Symbolic equality/Necessary v. Contingent

Fraser Valley (Not my photo)

Symbolic equality

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. The Langer philosophy text review, continues. Some key symbols from the textbook:

≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
<= Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0= Null class
---

Philosopher Langer next deals with the concept of Equivalent Expressions. This is complex and will be reviewed, bit by bit.

K= int (interpreted as) 'houses'.
nt = int (interpreted as) 'north of'.

She provides an example basically stating that if (149):

(a nt b) . (b nt c) ⊃ (a nt c)

House A is north of House B and House B is north of House C, is the same as House A is north of House C.

(y) Means no house is north of itself. This concept explained earlier in the text and in my website archives. No two houses are to the north of each other. (150)

(∃x)(∃y): y nt x (150).

X house exists, and Y house exists, equals Y house is north of X house.

The condition of being north of x may apply to any number of K=interpreted as houses. (150).

Langer then explains that for the purposes of the text, henceforth, y nt x shall be equivalent to y ε Ax. (150). Therefore it could be stated that (z) : (z nt y) ⊃ (z nt x) meaning z is north of y is the equivalent expression of z is north of x.

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Updated November 7, 2020

Necessary v. Contingent

1. The necessary must exist.
2. God is necessary.
3. God's plans are necessary.
4. The contingent exist.
5. The necessary supersedes the contingent.
6. Human beings are contingent.
7. Human being's plans are contingent.
8. Human being's needs are contingent.

Therefore, the suffering of the contingent is permissible.

I am not stating that God by nature had to create anything, or anything finite. God does have significant free will within divine nature. His plans reflect nature. I am stating that God's plans must occur and therefore are necessary. It could be stated that it is a weaker sense of necessity in point 3 than points 1 and 2. Some may view God’s plans as contingent as opposed to necessary.

If God’s plans for humanity are contingent, because he could have done otherwise, the fact these contingent plans come from a necessary being would still have them supersede the plans and needs of the contingent.

However...

Open Edition Journals: Philosophia Scientia What is Absolute Necessity? Bob Hale 16/2/2012 

Cited 

Absolute necessity might be defined as truth at absolutely all possible worlds without restriction. But we should be able to explain it without invoking possible worlds.

By my definition 1,2 are absolutely necessary in all possible worlds, in other words, of absolute necessity.

3. God's plans are necessary. 

This could be explained as relative necessity.

Relative Necessity Reformulated Bob Hale & Jessica Leech Journal of Philosophical Logic volume 46, pages1–26(2017)

Cited 

The standard account defines each kind of relative necessity by means of a necessitated or strict conditional, whose antecedent is a propositional constant for the body of assumptions relative to which the consequent is asserted to be necessary.

The relative necessity of (3) has as antecedent the absolute necessity of (1,2).

Further, God, within his infinite, eternal nature, would only be morally obligated to keep his revealed word, as in promises, in regard to contingent, human beings. These are documented in the Hebrew Bible and New Testament within a theistic, Christian worldview.

Brief on John 17: World v World

Venice: Google+

John 17 and two concepts of 'world' from the sermon today:

John 17

Excerpts from English Standard Version

5 And now, Father, glorify me in your own presence with the glory that I had with you before the world existed.

6 “I have manifested your name to the people whom you gave me out of the world.

