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Day, John, Robert Gordon and H. Emerton Cambridge: Cambridge University Press, Diesel, Anja A. Geburtstag Anja A. Diesel et al. Evans, Craig A. Eybers, I. Fensham and C. Labuschagne et al. Flanagan, J. Perdue eds. Gese, Hartmut. Gordis, Robert. Hausmann, Jutta. Tubingen: J. Kayandakazi, Lucie. Kayatz, Christa. Studien zu Proverbien Journal of Biblical Literature 86, Klimkeit, Hans-Joachim ed. September in Basel Wiesbaden: Otto Harrassowitz, Kraeling, C.
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Tucker ed. Clines, David J. Bigger ed. Cox, Dermot. R Gammie, J. Interpretation 39, R Hensell, Eugene.
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Catholic Biblical Quarterly 46, R Lust, Johan. Ephemerides theologicae Lovanienses R Malchow, Bruce V. Biblical Theology Bulletin 13, R Schrieber, Paul L. Concordia Journal 14, Craigie, Peter C. Crenshaw ed. Hayes ed. Crossan, John Dominic. Davidson, A. Paterson ed. Davidson, Robert. Wisdom and Worship.
Davison, W. Kelly, Dell, Katherine. Emerton ed. Dubarle, A. Wisdom 44 Eaton, John. Estes, Daniel J. McKenzie and M. Patrick Graham eds. Fichtner, Johannes. Fontaine, Carole R. Newsome and Sharon H. These folk are sheep-eaters, not sheep-feeders. They cannot give after the similitude of God's giving in Christ. They cannot give in the kingdom sense of giving because they have never been gripped by the kingdom. They are bad trees bearing bad fruit. Watch out for them. They cannot give up themselves as God has surrendered himself in Christ. They are strangers to suffering.
Their gospel contains no cross, and what cross they do speak of is merely image, form, symbol, nothing more. It scrutinizes and judges all of them. Therefore when you read in that 21st verse about entering the kingdom of heaven and that one who does the will of my Father who is in heaven, you are reading about the one in whom the reciprocal character of the kingdom is manifest. Those in whom Jesus recognizes himself are those alone who gain access to the fullness of the kingdom.
Therefore, as we come to verses and Jesus takes up this matter of hearing him and doing what he says, it is once more the reciprocal character of the kingdom that is in view. Those who hear Jesus and do what he says will endure. They will endure as houses anchored and built upon the rock. Even though rains and floods and winds assault, even though apocalyptic upheaval comes and the dissolution of the elements arise, they will endure.
Those who have learned to give, as they have been given unto, have learned to give like God gives in Christ. But those who either reject, or who hear but don't obey, are houses built on sand, incapable of standing when the storm of God's final judgment strikes. Even grasping things at the level where we see the reciprocal character of the kingdom tied up in verse 12 and working itself out through the whole is not enough to entirely satisfy Jesus' intent.
Is it not plain as we come to the conclusion of this sermon from Jesus, just how central he himself is to the whole matter? Certainly this should be clear to us from verses , as well as these concluding verses, Note the way Jesus speaks. He is bold to speak of himself in the first instance vv. It is the day of judgment.
And who is sitting on the throne? Who is making decisions in that day? Jesus is the one! He is the judge! He is alive, he is exalted, he is sitting on the throne and the day of judgment approaches. But note what he says in verses The image shifts a bit there. For now, Jesus portrays himself to be the primary, exalted source of all divine wisdom. You have to listen to me. It is my word and no one else's. It is my word and my word alone. He, Jesus Christ the one who speaks, in his person is the veritable appearance of the kingdom of God in the flesh! Jesus on one occasion will say to his detractors, "If I by the Spirit of God cast out demons, then the kingdom of God has come upon you.
He is the embodiment of the Golden Rule in the gift of himself upon the cross; he gives that others may be profited and benefited. He is the gate, he is the way, he is the door. He is the truth, he is the life. He is the good shepherd who stands over against all false prophets and false shepherds; he is the one who gives his life for his sheep. He is the Son of God who perfectly does the will of his Father who is in heaven. He is the rock; he is the stone rejected by men, but made most important of all, because by the activity of God he is transformed into a house, his body being raised on the third day as the new temple of God.
And we are his 32 house, his body, his temple, if we abide in him. And if we abide in him, we will reside in that one edifice of all the edifices of the world that is given this promise: "the gates of hell shall not prevail against her. So that as you come to perform the least of these in his name, you do in and from him alone. In him is life for all who trust and obey. Gregory Nazianzus ca. He is given vinegar to drink, mingled with gall. And who is he? The One who turned water into wine. The history of the kingdom of Israel is as puzzling at its conclusion as it was dazzling at its inception.
