, composite and perishable. The human soul is invisible too, and it investigates Forms without the aid of bodily senses. By ruling a particular body it resembles the divine which rules and leads. Thus the soul is ‘most like the divine, deathless, intelligible, uniform, and indissoluble’. Its uniformity and partlessness exempt it from the decomposition that destroys compounded bodies; for all these reasons we may conclude that it is immortal. (Significantly, it is never claimed that the soul actually is a Form, and the theory of soul-construction in the Timaeus 35 explicitly makes souls a third class of entities distinct from Forms and bodies.)
BRENNAN, TAD (2002). Immortality in ancient philosophy. In E. Craig (Ed.), Routledge Encyclopedia of Philosophy. London: Routledge. Retrieved February 22, 2015, from
Bold added for emphasis by me

As per Recollection argument above.....innate does not mean we become stifled and locked into position, but go through experience and instill further innate ideas in to our understanding. The objectified, becomes as part of this life experience. Objectified knowledge becomes part of the cycle regarding what comes with us through another round.


the theory of soul-construction in the Timaeus 35 explicitly makes souls a third class of entities distinct from Forms and bodies. see above link
If not the forms or the body what would they be referring too?


As Plato tells it, the beautiful orderliness of the universe is not only the manifestation of Intellect; it is also the model for rational souls to understand and to emulate. Such understanding and emulation restores those souls to their original state of excellence, a state that was lost in their embodiment. There is, then, an explicit ethical and religious dimension to the discourse. Plato's Timaeus -Zeyl, Donald, "Plato's Timaeus", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.), 
So justice in its examination may suggest that this is a faculty of the the rational mind according to historical context. Any attempts to illicit judgmental affairs as to the state would require a rational mind? What does this mean in the modernization of our cultures so as to express the most desired cultural definition of this return to the rationalistic fervor and recognition of this idea of the receptacle?

Doe this literally mean to create a third person, a judge?

The second main section begins with the introduction of the receptacle, a “third kind” alongside the familiar paradeigmatic forms and the generated images of the forms (49a1–4, 52a8, d2–4). The receptacle appears to have the dual role of serving both as material substratum, and as spatial field. Timaeus' account of the receptacle is elusive and presents several interpretive difficulties, some of which will be discussed below. In the “pre-cosmic” state (the state “prior to” the intervention of the Craftsman) the receptacle is subject to erratic and disorderly motions, and its contents are mere “traces” (ichnê, 53b2) of the subsequently articulated four “kinds” (the so-called elements): fire, air, water and earth. The Craftsman begins by constructing four of the regular solids as the primary corpuscles of each of these four kinds. These solids have faces that are made up (ultimately) of two types of right-angled triangles—the half-equilateral and the isosceles—and it is these triangles that are the ultimate “simples” of the physics of the dialogue. Because their triangles are similar (half-equilateral), only corpuscles of fire, air and water may be transformed into one another. Each of the four kinds has properties that are determined by the constitution of their respective corpuscles, and these properties in turn determine how the particles act upon and react to one another. (It is here that Necessity plays its important role in Timaeus' account.) Plato's Timaeus -Zeyl, Donald, "Plato's Timaeus", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.),.
A judge would have to over come disorderliness and exemplify the quest for rationalism. If these attributes are innate, what would the third person represent as if we were to sit in judgement of the life we had lived. How would we weight our souls truth of the rational mind to something that is of greater truth and import, as if to find it weighed against something else? The golden heart against some philosophical weighed universal truth as a feather. How deep and significant this challenge in our own lives?

I am really trying to decipher "the meaning" of Justice.

As a mechanism, this may imply, an objective method toward a subjective ideal as we hope to evolve. A rationalistic mind would be then gifted with morality? You'd already be gifted as to make the right choice? If I am to take your meaning further then?

Yes, I am thinking beyond, toward a definition of Justice as to the individual, and, in context of morality, then, how is it the same as Justice. Would you have used small groups, large groups, small towns and large cities. If the essence of this justice is innate, so to as morality, then, it would not matter where the individual is?

If, I was to propose a question without let's say the data base with which to respond to this question, then, what answer is given, The answer is based on what? Discard everything you've learned. What is Justice?

So the evolving question regarding morality is an experience of this life yes? Or, is that something which is innate and linguistically overridden. Culturally and linguistically, you learned the language of your small town, big city which would have to be discarded or set as, semantics to the original meaning of Justice.

