logic

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chad
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87872
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logic
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2011-05-27 16:44:41
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fundamentals of logic
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  1. What are the purposes of definitions and divisions in human thought?
    :Definition is a phrase setting forth the nature of a thing or the meaning of a term in such a way as to distinguish respectively this thing from everything else or this meaning from every other meaning.



    • Not all knowing is such, that you have to have a definition before you know what you
    • know. You can know what is vague, but that is not good, so you look for definitions.
  2. What are the type of definitions ?
    

    • Definitions
    • are nominal or real.

    • Nominal:
    • You don’t seek reality but the meaning of a word.

    Nominals

    • are
    • etymological or non-etymological.

    • - Etymological nominal definition looks for what is the meaning of
    • the word according to its original meaning. You look for the meaning of a word
    • as it is today in relation to its historical meaning. Etymological definitions
    • often are quite useful, but you are only dealing with the meaning of a term.

    - Non-etymological definitions are either syntactic or semantic.

    • -A syntactic nominal definition occurs when you know that one
    • lingustic symbol can be substituted for another linguistic symbol (i.e.
    • “Septuagint = LXX). You don’t have to know anything about the real thing, just
    • to know that you can substitute.

    • -Semantic nominal definition can be analytic and synthetic
    • (stipulative).

    • - Analytic, when you know that a word in one language is
    • substitutable for a word in another language, i. e. nominal definition analytic
    • of the word equus when I know that the word horse can be used any time equus
    • appears. You have to know something about the reality that is symbolized in the
    • original world. Bi-lingual dictionaries
    • are analytic nominal definitions.

    • -Synthetic occurs when you come upon a given reality and simply give
    • it a name. When you have a child and call this reality Mary-Jane. You define
    • that reality synthetically. It is a free choice of the person.



    • Real
    • (clarification of some reality, not some word)

    • definitions
    • are

    intrinsic or extrinsic.

    • - Intrinsic attends to clarify what something is through
    • intelligible notes that belong to the thing itself. You can also define what
    • you are talking about by using notes that are outside the thing you are talking
    • about. Intrinsic are either essential or descriptive or recursive.

    • - Essential will try to clarify what a thing is by only referring to
    • what is essential in the thing. Essential can be through physical (parts really
    • distinct from each other) parts or through metaphysical parts. Man as an
    • intelligent soul and prime matter, that is an essential definition of man but
    • through parts that are really distinct from each other. Man as a rational
    • animal: Those parts are not really distinct from each other. You can define the same thing perfectly in
    • different ways. The ways do not have to be compatible to each other.

    • -Descriptive definition can be through a property or through a
    • collection of accidents. Property: I can define man as a risible animal.
    • Perfectly good definition, indicates totally what man’s essence is and
    • distinguishes him from everything else but uses not only essential parts, but
    • also non-essential part, that is the risibility. You cannot use just the
    • property, you need one essential note. You can describe man by gathering a
    • number of accidents “featherless bi-ped with a moveable thumb”.

    • - Recursive: How can you define what a sentence is? Sentences can be
    • not only simple but very complex. A sentence consists of a subject and a
    • predicate or of two sentences joined by a logical conjunction (and, if, either
    • - or). That definition covers all sentences. ordinarily
    • definitions should not include what is to be defined in the definition. But
    • there are some realities in which the complexity is build up as in sentences
    • that you have to enter the thing to be defined into the definition. This is
    • legitimate, because you know what sentence means (subj. pred. or two or more…).
    • You have intelligibility. That is recursive definition.



    • -Extrinsic can be by final causality or by the efficient cause.
    • These causes are outside.

    • -Final: You can define a man as “a corporeal substance destined for
    • everlasting union with God”. Only man is that! But union with God is not part
    • of man’s intrinsic reality, that’s his final cause.

    • -Efficient: Man is a body whose soul is immediately created by God.
    • Or: A circle is what results if you take a point and a given distance to the
    • point and trace out all of the points on a plain surface are at the distance of
    • that point (genetic definition).
  3. Six rules of a good definition
    • What to do to make
    • a good definition: Six rules!
    • 1.) The definition should be convertible withthe defined.
    • .2.) The definition should be clearerthan the thing defined.
    • .3.) Definition should be ordered
    • 4.) Thing defined should not enter into thedefinition. ”5.) Definition should not be negative.
    • 6.) Definition ought to be brief, more becauseof elegance than necessity.

    • .1.) The definition should be convertible with
    • the defined. Means that when you have a sentence in which the subject is the definition and the defined is the predicate, that you can exchange the position of
    • subject and predicate and still have the same truth. Doesn’t work for instance with “man is a living
    • sensible thing” or “man is a learned animal”.

    • 2.) The definition should be clearer
    • than the thing defined.So that if somebody proports to define a “man” by saying he is a zoon
    • logicon.

    • 3.) Definition should be ordered
    • (lowest genus, specific difference). Notice that “rational animal” looks like a kind of definition
    • that fits into the porphyrian tree. You could also define man as a rational living thing.