Founded on the sure Word of God, supported by his victorious, royal right hand, we watch the formation of the kingdom of Israel in amazement. There God leads them in victory over thirty-one kings and he gives them the land. It was indeed a display of amazing grace! And Israel loved the land. She loved its milk and honey. She loved its grapes and figs. She loved the pomegranates and the water from the rain of heaven. Israel loved the land; she did not love the kingdom of heaven. But she was zealous for the law! Indeed Israel did have a great zeal for the law.
Twice a day the people of Israel would recite this creed reaffirming their devotion to the law. But this zeal was fueled only by a desire to pursue a righteousness of their own, not a righteousness from God which comes by faith. As a result, their interest in the law was self-centered; it was but a means to an end. This man-centered perspective on the law was satisfied with a mere external adherence to the law's precepts.
Israel reduced the law to "busy work. In her disobedience, Israel was granted kings like the other nations. For kings raised from among her own sons would so resemble the pagan leaders surrounding her that one could hardly distinguish between the Canaanite king and the ruler of Israel. Her subsequent spiritual decline would ultimately lead to exile. There the likes of the Assyrian King Shalmaneser and the Babylonian King Nebuchadnezzar ruled over her, just as Pharaoh had many years before.
She would ultimately have kings like the other nations because she would serve as slaves in those other nations. Because of her sin, Israel was removed from the beautiful land and cast into the darkness of exile. She was forced into a culture hostile to her own, forced to learn the ways of her captors. Her desire for the treasures of this world brought her to the brink of forfeiting the treasures of the world to come. Yet, even under foreign rule, she had the promise of a new kingdom: the throne of David would be established forever. There will be no end to the increase of His government or of peace, on the throne of David and over his kingdom Is.
But in the meantime Israel was called to wait. Wait for the Lord; Be strong, and let your heart take courage; Yes, wait for the Lord. Rest in the Lord and wait patiently for Him. Wait for the Lord, and keep His way. Wait for your God continually. And generations of waiting gave way to a lone voice in the wilderness saying, "Repent, for the kingdom of heaven is at hand" Mt. A Son of David called Immanuel "God with us" was born. This Immanuel, Jesus, came to usher in the new kingdom.
Did you hear the words of the Baptist? The kingdom of heaven has come! And for many, these words meant that God was about to free Israel from foreign rule and establish his sovereign dominion among them for all nations to see. They would once again rule in the land of Palestine; once again boast in their law and in the vast dominion of their great kingdom; once again pound their chests with national pride.
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The Kingdom of heaven has come! But Israel was not greeted with the open arms of an earthly king. This call to repentance was at the same time a declaration of Israel's apostasy! The language of impending judgment was to be a signal to her that she was not right before God. Israel was called to bring forth the fruit of repentance or face the ultimate, eternal exile in the place reserved for the ultimate enemy and his followers. She must repent. She must change her perspective on the law.
She must get a new heart! But how? A new king is needed who can lead in ultimate victory, one who can soften Israel's heart, one who can take away the sting of sin and death and replace it with the abundance of everlasting life. A 38 mighty warrior is needed who can take on the great enemy and establish a lasting, heavenly kingdom. And Jesus was going about in all Galilee, teaching in their synagogues, and proclaiming the gospel of the kingdom, and healing every kind of disease and every kind of sickness among the people.
And the news about him went out into all Syria; and they brought to Him all who were ill, taken with various diseases and pains, demoniacs, epileptics, paralytics; and he healed them. A new King named Jesus came proclaiming the Good News of the coming kingdom, healing every kind of disease and pain. He healed lepers, the blind, the lame, and even raised the dead. What kind of King is this? How far does his dominion stretch that he can heal disease, even raise the dead, and bring everlasting joy into a fallen world?
Who is he that can bring good news to the afflicted, bind up the brokenhearted, proclaim liberty to captives and freedom to prisoners? He is one whose throne is in heaven and whose dominion is everlasting. Jesus transformed the cries of despair and sorrow into joyous melodies of hope and renewal, a foretaste of the world to come. In his miraculous healings, this world was momentarily taken captive by a culture hostile to its own; this world was exiled and forced to learn the ways of heaven!