So as Universal Declaration in Preamble to the Charter, leads to article one.

All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.Universal Declaration of Human Rights -
Bold added for emphasis by me.

To be able "to reason" would mean having the capacity for understanding Justice? So was it right to say Justice has some first order logic to it so as to declare it as a universal law? Are we all gifted with rationalism?

 Brain scans link concern for justice with reason, not emotion - See more at: http://news.uchicago.edu/article/201...-emotion#.dpuf

I think it is more a recognition of something that already exists in you, our side of the small town, big town, that an insight as to the nature of this attribute, is how we as a soul may weight these things. This as to how a soul accomplishes from one life to the next. It has to be an inherent feature, for the idea of the rules(arguments) as listed earlier, to become an ideal.

So if you accept a NDE as part and parcel of the innate feature of our human condition then what attribute of the human mind would seek to accomplish that which we had taken to burden in this phase of our life being lived now? Are you living the truth with which you weigh against something to be defined as a "universal truth." How would you know this? How would you know what this truth is for you, is a process which all human would seek to verify, set as as a accomplishment as to having successful been living with that truth in order to say they indeed had lived life to this universal truth.

We would see an extroverted and objectified example of societies and not an internal perception, as to the nature of this judgement which may be held in abeyance until more information came through.

If you take in the picture of Raphael's school of Athens where do you see Plato pointing too. So to me, as a central figure, is a point exemplified as to what the soul is versus the body, as Aristotle with this ancient view expresses, as the body expressing mind. Seeing physically, all that is around you. Such an idea of balance in the world would have been a recognition of that which would become self evident through this interplay between Plato and Aristotle. This to exemplify this middle of the road. So it could not be Plato alone that Raphael wish to express, but something that required both, in order for the interaction of the world to allow something to become self evident. And, a leap of mind

I brought up the latest research of the manufacture of the thought body as something separate and manageable from the way in which we could create this third person. To free one self of the reins of the physicals as to explore with consciousness as one travels to what ever destination.....looses sight of this thought body.

But more importantly, there are these archetypes which we create, where as some form of this can be and is realized when we recognize higher consciousness as a functioning of this wisdom imparted within the dream world, to suggest, that this is wisdom of your own soul that sits in Judgement.

So such a model of this Justice would have to exist in my view, so as to impart something greater then a judgement in the natural world of the objectified, but truly opens the door to what we as humans also come into the world as retaining this pattern towards living of this life now. Your internal third person and guidance. Call it the higher self maybe?

This meta-cognitive view then would have relinquished the mind to a form, that mind leaps toward something of a more spiritual kind, not just deductive faculties in the state of Justice as explained in the natural world and objectified. Not just ethics and moral virtues.......but a history to draw from, and a spiritual one at that. But how fine and rarefied such a mind to leap where, and then we are back in the world.

Plato's Problem

Anamnesis

Meno

The claim is that one does not need to know what knowledge is before gaining knowledge, but rather one has a wealth of knowledge before ever gaining any experience

Perception and judging while decisive with regard to an attribute gifted of reason, shows what the person by character exemplifies according to this attributes judging or withholding judging until more information is attainable.

Brain scans link concern for justice with reason, not emotion - See more at: http://news.uchicago.edu/article/201...-emotion#.dpuf


Is Justice blind to the individual acting from innate abilities and carry overs who decides quickly? I can show from previous link this is not an emotive thing happening when given reasonable thought about Justice as brain is used with respect to the MRI and brain activity......so we use the body as a residual affect of what our consciousness does?

Yes I am aware now if taken from Plato alone......a revision in the Church then, and we may see Aristotle as to what exist around us as a focal point in the same person. This as a question about what is innate then and we listen to all the reasons why through inductive and deductive efforts......but indeed, we are talking about something else here. About the type of knowledge that a soul has gained from the incarnations versus what is gained from data in this life.


Socratic questioning (or Socratic maieutics)[1] is disciplined questioning that can be used to pursue thought in many directions and for many purposes, including: to explore complex ideas, to get to the truth of things, to open up issues and problems, to uncover assumptions, to analyze concepts, to distinguish what we know from what we don't know, to follow out logical implications of thought or to control the discussion. The key to distinguishing Socratic questioning from questioning per se is that Socratic questioning is systematic, disciplined, deep and usually focuses on fundamental concepts, principles, theories, issues or problems.