9 I am praying for them. I am not praying for the world but for those whom you have given me, for they are yours. 10 All mine are yours, and yours are mine, and I am glorified in them. 11 And I am no longer in the world, but they are in the world, and I am coming to you. Holy Father, keep them in your name, which you have given me, that they may be one, even as we are one. 12 While I was with them, I kept them in your name, which you have given me. I have guarded them, and not one of them has been lost except the son of destruction, that the Scripture might be fulfilled. 13 But now I am coming to you, and these things I speak in the world, that they may have my joy fulfilled in themselves. 14 I have given them your word, and the world has hated them because they are not of the world, just as I am not of the world. 15 I do not ask that you take them out of the world, but that you keep them from the evil one.[a] 16 They are not of the world, just as I am not of the world. 17 Sanctify them[b] in the truth; your word is truth. 18 As you sent me into the world, so I have sent them into the world. 19 And for their sake I consecrate myself,[c] that they also may be sanctified[d] in truth. 20 “I do not ask for these only, but also for those who will believe in me through their word, 21 that they may all be one, just as you, Father, are in me, and I in you, that they also may be in us, so that the world may believe that you have sent me. 22 The glory that you have given me I have given to them, that they may be one even as we are one, 23 I in them and you in me, that they may become perfectly one, so that the world may know that you sent me and loved them even as you loved me. 24 Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world. 25 O righteous Father, even though the world does not know you, I know you, and these know that you have sent me. 26 I made known to them your name, and I will continue to make it known, that the love with which you have loved me may be in them, and I in them.”

Bible Hub

'Strong's Concordance

kosmos: order, the world

Original

Word: κόσμος, ου, ὁ
Part of Speech: Noun, Masculine
Transliteration: kosmos
Phonetic Spelling: (kos'-mos)

Short Definition: the world, universe

Definition: the world, universe; worldly affairs; the inhabitants of the world; adornment.

Strong's page 56, states see probably from the base of 2865:

Strong's Concordance

komizó: to bear, carry
Original Word: κομίζω
Part of Speech: Verb
Transliteration: komizó
Phonetic Spelling: (kom-id'-zo)

Short Definition: I bring, receive, recover Definition: (a) act: I convey, bring, carry, (b) mid: I receive back, receive what has belonged to myself but has been lost, or else promised but kept back, or: I get what has come to be my own by earning, recover.'
---

My interpretation is that Jesus Christ desired his disciples to not live as the inhabitants of the world (Strong) live. These disciples are given by the Father to the Son, out of the world (6). As was pointed out in the sermon today, Jesus Christ is praying for these disciples and not for those in the world (society) (9).

Disciples of Jesus Christ are not to embrace and society in the world. They are not to embrace the world system. Disciples are to embrace the gospel via the triune God and Jesus Christ's atoning and resurrection work for those of humanity in Jesus Christ. Disciples are to embrace the Kingdom of God and the culminated Kingdom of God. The world (system my add) is renounced. Browning (398). At the same time, Jesus Christ in John 17, did not want his disciples to withdraw from the world, in the sense of withdrawing from society. Browning (398).

Browning reasons that there is no single or unitary concept for the world in the Bible. (399). This is in agreement with Bauer that has several definition headings based on the New Testament Greek, for κόσμος (445-446). There are also sub-headings based on these headings within the Bauer text, but there is no need to document these here.

1. Adornment. Adornment of women. 1 Peter 3:3. Perhaps Bauer means here that women are not to be of the world with adornment.  (This does not seem as relevant to this article.)

2. In philosophy, the world as the sum total of everything here and now.

3. The world as the sum total of all beings above the animals.

4. The world as the earth and the planet.

5. The world as mankind.

6. The world as the scene of earthly joys and possessions and sufferings.

7. The world and everything in it as hostile to God.

Within (7) based on what Bauer presents from John 15-17, the idea is that Jesus Christ has chosen his disciples out of the world, but for the present they must live in the world (2-6). (447).

BAUER, WALTER. (1979) A Greek-English Lexicon of the New Testament, Translated by Eric H. Wahlstrom, Chicago, The University of Chicago Press.

BROWNING, W.R.F. (1997) Dictionary of the Bible, Oxford, Oxford University Press.

STRONG, J. (1890)(1986) Strong’s Exhaustive Concordance of the Bible, Pickering, Ontario, Welch Publishing Company.