Christ's miracles remind us that the blessings of his kingdom come by grace through the work of God. He healed the sick, remedying conditions beyond the control of man, pointing to God's ultimate healing of our dead souls. He fed multitudes providing food well beyond human means, teaching that the bread from heaven abundantly satisfies and is freely given. He cast out demons declaring that the kingdom of God has come upon us and that God alone binds the strong man. Could there have been a more clear expression of the kingdom of heaven in our world?
Yet those whose eyes were trained on this world, those who were looking for an earthly, political kingdom based on their own deeds could not 39 see it. With these living pictures of Paradise all around them, they blindly continued in their earthly gaze. He did not come to establish the kingdom of man nor the kingdom of this world. His mission was to fulfill the promise of Immanuel.
He came to establish the kingdom of heaven. He came to draw sinners unto God in covenant union. Jesus did not do this through a mere formal, external adherence to the law. Rather he loved his Father with all his heart, and soul, and might, fulfilling the law in thought, word and deed. He showed himself to be the true man after God's own heart, submitting himself to the law at every point, refusing even to withhold his own life when called to place it on the altar of the cross. The law for Christ was not merely a means to an end. He delighted in the law. It was a glorious expression of the kingdom of heaven.
His obedience flowed from the loving union he enjoyed with the Father. His obedience was the expression of a heart entirely focused on the blessing of glorifying and enjoying God forever. This is the same obedience he requires of his subjects. This must be at the heart of our repentance. No Pharisaical righteousness will do, for "unless your righteousness surpasses that of the scribes and Pharisees, you shall not enter the kingdom of heaven" Mt.
You cannot gain access to his kingdom through some external adherence to a set of laws. You must first and foremost love the King. He leaves no room for misinterpretation. He demands our heart. And he who does not take his cross and follow after Me is not worthy of Me. He who has found his life shall lose it, and he who has lost his life for My sake shall find it" Mt. It is "like a treasure hidden in the field, which a man found and hid; and from joy over it he goes and sells all that he has, and buys that field" Mt.
A true child of the King would not trade his place in the kingdom of heaven for all the kingdoms of this world and all their glory, for he seeks first God's kingdom and His righteousness. But where is the good news? How is this any better than the legalism under which Israel operated? It seems as though the burden is even greater. Not only must we adhere to God's law in deed, but we must also adhere from the heart.
In truth, this was always the requirement; even in the shema that creed calling out devotion to the law , Israel was called to love the Lord with all their heart. No, the burden is not greater. The difference is this: Israel pursued the law for self-justification. Israel pursued the law for self!
For them, the law was a burden; it was their prerequisite for blessing. For believers, justification has been completed in Christ. The law, in describing the character of God, becomes for us part of the Immanuel blessing itself. It is the fruit of our salvation in Christ and it anticipates our consummate, eschatological life. The final manifestation of the kingdom will be the complete enjoyment of what we already have.
Says Geerhardus Vos, ". Put chronologically, the behavior to be crowned bears an organic relation to the reward. The demands of the law are at one point the basis for blessing, and at the same time, prophetic of our blessed, heavenly state. Jesus said "Blessed are those who hunger and thirst for righteousness, for they shall be satisfied" Mt. The righteousness which the law requires, the righteousness which we hunger for, pursue and make progress toward in this world, is the righteousness we will be rewarded with in full in heaven.
Do you see what a blessing the law is for us? When we, as believers, strive to conform our 41 life to the law, we are striving for a greater comprehension now of what we will have in glory. As such our obedience to the law becomes a reward in itself. The call to repentance is a call to a godly, heavenly life. It is a call to enjoy God now and forever. In Matthew 10, Jesus commanded the disciples to go throughout all Israel and proclaim the Good News that the kingdom of heaven was at hand.
In Matthew 28, the church is commanded to go out into all the world with that same message. We are to exhort sinners to turn from their ways, to forsake all in this world, to follow Christ, for the kingdom of heaven has come. As we do this, we carry with us the ultimate blessing of the Immanuel promise, for Jesus says to the church "and lo, I am with you always till the close of the age" Mt. But the children of the true Israel love the Lamb; and in loving the Lamb, love the kingdom of heaven; and in loving the kingdom of heaven, love the law of God.
At the tabernacle in the wilderness, At the temple on Mt. With heavenly host and angel We will sing and dance; In the midst of everlasting Glory We will sing an endless Song! McElroy This is a brief examination into the subject of randomness. Namely, what do we mean by "random"; what do we mean by "chance"? These seem to be philosophically loaded terms, and one cannot employ them without invoking religious presuppositions. This essay is an attempt to delineate the various approaches taken to the concepts of chance, randomness, and determinism. We can only provide an introduction to the rich collection of concepts, else this minor endeavor would swiftly become a book.