Socratic questioning is referred to in teaching, and has gained currency as a concept in education particularly in the past two decades.[citation needed] Teachers, students or indeed anyone interested in probing thinking at a deep level can and should construct Socratic questions and engage in these questions.[2] Socratic questioning and its variants has also been extensively used in psychotherapy.
So in reference to what has survived for so many years what is the conceptual law of justice while the idea could have deeper implications to it? How did you come to know what you know, or don't know. So the method for determination? Nicomachean Ethics?

Aristotle as a central figure in the picture of Raphael, was a response to Plato. It was a revision that philosophical may have been thought of by Raphael to exemplify the attributes of the Church at that point in time. This so as to question the significance of what evolved in the Church as well, as to what becomes self evident eventually requires a leap of mind.

Socrates
Socratic method
Socratic questioning


Meno (/ˈmiːnoʊ/; Greek: Μένων) is a Socratic dialogue written by Plato.
Bold and underline added by me for emphasis


The theme of the work is the Socratic question which had previously been explored in the works of Plato, Aristotle's friend and teacher, of how men should best live. In his Metaphysics, Aristotle described how Socrates, the friend and teacher of Plato, had turned philosophy to human questions, whereas Pre-Socratic philosophy had only been theoretical. Ethics, as now separated out for discussion by Aristotle, is practical rather than theoretical, in the original Aristotelian senses of these terms.[1] In other words, it is not only a contemplation about good living, because it also aims to create good living. It is therefore connected to Aristotle's other practical work, the Politics, which similarly aims at people becoming good. Ethics is about how individuals should best live, while the study of politics is from the perspective of a law-giver, looking at the good of a whole community.Nicomachean Ethics -http://en.wikipedia.org/wiki/Nicomachean_Ethics

For what purpose? To be able to arrive at some distinction about what we know and how we know it or some relevance to the way in which some knowledge is innate, or that learned in this life by living it now?


Book V: Justice and Fairness: a moral virtue needing special discussionParticular justice is however the subject of this book, and it has already been divided into the lawful and the fair, which are two different aspects of universal justice or complete virtue. Concerning areas where being law-abiding might not be the same as being fair, Aristotle says that this should be discussed under the heading of Politics.[73] He then divides particular justice further into two parts: distribution of divisible goods and rectification in private transactions. The first part relates to members of a community in which it is possible for one person to have more or less of a good than another person. The second part of particular justice deals with rectification in transactions and this part is itself divided into two parts: voluntary and involuntary, and the involuntary are divided further into furtive and violent divisions.[74] The following chart showing divisions with Aristotle's discussion of Justice in Book V, based on Burger (2008) Appendix 3.
Justice in the City, or Justice in the soul(Appendix 3)?
In several of Plato's dialogues, Socrates promulgates the idea that knowledge is a matter of recollection, and not of learning, observation, or study.[46] He maintains this view somewhat at his own expense, because in many dialogues, Socrates complains of his forgetfulness. Socrates is often found arguing that knowledge is not empirical, and that it comes from divine insight. In many middle period dialogues, such as the Phaedo, Republic and Phaedrus Plato advocates a belief in the immortality of the soul, and several dialogues end with long speeches imagining the afterlife. More than one dialogue contrasts knowledge and opinion, perception and reality, nature and custom, and body and soul.Recurrent themes -
Is divine insight a leap of mind then, so as to arrive a some conclusion? We see such attributes of the historical overlay by today's world of events. We use systemic versions of historical significance to arrive at a understanding of where we are today, and in this sense we can talk about what survived and didn't survive. It is all in context of the virtual reality of this discussion? How relevant is it to today's world? Maybe, just write a virtual dialogue to help understand the spiritual essence of the principle of the divine as one takes that leap of mind?

I think we are arriving some consensus here even though we point to this dialogue, point to the writer of the dialogue, and raise the issues of the deeper questions about the relevance of Justice in today's world. About what people are talking about in regards to Reincarnation, or, about the raising of the dead, as a metaphor for what we can arise too?? Are these "good virtues" to have been given are the dialogues that verge on the ephemeral?