Mahavishnu Orchestra

Uncle Chuckles visited last night and shared an interesting 'bedtime story'. I do not embrace the conspiracy, as in there is a lack of evidence, but as a friend I provide the You Tube videos Uncle Chuckles provided, in comments. As I stated in the audio, based on sinful human nature, I can grant that this type of conspiracy in within the range of human sin. But, after our discussion and viewing the other videos, I still do not see the evidence to prove this particular conspiracy.

All truth is God's truth: II

Germany: Colourized

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.

The Langer philosophy text review, continues. Some key symbols from the textbook:

≡df = Equivalence by definition : = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0= Null class
---

Null class entails the class of cats and the class of not-cats. The null class 0 is included in each complementary pair (147). Every class has a complement and therefore every class includes null class 0. (147).

Langer continues:

As every class in the universe of discourse has a complement, the sub-classes of any class, also has a complement. (147). If two classes overlap we have like, the following example from the author:

Class A: Soldiers

Class B: Brave men (Note this was written in 1953 and revised in 1967)

Class C: Brave soldiers (148).

Class C: Brave soldiers is a sub-class of Class A and Class B. (148).

C = A x B (148). (Note it is A x B, not A + B; these groups overlap, they are not combined. Not all soldiers are brave, and some brave men are not soldiers and may be police officers, for example.)

The negative complement to Class C, is Class -C. This class is also known as -(A x B). (148). Langer states this everything that is not both a soldier and brave. (148).

This is Class A which is not Class B.
This is Class B which is not Class A.
This is everything that is neither Class A or Class B. (148).

Langer reasons that the sum (now +) of Class A and Class B is Class D.

This is all soldiers, brave or not, and all brave men, soldiers or not. (148).

D= A+B (148). (Not x/times. Here they are combined).

The complement of D is -D, which is -(A + B).

This is the class that is neither soldiers or brave men. (149).

Is this technical and somewhat tricky presentation from Langer, I can again philosophically appreciate how the idea of Class (Which Pirie also mentions in his philosophy text) allows one to reason and avoid contradiction and the illogical.

I also appreciate that in philosophy there is both positive and negative class and premises. Christian theology both emphasizes the positive and the negative counterpart.

Once again, this demonstrates within a theistic model, that all truth is God's truth.

C x T = Y

Christians x theologians equals Christian theologians.

C + T = Z

Christians + theologians equals Christians and all theologians, Christian or not.

Christian theologians is not the same as Christians and theologians in reasoning.

Y ˜ ⊃ Z

All truth is God's truth: I

All truth is God's truth: I

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.

The Langer philosophy text review, continues.

Some key symbols from the textbook:

≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
< = Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0= Null class
---

To combine various classes, that are not the same, through the use disjunction or conjunction, positive statements are required to connect membership. (145-146). Langer's example:

C = Cats D = Dogs

(x) : x ε C ⊃ (x ε -D) (146).

Variable equals variable is Cats, is the same as variable is not Dogs.

Philosopher Langer then once again discusses null class (147). Null class is the class which has incompatible properties (147). She suggests for example, a class of cats and not-cats.

x ε A . x ε -A  (147).

Variable is cats and variable is not cats. Based on Langer's writing, this is an incompatible premise.

0 represents null class.

(x ε 0) ⊃ (x ε A) . (x ε -A)

Null class is the same as the class of cats and the class of not-cats.

0 ⊨ A . -A

or

0 ⊨ C . -C

Null class entails the class of cats and the class of not-cats.

The null class 0 is included in each complementary pair (147). Every class has a complement and therefore every class includes null class 0. (147).

0 &lt; A

Null class is included in each class. (147).

Practical theology? This is technical philosophical material and even somewhat mathematical. It will help one to read academic materials within philosophy that use symbolic logic. But thinking in theological terms, I appreciate how each class has its complement, its opposite. Therefore, for example, a Christian has a non-Christian as opposite. Academically in both philosophy and theology logic and reason demands that opposites are complementary and cannot be intellectually spun to be otherwise based on worldviews that oppose biblical Christianity.

All truth is God's truth and here philosophy lends support.