More meticulous readers, disturbed by the cursory treatment of epochal metaphysical topics, should consult the references for further information. The latter portion of this essay takes an innovative "density" approach to the concept of probability, and thereby places a non-standard interpretation upon the axiomatic definition; this is an attempt to utterly remove the ambiguous notion of "chance" from the parlance of probability theory.
Glossary The terminology is profuse, and, unfortunately, in practice the definitions are not standardized. For the purposes of clarity, the following definitions will be used throughout this paper. Chance: An abstract principle, which governs the outcome of events in our cosmos this term will hereafter refer to the empirically knowable universe, our own space-time domain.
Roughly speaking, the doctrine of chance states that when an event occurs, it could have just as easily come about some other way, and there is no particular reason or cause for things having occurred this way. Note that the principle of chance is assumed to operate through certain rules or laws the probabilities.
Ergodic: This is a precise mathematical term, which in various contexts usually means that spatial and temporal averages or computations are asymptotically identical. Stochastic: An adjective, which denotes that which pertains to probability theory. A stochastic object does obey certain rules and patterns, but is not completely predictable. Chaos: The common usage of the term denotes disorder, unpredictability, and fluctuation.
Paradoxically, it cannot be the complete absence of order such a concept can never be defined, since "defining" is an order-imposing operation , but rather is the apparent loss or corruption of order, perhaps relative to some subjective aesthetic. In mathematics, a chaotic phenomenon is a deterministic structure i.
Random: Some use this word when they discuss raw chance. Others mean a stochastic number between zero and one, generated in such a way that any outcome is equally likely i. This is a quite limited meaning. Others refer to a sequence of numbers that have no probabilistic relationship to one another; this is redundant terminol- 46 ogy, since the probabilistic concept of independence covers this idea.
Deterministic: This idea says that a phenomenon has some cause, which necessarily determines the outcome which often comes temporally. From a scientist's standpoint, these secondary causes become somewhat moot, since they may never be detected or measured. As used in this paper, determinism can allow for non-predictability in the cosmos, and at the same time allow full causality once the viewpoint is extended beyond the boundaries of this world.
This concept will be fleshed out more fully below. This view seems to bear uncomfortably against the edifice of quantum mechanics, which preaches the inherent unpredictability of the small particles within the bed of quantum foam. The measure-theoretic or axiomatic formulation of the theory nicely lends itself to a density interpretation, which is described below. We often speak of the "probability of an event," by which we mean the chance that something happens. Depending on our notion of chance, this has various nuances. Natural Philosophy The term "natural philosophy" refers to the belief that there are sufficient explanations of the observed phenomenon to be found within the cosmos.
Thus the natural includes the full scope of the "possible," so that the supernatural becomes synonymous with the "impossible. Certain laws and rules appear to be operating in the cosmos. Physics, chemistry, and the other sciences have attempted, over the past centuries, to trace these relationships through a partnership of reason and empiricism. The premise that empiricism leads to true knowledge is taken as a given in the current academic community. If a certain phenomenon is observed repeatedly, we notice the pattern and look for a cause.
Upon such foundations modern science is avidly and faithfully pursued, and new truths established. For each observed phenomenon, some cause within the cosmos is to be sought; if no such reason can be determined, then one may either speculate or attribute the behavior to chance. Now there is considerable variation in the natural philosopher's position on the concept of chance. Perhaps in older times i. This would imply strong fatalism, and a mechanistic conception of man and his realm.
But certain experiments in quantum mechanics have cast serious doubts on the tenability of such doctrine. Apparently, small particles move about randomly in the fullest sense of the word. Without any traceable cause, a particle may move to one location or another, and nothing in this world can account for the difference!
It appears that a probability distribution on space is attached to each particle, and after "rolling the dice," the little particle moves to the appropriate location. Beyond this, no further progress can be made. We have no hope of comprehending the impersonal "chance" any more than the ancient pagans did they often conceived of Fortune as a fickle woman! As a passing remark, we observe that similar conclusions from the premise of natural philosophy have been used to logically deduce the theory of evolution. To some of us, this is extremely questionable.