How strange that not only that such a perception might have saw a foundational method toward an attribute of the forms could have survived as a subject regarding quasi-crystals as to this underlying feature theorized so many years ago. But so too, much more then the survivability of a method by which we question and arrive at, a place in mind?

Just quickly, if no one told you how "to reason," how would you know to be able to do this? If you did not have this life experience, as of the now, then can we reason? Self evident or leap of mind is a position, which allows access to information that is intuited and comes from the soul?

Sure we can create false things so as to believe, describe a experience that doesn't match the events of say as a journalist, but we are talking about access to something else here. So you do have experience, but it comes from the soul?

If you are a good writer of the dialogues what survives by your example of the archetype as you become aware of it. What survived of Plato's writings? What survived of Socrates in Plato's writings.

Rationalists generally develop their view in two ways. First, they argue that there are cases where the content of our concepts or knowledge outstrips the information that sense experience can provide. Second, they construct accounts of how reason in some form or other provides that additional information about the world. Empiricists present complementary lines of thought. First, they develop accounts of how experience provides the information that rationalists cite, insofar as we have it in the first place. (Empiricists will at times opt for skepticism as an alternative to rationalism: if experience cannot provide the concepts or knowledge the rationalists cite, then we don't have them.) Second, empiricists attack the rationalists' accounts of how reason is a source of concepts or knowledge. SEE: Markie, Peter, "Rationalism vs. Empiricism http://plato.stanford.edu/entries/ra...sm-empiricism/ , The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.),


Do you see a dichotomy within the way you are seeing? Point to the collective unconscious....where is that?


Michael Newton talks about his journey to his Past Life Therapy practice. Filmed in 2007 and finally uploaded for you all to see this amazing guy.

http://youtu.be/Fk3s40UnoDE
How would reason then manifest within context of any archetype given, that we would sit to reason according to the archetype our subconscious presents? Would there not be a difference between what you observe "as the archetype" that is present(the awareness of your lucid dreaming where recognition as EGO manifests[remember you are the story teller.]), versus, living the experience of the person?


If the late character of our sources may incite us to doubt the authenticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible. And geometry, as can be seen through the experiment with the slave boy in the Meno (Meno, 80d1-86d2), can also make us discover the existence of truths (that of a theorem of geometry such as, in the case of the Meno, the one about doubling a square) that may be said to be "transcendant" in that they don't depend upon what we may think about them, but have to be accepted by any reasonable being, which should lead us into wondering whether such transcendant truths might not exist as well in other areas, such as ethics and matters relating to men's ultimate happiness, whether we may be able to "demonstrate" them or not. See: Frequently Asked Questions about Plato by Bernard SUZANNE


Bold added for emphasis by me.

Secondly, I would ask that you pay attention to what you presented as frequency and energy, so as to see its use in the way in which Newton speaks. Is deeper in alpha or theta, really "out there in the world, or, inside the person"? Is the soul inside or outside the person?

Alva Noë - Why is Consciousness so baffling?

What is Consciousness? Why are we still baffled by this question? Our host Robert Lawrence Kuhn asks Alva Noë, in an interview from our series "Closer To Truth," currently airing on PBS stations nationwide. Check your local listings for air times.
For more videos and information, visit http://www.closertotruth.com

http://youtu.be/1aPeWc7Um1A
We've Been Looking for Consciousness in Wrong Place-Alva Noë
Getting Out of Our Heads - Alva Noë

The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann

In a projective sense(into the eye to the back of the brain) Alva Noe may referring to experience as if to include, the back of the apple as more then a direct examination......would include another form of experience, a wider view as if to see more then from this projective sense of being.

The way in which I see this expository view unfold is to recognize the geometry as higher versions being exemplified to include a explanation of Alva Noe's view as to the nature of consciousness as more then a restricted view. Alva I feel is speaking to that which rests in the sensorial world of the projected, as an inner expression of the outside world. But now more too, a "meta cognitive view." I see the question pushing the "boundaries of this limited projected view, " as less then what Alva Noe is speaking too.

It brings to mind what is suggested of Meno, as to the larger capacity of what Plato wrote of in the story of Meno with regard to the abstract. The quote above, as to suggest, Riemann is exemplary as well.


If the late character of our sources may incite us to doubt the authenticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible..... See: Frequently Asked Questions about Plato by Bernard SUZANNE
Bold added by me for emphasis.