    • 4.) Thing defined should not enter into the
    • definition. Otherwise how would you make the defined clearer, if the thing entering the definition is not clear. Recursive definitions: Kinds of realities in which the only way to define them is by the defined entering into the definition. “A sentence is a subject and a predicate or a combination of sentences joined by logical…”

    • 5.) Definition should not be negative. But
    • there are things we know only through the
    • negative, i. e. the only way we can define a
    • spirit is, that it is a substance that is not material

    • 6.) Definition ought to be brief, more because
    • of elegance than necessity. “Man is a
    • rational animal”. Or: “Man is a risible
    • animal”. Logic has the ideal of not saying more
    • than you need to say. So it is not elegant
    • to define man as a rational risible animal.
  4. what is a division?
    • A division is taking a whole and dividing it into its parts.
    • Whenever you have a division there’s always a third part, the foundation of a division:
  5. what are the types of divisions?
    • Division
    • Of names
    • Equivocal (bark)
    • Univocal (animal)
    • Analogical (high)

    • Of things
    • Universal wholes
    • Univocal
    • Analogical

    • Singular wholes
    • Essentially (
    • Physical
    • Metaphysical
    • Non-essentially Entitative
    • Non-entitative Integral division

    Potestative


    Equivocal (bark)

    Univocal (animal)

    Analogical (high)

    Of things

    • Universal wholes (insofar as things
    • exist in the consideration of the mind)

    • Univocal (not about the name
    • “animal” but the universal intelligibility) (parts present only potentially: Plant, there’s not
    • present a notion of rose, oak…)

    • Analogical (not about the name
    • “being” but as in created, uncreated…) (parts present actually, when you talk about
    • being, the differences of accidents or so are actually there

    • Singular wholes (insofar as they exists
    • real)

    • Essentially (divide it according to
    • the parts of its essence,

    • Physical (parts that are really
    • distinct, “Harry” divided into PM + SF)

    • Metaphysical (parts that are
    • not really distinct, “Harry” divided into the singule animal he is and the rational that
    • he is)

    Non-essentially

    • Entitative (divide “Harry” into
    • what he is essentially and that by which he is, divide between essence and
    • existence)

    • Non-entitative Integral division (through
    • integral parts, divide myself, hair brast legs feet toes:

    • non essential, non entitative but
    • integral

    • Potestative (“Harry”
    • according to his substance and according to his intellectual activity.)
  6. Rules for making a good division
    • Rules for making
    • good division:
    • 1.) Don’t change the foundation in a division,
    • 2.) Division should be complete.
    • 3.)The parts should be mutually exclusive.
    • .4.) Division should be brief (as brief as it can)
    • .5.) Division should be ordered.

    .1.) Don’t change the foundation in a division, i.e. divide man according to female and male, then don’t add Italians

    2.) Division should be complete. In every good division parts should add up to indicate the whole. Italians into Romans, Milanese and Neapolewhatevers is not good.


    • 3.)The parts should be mutually exclusive. Not good to divide man into women, men and children. This kind of division is said to be inadequate. Careful: If you’re the captain of a ship and you want to get people out of a sinking ship in lifeboats you may well divide men to the right, women and children to the left.

    • 4.) Division should be brief (as brief as it can).

    • 5.) Division should be ordered. Think of dividing things in a porphyrian tree: First the most general kind of substance between complex + non-complex, don’t start with sensible and non-sensible immediately, that would be not ordered.

  7. What are sentences and what are their types?
    • Sentences 2nd act of the mind
    • Anytime you have a sentence the agent who
    • utters the sentence always has an attitude, assumes some kind of stance towards what he says. Whereas in thought (1st act) there is no stance taken on the part of the one who has the thought. But if you say “Elephants are eating my grass”. You do not only think about it, but you say that is the way things are!
    • Imperfect
    • Perfect

    Speculative


    Ordinative (Vocative:


    information

    depreciative (more requesting)

    optative:

    Expressive

    Performative


    Imperfect (you can have one or more words but never finish the sentence: If Harry is an Italian…, or “Elephants” out of “Elephants are nuts”) Clauses, phrases, simple words

    Perfect

    • Speculative (A judgment. The sentence isn’t
    • ordered to doing anything, it is just indicating the way things are
    • or are not.)

    • Ordinative (Vocative: ordered to get attention: “Harry!”, you are taking a
    • stance,being that you want to get
    • someone’s attention; interrogative: you try to get information “What do you want?”;
    • imperative: “Get
    • that elephant out of my
    • garden!”;
    • depreciative (more requesting): “Your
    • Excellency, there’s an elephant in
    • the garden, would you mind to
    • do something about it?”;
    • optative: “I wish the elephant would leave”, if
    • there’s no way to get the elephant out of the garden)

    Expressive (“ouch!”, “Dang that mosquito!”)

    • Performative (There are times when we utter
    • sentences in which the sentence affects something. For instance I took final vows and promise obedience to X for the rest of my life. By saying “I promise”
    • I affected something on myself. Or a marriage: The “I take you” effects something.Not only attempt to get something done, but do something while you are sying
    • it. Sacraments: Signs that affect what they signify)
  8. What are declarative sentences (judgments)?
    • A judgment is that which combines or
    • divides concepts by affirming or denying.

    • In every judgment you have notions,
    • subject, predicate. But just putting notions together isn’t a judgement, but a
    • complex concept belonging to the first act of the mind. You have to have an affirmation, when you put the concepts together, or a negation when you divide
    • the concepts (“is”, “is not”).

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