If indeed there is "something" beyond and outside our own cosmos, and if interaction in some definable sense is possible, then we may have an alternate explanation for the phenomenon we observe. First of all, perhaps we should present a brief argument as to why this would be a desirable situation. The objective of science is to explore and describe various aspects of our own cosmos, employing axioms laid down centuries ago. Thus, the extent to which we can eliminate "unknowns" determines the breadth and depth of our knowledge. For example, if a believer in the supremacy of raw chance also claimed belief in God an all-powerful being who created the cosmos , they would conclude that the God could not control everything , since things, in the last analysis, were left to chance.
This person might say that God sets up the distributions for events, but has no actual control over the random number generator! A random number generator is a theoretical item, which spits out strings of zeroes and ones each with probability of one half. God would not be all-powerful after all. Thus, to a scientific mind, order is preferable to raw chance. So a few words should be said to show that "raw chance" is intellectually repugnant.
It is fruitless to seek order in a world where that appearance of order only came about by chance. Now in defense of the opposition, one could mention that there is structure together with chance; perhaps the variance of the distributions is low, so that there is a concentration of events, and "on average" things tend to obey strict rules. This is to be developed in the next section; Christianity presents the most coherent treatment of a supernatural system. Here I will attempt to outline the corollaries of the basic doctrines which apply to this discussion.
As a weak formulation, some theologians have conceived of God as only possessing foreknowledge; such a being would be too deficient in puissance to merit the epithet of "omnipotent", and thus we discard such feeble conceptions. In fact, God foreordains all events in this cosmos. Also, we must keep in mind that this entity "resides" outside and beyond our own cosmos, and thus it is utterly fallacious to apply our own limitations of space and time to One who transcends this order. And as God made the laws and rules of this cosmos, he also has power and authority to break or surpass them.
Now it becomes apparent that objects in this world, on the average, obey the laws discovered by science. As for the mysterious quantum effects, we can now assert that the particles move according to the direction of God; and if the overall pattern is measured, it is seen to follow certain well-studied probability distributions. Of the three religions, the author feels that Christianity has the most internal coherence.
Then, we observe only the values of the functions, but sadly have no knowledge of the function itself. In addition, this is a formulation with which theologians should be quite comfortable: God is continually managing the most minute matters of our world, operating upon matter supernaturally. This does not constitute miraculous activity, since there are no natural laws being broken; rather the supernatural economy is the foundation for natural law.
Fatalism and Chaos Let us now contrast the former view with fatalism. In this picture, God or a supernatural agent merely makes one initial cause, which commences the growth of the cosmos; from that point onwards, every event causes every subsequent event in a theoretically predictable fashion. This is disagreeable to Christianity, which preaches a God that continually upholds the universe. It is at odds with modern science, which has noticed theoretically unpredictable phenomena. And it is odious to the human aesthetic.
Every empirical pattern has a theorem behind it, and behind each theorem is the Primal Mathematician. The concept of chaos, as defined above, gives the only tenable sense. Indeed everything is caused and determined by prior cosmic events, but this is so intricate and complicated that no computational machine could possibly make sense of the data. Thus, while being in essence cosmically deterministic, phenomena are nevertheless apparently stochastic, defying even the most diligent scrutiny. In fatalism, the probability theory is a convenient tool, which is implemented due to the loss of information in the whirl of chaos.
Between these extreme views, supernatural determinism preaches a probability theory, which is concrete and undecipherable from a finite perspective, and yet is completely tangible to the supernatural entity generating cosmic events. The mathematical definition of random variables and probability spaces lends itself nicely to this latter interpretation. Ergodicity and Stochastics Some discussion should now be given on the issue of "ergodicity" and stochastic structures in general.
First, some important terminology will be introduced. The distribution is the collection of probabilities associated to each possible value of a random variable. If I measure the value of a tossed die, the outcome is a random variable, which 53 can take on any integer value between one and six. The distribution tells me what the chance is for each outcome for a fair die, each outcome has probability of one-sixth. Since the phenomenon is the same even though the outcome may be different each of the three times, we say that the distributions of the random variables are identical.
This concept of identical distribution is extremely important in the subsequent discussion. We could compute an average of a random variable two different ways: theoretically and empirically. The theoretical average would involve taking a sum of the values weighted by their corresponding probabilities, which are determined by the distribution. The empirical average would be obtained by repeating a phenomenon in such a way that we generate a sequence of identically distributed random variables. Then we simply measure each outcome, and take the usual average of all the observations.