These 4 stages also correspond to Plato's 4 levels of understanding, as described in his Analog of the Divided Line.

Tabular summary of the Divided Line

Segment Type of knowledge or opinion Affection of the psyche Type of object Method of the psyche or eye Relative truth and reality
DE Noesis (νόησις) Knowledge: understanding of only the Intelligible (νοητόν) Only Ideas, which are all given existence and truth by the Good itself (τὸ αὐτὸ ἀγαθόν) The Psyche examines all hypotheses by the Dialectic making no use of likenesses, always moving towards a First Principle Highest
CD Dianoia (διάνοια) Knowledge: thought that recognizes but is not only of the Intelligible Some Ideas, specifically those of Geometry and Number The Psyche assumes hypotheses while making use of likenesses, always moving towards final conclusions High
BC Pistis (πίστις) Opinion: belief concerning visible things visible things (ὁρατά) The eye makes probable predictions upon observing visible things low
AB Eikasia (εἰκασία) Opinion: conjectures concerning likenesses likenesses of visible things (εἰκόνες) The eye makes guesses upon observing likenesses of visible things lowest
The Stage 1s argue and understand in terms of Eikasia.

The Stage 2s argue and understand in terms of Pistis.

The Stage 3s argue and understand in terms of Dianoia.

The Stage 4s argue and understand in terms of Noesis.

Socrates asks Glaucon to not only envision this unequally bisected line but to imagine further bisecting each of the two segments. Socrates explains that the four resulting segments represent four separate 'affections' (παθήματα) of the psyche. The lower two sections are said to represent the visible while the higher two are said to represent the intelligible. These affections are described in succession as corresponding to increasing levels of reality and truth from conjecture (εἰκασία) to belief (πίστις) to thought (διάνοια) and finally to understanding (νόησις). Furthermore this Analogy not only elaborates a theory of the psyche but also presents metaphysical and epistemological views. Analogy of the Divided Line -


Maybe in the context of what Justice is to mean in the larger context of the idea as a first principle. Applying any search to the "inherent truth" is as much a trail as that toward what the language spoken by you, is to ascertain as being your truth. So we all recognize that, and recognize your bias......and for some of us it is an understanding of the process itself as you speak toward your truth.


Plato describes "The Form of the Good", or more literally "the idea of the good" (ἡ τοῦ ἀγαθοῦ ἰδέα), in his dialogue the Republic (508e2–3), speaking through the character of Socrates. Plato introduces several forms in his works, but identifies the Form of the Good as the superlative. This form is the one that allows a philosopher-in-training to advance to a philosopher-king. It can not be clearly seen or explained, but once it is recognized, it is the form that allows one to realize all the other forms. Form of the Good
Bold added for emphasis

Plato identifies how the Form of the Good allows for the cognizance to understand such difficult concepts as justice. He identifies knowledge and truth as important, but through Socrates (508d–e) says, “good is yet more prized”. He then proceeds to explain “although the good is not being” it is “superior to it in rank and power”, it is what “provides for knowledge and truth” (508e).[1] Usages in The Republic -

Monday, February 16, 2015

Aristotle-The Square of Opposition (Whiteboard Animation)



Aristotle laid out the principles of his logic in his writing Περὶ Ἑρμηνείας, in Latin De Interpretatione, in English On Exposition. It is a graphical representation of the relations between propositions that guarantee their truth. If philosophers and scientists would internalise the logical rules in Aristotle's square of opposition, a lot of misunderstandings would be prevented. SEE: The Square of Opposition as a Whiteboard animation

 Basics of the Square of Opposition of Aristotle

0:06 A proposition (e.g. "All Greeks are men.") consists of a subject ("Greeks") and a predicate ("men").
The four types of propositions are:
Universal positive ("All Greeks are men.", abbreviated "aGM"),
Universal negative ("No Greeks are men.", abbreviated "nGM"),
Particular positive ("Some Greeks are men.", abbreviated "sGM") and
Particular negative ("Some Greeks are not men", abbreviated "sGnM").

1:38 Contradiction (Aristotle)

Universal positive and particular negative, as well as universal negative and particular positive are contradictory. They can't both be true and can't both be false at the same time.

1:59 Contraries (Aristotle)

Universal positive and Universal negative propositions are contraries. They can't both be true, but can both be false at the same time.