The basic "ergodic theorem" states 9 that under some conditions , the empirical average gets closer and closer to the theoretical average with a high probability as we increase the number of repeated experiments. In other words, the sampling empirical average is asymptotically identical with the distributional theoretical average. It is strangely apparent that our universe is ergodic. By this, I mean that many phenomena satisfy the ergodic theorem in practice. In some cases, one may have postulated the distribution of a random variable, computed the theoretical average; then this is compared with an empirical average conducted upon data generated by the same stochastic mechanism, and behold!
Why should this be the case? Since the conclusions of the ergodic theorem surround us as well as the subtler "central limit theorems" , it seems to lend validity to our probabilistic modeling of the cosmos.
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So it behooves us to take a closer look at the precise statement of the ergodic theorem which, under other contexts, is called the "Law of Large Numbers". What do we mean by an average of random variables converging to a fixed number? In its strongest formulation, the theorem can be interpreted in the following way: with probability one i. Thus, in theory it could happen that for a given experiment convergence would not occur, but in practice you would never see it happen. A Brief Survey of Probability Probability theory is a fairly recent development upon the scale of human civilization.
The classical formulation dealt with a class of random variables where the number of possible outcomes was finite, and each was equally likely for example, the flipping of a fair coin has two equally likely outcomes. But what if some outcomes are just more likely than others consider an unevenly shaped coin, which gives a bias to one outcome over another? Clearly a better theory was needed. This is essentially equivalent to assuming the ergodic theorem from the beginning and using it as a definition. In the event that the ergodic theorem does not hold for certain phenomena this can and does happen, e.
An axiomatic approach was developed in the twentieth century by A. Kolmogorov 10 , which was built on the foundations of mathematics' real analysis. This seems to be the most successful and most elegant of the approaches. See Kolmogorov for details. Questions like "how do we know it is true?
The method merely consists of the declaration of certain delicate axioms, from which the subsequent collection of Theorems, Propositions, Lemmas, and Corollaries are carefully constructed through the operation of logic "modus ponens" 11 and the law of non-contradiction , laid upon a bed of supplemental definitions. No attempt is made to "prove" the axioms, though we may attempt to justify them on an aesthetic or practical basis.
We merely ask that one accept the rules of logic of course, Buddhists may have a problem with this in order to deduce the resulting mathematics. One other paradigm, the "subjective" theory of Bayesian probability, conceives of probabilities as perceived "degrees of confidence"; the resulting mathematics is identical with the above axiomatic formulation, but a very different interpretation is placed upon the quantities of interest. I will not comment further on this intriguing theory, but concentrate on Kolmogorov's system. Modern probability theory has great explanatory power.
It is from these axioms that such results as the ergodic theorem were established. This is, however, only the first item among a wealth of propositions. As a passing remark, we observe that the subject got its beginning in the various gambling problems of the Renaissance, bantered back and forth between intellectuals. It seems worthwhile to construct a coterie of examples drawn from a less nefarious context.
The Density Model Below is a mathematical formulation which gives an acceptable model of the cosmos and is compatible with the above observations. It is typically called a random variable under some subtle "measurability" conditions. Perhaps one way to picture this set of histories is to imagine a tree that is constantly bifurcating in time, according to which many possible cosmic alternatives occurs.
It follows that the set of all such histories, denoted by W , is unimaginably vast. Now the "probability" itself is a measure on the space W , which assigns to each set a number between 0 and 1; the axioms of Kolmogorov state that some monotonicity and summability properties should be satisfied. Let us see how this concept may be applied. Consider some cosmic event which we wish to model statistically.
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Then we generally conceive of the event as some subset of all possible histories w , 57 such that specified outcomes occur. Stated another way, we are interested in all possible worlds w for which the phenomenon occurs. The following specific example illustrates these ideas concretely. If at a particular time we measure the location, we can model this by considering the random variable C , with possible values of R or L. The event that "it's on the left side" is equal to the set of all w 's all world histories in which the electron really is on the left side.
In general, C w can be either R or L. But this event is actually a subset of W , and we may and will apply the probability measure P to it; then P A gives us a number between 0 and 1, which is interpreted as the "probability that it's on the left side. Interpretations A probabilist will notice that there is nothing innovative in these definitions, except for the idea of "histories".
But let us further imagine that we calculate the probability of an event by taking the following ratio: consider the count of all histories w in which the event occurs, and divide this by the count of all histories w in W. Thus, if we think of each w as a "particle" within the total "object" W , then the probability of an event is simply the density of the corresponding histories within the scope of cosmic possibility.
Thus the name "density model". With this in mind, we can explain the apparent randomness of our world. From the perspective of natural philosophy, the random variables come at us any which way, and there is no possible way of knowing the functions C. From the perspective of supernatural determinism, we should view the space W as grounded outside our cosmos, so that the functions C are movements or mappings between a supernatural realm into a collection of potential universes not just our cosmos, but all subjunctive cosmoses as well! Probability and Measure Greene, Brian.
Grene, David and Richmond Lattimore, eds. Johnson, Phillip E. Kolmogorov, Andrei. Grundbegriffe der Wahrscheinlichkeitsrechnung Van Til, Cornelius. Welch, ed. ISBN: John W. Welch and Daniel B. McKinley, eds. Provo, UT: Research Press, In our search for tools which analyze the structure of Old and New Testament texts, Chaismus in Antiquity has proved a watershed.
When it was first released in , it became the "place to begin" for investigation of biblical chiasms. Welch was the only tool with an indexed compilation of the literature on Old and New Testament chiasms. Now we have the marvelous supplement Chiasmus Bibliography to the volume which updates the index bibliography to What a treasure house of information! The companion volume is indexed alphabetically by author with a brief outline of the chiastic pattern in a given Old or New Testament passage.
Complete bibliographical information is provided should the reader wish to pursue the entire article and complete explanation. But that is not all. The companion volume also contains a complete Scripture index of all articles on chiastic patterns, cross-referenced to the author index at the front of 60 the book. In other words, the Chiasmus Bibliography is a "one-stop" reference for chiastic patterns in the Bible. The original volume by Welch reminded us that chiasm was not unique to the Bible.
It was, in fact, a common literary device in the Ancient Near Eastern milieu. We are not surprised therefore when we discover the device in inspired Hebrew and Christian literature. Here are two examples. The Old Testament example underscores the reciprocity between the female and male lover of the Song certainly one of the lovely features of the book. The New Testament example reinforces the emphatic position of the Sabbath in man's history even as the Sabbath's Lord hallows the day. Chiastic patterns in Scripture therefore contain theological insights.
And the careful student of the Word of God is alert to the richer dimension of revelation provided via chiastic structure. Both of these volumes contain chapters on the "omnipresent chiasm. By means of fifteen criteria, he analyzes the factors making up a true chiasm as distinct from a contrived or artificially imposed thematic chiasm. Together, these volumes are a wonderful entrance into and index to chiasm in the Bible.
They belong on the shelf of every serious pastor and student. NB: both volumes also include chiastic analysis of the Book of Mormon. Wendland, ed. New York: United Bible Societies, This volume is a collection of essays on discourse analysis of Hebrew poetry in the Old Testament. One of the refreshing features of recent literary and narrative approaches to the Word of God is the studied defense of the unity and coherence of the texts. Whether pericopes, chapters or whole books of the Bible, those exploring the linguistic artistry of the divinely inspired writers have renewed our well-founded allegiance to the integrity of Scripture.
This volume is a superb case-in-point. Since exegesis is the analysis of the text, treating the text as "discourse" involves examination of the form or genre , the semantics or words and the rhetoric or the emotional appeal. While noting that several of Wendland's principles retain "critical" foundations, nonetheless his application of the method to Psalm 30 "Continuity and Discontinuity in Hebrew Poetic Design: Patterns and Points of Significance in the Structure and Setting of Psalm 30" presents a fresh structural and discourse analysis of "exalting the Lord.
Bascom finds very little grounds for the frequent emendations to the Hebrew text suggested by critics and commentators. This reviewer would only note that the chapter is chiastic as well as strophic, i. The final chapter is an intriguing reading of Moses' Song of the Sea Ex. This is a helpful collection which allows the text of the Old Testament to speak for itself.
Pastors and students will find it very stimulating. Soulen and R. Kendall Soulen, Handbook of Biblical Criticism. Louisville: Westminster John Knox Press, The writer at that time, Richard N. Soulen, has been joined in this version by R. Kendall Soulen. The current addition is a vade mecum of succinct articles on terms, personalities, movements, even tools in the area of biblical criticism.
The entries are listed in alphabetical order with numerous cross-references for ease of use. Many of the entries contain bibliographical citations for further or more detailed study. More than entries by my count, articles, cross-references provide useful orientations to Old and New Testament criticism. For the advanced student, 63 this is a useful refresher. Even for the expert, there are surveys of topics related to, but outside his or her specific field of investigation.