2:15 Subcontraries (Aristotle)

Particular positive and Particular negative propositions are subcontraries. They can't both be false, but can both be true at the same time.

2:35 Implication (Aristotle)

Implied propositions (particular positive and particular negative) are true, when their implying propositions (universal positive and universal negative) are true.

2:55 Counter Indication (Aristotle)

Universal propositions (positive and negative respectively) are false, when their particular propositions (positive and negative respectively) are false.

3:19 Converse propositions (Aristotle)

In converse propositions, subjects (e.g. Greeks) and predicates (e.g. men) can be switched without altering the proposition's truth.

Converse Propositions are:
"No Greeks are men" and
"Some Greeks are men".
so it is also true that
"No men are Greeks" as well as
"Some men are Greeks".

3:44 Complements (Aristotle)

A complement of a subject or predicate is everything that it is not.
E.g. "all that is not a man" and "all that is not a Greek".

3:58 Contrapositive propositions (Aristotle)

In contrapositive propositions ("all Greeks are men" and "some Greeks are not men"), if the subjects' and predicates' complements are switched, the proposition retains its truth.

***

See Also:

Friday, February 06, 2015

Plato's Theory of Forms



The Golden Mean (philosophy)

Ancient Greek Philosophers


In philosophy, especially that of Aristotle, the golden mean is the desirable middle between two extremes, one of excess and the other of deficiency. -The Golden Mean (philosophy)


In the Eudemian Ethics, Aristotle writes on the virtues. Aristotle’s theory on virtue ethics is one that does not see a person’s actions as a reflection of their ethics but rather looks into the character of a person as the reason behind their ethics. His constant phrase is, "… is the Middle state between …". His psychology of the soul and its virtues is based on the golden mean between the extremes. In the Politics, Aristotle criticizes the Spartan Polity by critiquing the disproportionate elements of the constitution; e.g., they trained the men and not the women, and they trained for war but not peace. This disharmony produced difficulties which he elaborates on in his work. See also the discussion in the Nicomachean Ethics of the golden mean, and Aristotelian ethics in general.-http://en.wikipedia.org/wiki/Golden_mean_(philosophy)#Aristotle

Book VI: Intellectual virtue 

 Book VI of the Nicomachean Ethics is identical to Book V of the Eudemian Ethics. Earlier in both works, both the Nicomachean Ethics Book IV, and the equivalent book in the Eudemian Ethics (Book III), though different, ended by stating that the next step was to discuss justice. Indeed in Book I Aristotle set out his justification for beginning with particulars and building up to the highest things. Character virtues (apart from justice perhaps) were already discussed in an approximate way, as like achieving at middle point between two extreme options, but this now raises the question of how we know and recognize the things we aim at or avoid. Recognizing the mean recognizing the correct boundary-marker (horos) which defines the frontier of the mean. And so practical ethics, having a good character, requires knowledge.-

Acquiring Knowledge

A priori and a posteriori knowledge

The nature of this distinction has been disputed by various philosophers; however, the terms may be roughly defined as follows:

A priori knowledge is knowledge that is known independently of experience (that is, it is non-empirical, or arrived at beforehand, usually by reason). It will henceforth be acquired through anything that is independent from experience.
A posteriori knowledge is knowledge that is known by experience (that is, it is empirical, or arrived at afterward).

A priori knowledge is a way of gaining knowledge without the need of experience. In Bruce Russell's article "A Priori Justification and Knowledge"[19] he says that it is "knowledge based on a priori justification," (1) which relies on intuition and the nature of these intuitions. A priori knowledge is often contrasted with posteriori knowledge, which is knowledge gained by experience. A way to look at the difference between the two is through an example. Bruce Russell give two proposition in which the reader decides which one he believes more. Option A: All crows are birds. Option B: All crows are black. If you believe option A, then you are a priori justified in believing it because you don't have to see a crow to know it's a bird. If you believe in option B, then you are posteriori justified to believe it because you have seen many crows therefore knowing they are black. He goes on to say that it doesn't matter if the statement is true or not, only that if you believe in one or the other that matters.