Included in this edition is a discussion of pre- and postcritical biblical interpretation, thus bringing the reader up-to-date with postmodernism, feminist approaches, etc. All the bewildering German technical terms are found here and clearly defined: Formgeschichte , Redaktionsgeschichte , Religionsgeschichtliche Schule , Vorlage , Festschrift , and many more.
And the explanations are accurate, helpful, easy to assimilate. I have had the first edition at hand for many years and find myself taking it down frequently. This expanded edition is even more useful. No student or pastor will regret the purchase. Every student and pastor will be better informed with the Soulens close by. Beck, eds. They are the stock and trade of the scholarly sleuths in search of a solution to the elusive synoptic problem. The synoptic gospels Matthew, Mark and Luke are so-called because they contain similar or parallel material which may be "viewed together" syn opsis , in Greek as is demonstrated in the standard Synopsis Quattuor Evangeliorum Kurt Aland English edition: Synopsis of the Four Gospels.
For nearly two hundred years, New Testament scholars have attempted to explain the similarities in stories, order of events and vocabulary in the synoptic gospels. Noting that much of Mark's gospel is paralleled in Matthew and Luke, the majority of scholars have argued that Mark's work was written first and Matthew and Luke used him as their primary source.
This is the so-called Markan priority position of Heinrich J. Holtzmann of Strassbourg and especially B. Streeter of Oxford University Streeter also noted that Matthew and Luke include material not in Mark; he therefore posited a 64 hypothetical document called Q for Quelle [German] meaning "source" to account for the unique material.
He further posited a document M to account for this material. And he acknowledged that there was material in Luke not found in Matthew, Mark or Q. This material he labeled document L. If all this seems to our readers to be an alphabet soup morass, you are getting the picture. Another group of scholars, led by William R. Farmer, have rejected Markan priority now being called the Oxford Hypothesis because of Canon Streeter and "mythical Q" for a proposal advanced in the 18th century by J.
The Griesbach Hypothesis for the formation of the synoptic gospels asserts the priority of Matthew. No hypothetical L, M, Q documents are necessary on the basis of Matthean priority. While this whole discussion may seem equivalent to how many angels can dance on the head of a pin, it is very serious business, as the volume under review makes clear. Assembled within the pages of Rethinking the Synoptic Problem are four essays by advocates of : 1 the quest for the synoptic solution Craig Blomberg ; 2 the elusive Q document Darrell Bock ; 3 the priority of Mark Scot McKnight ; 4 the priority of Matthew William Farmer.
The whole is admirably introduced David Black and David Beck and concludes with an epilogue "Response" from Grant Osborne subject and Scripture indexes are appended. The volume is a handy summary of the "state-of-the-art" in synoptic studies. Each essay is a helpful summary of the current state of the discussion by an advocate of that point of view. We learn how, in , Farmer upset the "assured results" of New Testament criticism i. So much for critical fundamentalism! And we learn that the post-Enlightenment pursuit of the synoptic problem is closely associated with Christianity as a "civil religion.
While this book and the Symposium is useful in what it does present, what is omitted is troubling. Black and Beck admit that the only members admitted to this "symposium club" were "representatives of. The "lepers", those left "outside the gate" at this gathering, are the defenders of yet another view of the origin of the synoptic gospels. These are the scholars who defend the "independent" view of the synoptics indeed, all four gospels.
They argue that each gospel was inspired by the Holy Spirit as a complete unit, independent of the others. The leading defenders of this view are Eta Linnemann former student of Rudolf Bultmann, wonderfully converted to evangelical Christianity and author of the book Is There a Synoptic Problem? David Farnell. The message which this book sends with only slight qualification is that only the favored few are welcome to the discussion. Especially since the authors of these essays with the exception of Farmer are well known evangelicals.
Has intolerance trickled down into scholarly evangelical circles? And will that mean another pin-prick to the "assured results" of New Testament evangelical criticism in the future encore?! Stay tuned. The Eschatology of the Old Testament. Through the labors of James T. In the "Editor's Preface," Mr. Dennison states that among the papers of Vos were five different manuscripts and lecture notes dealing with the topic of Old Testament eschatology.
Taking these sources and weaving them together, Mr. Dennison has constructed "the most complete text possible of Vos's materials on Old Testament eschatology" vii. In The Pauline Eschatology , the opening words put forth the following definition of eschatology. Eschatology is "the doctrine of last things. In The Eschatology of the Old Testament, the opening sentences once more provide a definition of eschatology.
Etymologically, the term eschatology eschatos logos means "a doctrine of the last things. It is the doctrine of the consummation of the world-process in a supreme crisis leading on into a permanent state.