The idea of a priori knowledge is that it is based on intuition or rational insights. Laurence BonJour says in his article "The Structure of Empirical Knowledge",[20] that a "rational insight is an immediate, non-inferential grasp, apprehension or 'seeing' that some proposition is necessarily true." (3) Going back to the crow example, by Laurence BonJour's definition the reason you would believe in option A is because you have an immediate knowledge that a crow is a bird, without ever experiencing one.
- Acquiring Knowledge

***
In epistemology, rationalism is the view that "regards reason as the chief source and test of knowledge"[1] or "any view appealing to reason as a source of knowledge or justification".[2] More formally, rationalism is defined as a methodology or a theory "in which the criterion of the truth is not sensory but intellectual and deductive".[3] Rationalists believe reality has an intrinsically logical structure. Because of this, rationalists argue that certain truths exist and that the intellect can directly grasp these truths. That is to say, rationalists assert that certain rational principles exist in logic, mathematics, ethics, and metaphysics that are so fundamentally true that denying them causes one to fall into contradiction. Rationalists have such a high confidence in reason that proof and physical evidence are unnecessary to ascertain truth – in other words, "there are significant ways in which our concepts and knowledge are gained independently of sense experience".[4] Because of this belief, empiricism is one of rationalism's greatest rivals. -Rationalism

***
 
Empiricism is a theory which states that knowledge comes only or primarily from sensory experience.[1] One of several views of epistemology, the study of human knowledge, along with rationalism and skepticism, empiricism emphasizes the role of experience and evidence, especially sensory experience, in the formation of ideas, over the notion of innate ideas or traditions;[2] empiricists may argue however that traditions (or customs) arise due to relations of previous sense experiences.[3]
Empiricism in the philosophy of science emphasizes evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on a priori reasoning, intuition, or revelation.
Empiricism, often used by natural scientists, says that "knowledge is based on experience" and that "knowledge is tentative and probabilistic, subject to continued revision and falsification."[4] One of the epistemological tenets is that sensory experience creates knowledge. The scientific method, including experiments and validated measurement tools, guides empirical research.

Symbolic Logic

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms  Mathematical proof

Direct proof
Proof by mathematical induction-
Proof by [S]contraposition[/S]/transposition (P → Q) \Leftrightarrow (¬ Q → ¬ P)
Proof by construction
Proof by exhaustion
Probabilistic proof
Combinatorial proof
Nonconstructive proof
Statistical proofs in pure mathematics

----------------------------------------------------


Modus Ponens-   
                                                      p → q
                                                      p
                                                      _____
                                                      q   

Modus Tollens-   
                                                       p → q
                                                       ~q
                                                       _____
                                                       ~p   

Hypothetical Syllogism-   
                                                       p → q
                                                       q → r
                                                       _____
                                                       p → r   

Disjunctive Syllogism-   
                                                       p ∨ q
                                                       ~ p
                                                       _____
                                                       q   

Constructive Dilemma-   
                                                      (p → q) • (r → s)
                                                      p ∨ r
                                                      ______
                                                      Q ∨ S
   
Destructive Dilemma-   
                                                      (p → q) • (r → s)
                                                      ~q ∨ ~S
                                                      ______
                                                      ~P v ~R
   
Conjunction    -
                                                       p
                                                       q
                                                       _____
                                                       p • q   

Simplification-   
                                                       p • q
                                                       ____
                                                       p   

Addition   
p
_____
p ∨ q


----------------------------------------------------------------------

¬     negation (NOT)                     The tilde ( ˜ ) is also often used.
∧     conjunction (AND)             The ampersand ( & ) or dot ( · ) are also often used.
∨     disjunction (OR)                     This is the inclusive disjunction, equivalent to and/or in                                              English.
⊕     exclusive disjunction (XOR)     ⊕ means that only one of the connected propositions 
                                                is true, equivalent to either…or. Sometimes ⊻ is used.
|     alternative denial (NAND)     Means “not both”. Sometimes written as ↑
↓     joint denial (NOR)             Means “neither/nor”.
→     conditional (if/then)             Many logicians use the symbol ⊃ instead. This is also 
                                                known as material implication.
↔     biconditional (iff)                     Means “if and only if” ≡ is sometimes used, but this site
                                                reserves that symbol for equivalence.

Quantifiers

∀     universal quantifier             Means “for all”, so ∀xPx means that Px is true for every x.
∃     existential quantifier             Means “there exists”, so ∃xPx means that Px is true for at
                                                least one x.
Relations

⊨     implication                             α ⊨ β means that β follows from α
≡     equivalence                     Also ⇔. Equivalence is two-way implication, so α ≡ β
                                                means α implies β and β implies α.
⊢     provability                             Shows provable inference. α is provable β means that
                                                from α we can prove that β.
∴     therefore                             Used to signify the conclusion of an argument. Usually
                                                taken to mean implication, but often used to present
                                                arguments in which the premises do not deductively imply
                                                the conclusion.
⊩     forces                            A relationship between possible worlds and sentences in
                                               modal logic.
Truth-Values

⊤     tautology                            May be used to replace any tautologous (always true)
                                               formula.
⊥     contradiction                    May be used to replace any contradictory (always false)
                                              formula. Sometimes “F” is used.

Parentheses

( )     parentheses                   Used to group expressions to show precedence of
                                             operations.
Square brackets

[ ]                                          are sometimes used to clarify groupings.
Set Theory

∈     membership                   Denotes membership in a set. If a ∈ Γ, then a is a member
                                             (or an element) of set Γ.
∪     union                          Used to join sets. If S and T are sets of formula, S ∪ T is a
                                             set containing all members of both.
∩     intersection                  The overlap between sets. If S and T are sets of formula, S
                                             ∩ T is a set containing those elemenets that are members
                                             of both.
⊆     subset                          A subset is a set containing some or all elements of another
                                             set.
⊂     proper subset                  A proper subset contains some, but not all, elements of
                                             another set.
=     set equality                  Two sets are equal if they contain exactly the same
                                             elements.
∁     absolute complement          ∁(S) is the set of all things that are not in the set S.
                                             Sometimes written as C(S), S or SC.
-     relative complement          T - S is the set of all elements in T that are not also in S.
                                             Sometimes written as T \ S.
∅     empty set                          The set containing no elements.

Modalities

□     necessarily                     Used only in modal logic systems. Sometimes expressed as []
                                            where the symbol is unavailable.
◊     possibly                         Used only in modal logic systems. Sometimes expressed as
                                           <> where the symbol is unavailable.

Propositions, Variables and Non-Logical Symbols

The use of variables in logic varies depending on the system and the author of the logic being presented. However, some common uses have emerged. For the sake of clarity, this site will use the system defined below.

Symbol             Meaning                     Notes

A, B, C … Z     propositions     Uppercase Roman letters signify individual propositions. For example, P may symbolize the proposition “Pat is ridiculous”. P and Q are traditionally used in most examples.

α, β, γ … ω     formulae     Lowercase Greek letters signify formulae, which may be themselves a proposition (P), a formula (P ∧ Q) or several connected formulae (φ ∧ ρ).

x, y, z             variables     Lowercase Roman letters towards the end of the alphabet are used to signify variables. In logical systems, these are usually coupled with a quantifier, ∀ or ∃, in order to signify some or all of some unspecified subject or object. By convention, these begin with x, but any other letter may be used if needed, so long as they are defined as a variable by a quantifier.

a, b, c, … z     constants           Lowercase Roman letters, when not assigned by a quantifier, signifiy a constant, usually a proper noun. For instance, the letter “j” may be used to signify “Jerry”. Constants are given a meaning before they are used in logical expressions.

Ax, Bx … Zx     predicate symbols     Uppercase Roman letters appear again to indicate predicate relationships between variables and/or constants, coupled with one or more variable places which may be filled by variables or constants. For instance, we may definite the relation “x is green” as Gx, and “x likes y” as Lxy. To differentiate them from propositions, they are often presented in italics, so while P may be a proposition, Px is a predicate relation for x. Predicate symbols are non-logical — they describe relations but have neither operational function nor truth value in themselves.

Γ, Δ, … Ω     sets of formulae     Uppercase Greek letters are used, by convention, to refer to sets of formulae. Γ is usually used to represent the first site, since it is the first that does not look like Roman letters. (For instance, the uppercase Alpha (Α) looks identical to the Roman letter “A”)

Γ, Δ, … Ω     possible worlds     In modal logic, uppercase greek letters are also used to represent possible worlds. Alternatively, an uppercase W with a subscript numeral is sometimes used, representing worlds as W0, W1, and so on.

{ }     sets     Curly brackets are generally used when detailing the contents of a set, such as a set of formulae, or a set of possible worlds in modal logic. For instance, Γ = { α, β, γ, δ }