(Reverse) Polish Notation in JavaScript

There was a time when I despised JavaScript. True story. But things have changed much since. What I like about modern JS is its versatility and ease of use. It has a relatively simple syntax, making it accessible to developers with varying levels of experience.

Consider a common problem used during programming teaching courses: the Polish Notation (and Reverse Polish Notation, too). Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands. PN and RPN do not need any parentheses as long as each operator has a fixed number of operands. The description “Polish” refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924.

Traditional notationPolish NotationReverse Polish Notation
3 + 4+ 3 43 4 +
3 – (4 * 5)– 3 * 4 53 4 5 * –
(3 + 4) * 5* + 3 4 53 4 + 5 *
(3 – 4) / (5 + 2)/ – 3 4 + 5 23 4 – 5 2 + /
Comparing standard notation to PN and RPN.
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KEDS Essays — Applying 1 Corinthians in Church Ministry Today

Discuss how Paul’s teaching on ministry by women in 1 Corinthians should be applied in today’s church.


How do Pauline teachings in First Corinthians impact the ministry and role of women in today’s church life? Are women permitted to be in positions of authority and leadership, such as pastoring, preaching and teaching? The matter is debated today more than it ever was in the past (Laney, 2002, p. 8), and scholars are divided in two broad categories: complementarians and egalitarians. Both sides claim scriptural support for their positions, therefore the different conclusions must be determined by exegetical differences, presuppositions, the role of textual criticism, and the understanding of the Sitz im Leben, amongst other factors.

We shall begin by describing each side’s general stance, looking at foundational verses. We shall then carry out comparative exegesis of relevant texts. Finally, we shall determine the applicability of such texts to modern day church as we come to our own conclusions regarding women’s role in ministry.

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When believing is never enough

The only book of the Bible that has the specific and stated purpose of preaching the message of eternal life is the Gospel of John. He himself tells us: 

Now Jesus did many other miraculous signs in the presence of the disciples, which are not written in this book; but these were written, that you may believe that Jesus is the Christ, the Son of God, and, that, by believing, you may have life in his name.

JOHN 20: 30-31

John repeatedly reiterates the only condition to obtain eternal life: to believe in the One whom God has sent (cf. Jn 6:29). In fact, the Greek verb pisteou (to believe) appears 98 times in the Gospel according to John , almost a third of all biblical occurrences.

In the first letter of John the verb appears 7 more times, and the noun also appears once, in one of the most beautiful verses of the epistle:

For whatever is born of God overcomes the world; and this is the victory that has overcome the world—our faith.

1 JOHN 5: 4
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Two new studies about CO2 and face masks

  1. First study is an all-Italian study still in preprint: CO2 levels whilst wearing a face mask go beyond the safety threshold. 40% of subjects with surgical masks inhale CO2 over the threshold. 99% of subjects wearing an FFP2 inhale CO2 over the threshold. The safety threshold is 5000ppm. The CO2 concentration with the surgical masks was measured to be 4965 ± 1047ppm. With FFP2, it was 9396 ± 2254ppm. It gets worse the younger the subject is. Up to 3 times the threshold in children wearing an FFP2, with an average of more than 2 times (12,847 ± 2898 ppm).
  2. Peer-reviewed study: Carbon dioxide rises beyond acceptable safety levels in children under nose and mouth covering: Results of an experimental measurement study in healthy children.

Masks are bad for you, study confirms (yet again)

[T]he lack of negative correlations between mask usage and COVID-19 cases and deaths suggest that the widespread use of masks at a time when an effective intervention was most needed, i.e., during the strong 2020-2021 autumn-winter peak, was not able to reduce COVID-19 transmission. Moreover, the moderate positive correlation between mask usage and deaths in Western Europe also suggests that the universal use of masks may have had harmful unintended consequences.

Study: Correlation Between Mask Compliance and COVID-19 Outcomes in Europe

KEDS Essays — The Church and Israel

Identify and evaluate both the exegetical and theological problems raised by supersessionism.


Supersessionism can be defined as the view that the New Testament (NT) Church is the replacement, continuation or fulfilment of the nation of Israel as the people of God (Vlach, 2007, p. 217), with Old Testament (OT) promises and covenants transferred from ethnic Israel to the Church (Diprose, 2004, p. 2), now seen as the new or true Israel (Marshall, 2012). 

There is a variety of views within supersessionism (Vlach, 2010, p. 13-14), such as punitive supersessionism (Israel was punished for their rejection of the Messiah), and economic supersessionism (Israel fulfilled its pre-established role in God’s plan and is now obsolete). Within both camps we may find moderate supersessionists (p. 20), who would hold to a future nationwide conversion of the Jews. All supersessionists, however, reject the future restoration[1] of Israel in their land as God’s chosen covenant nation (p. 19-20), as well as its implications for God’s plan for humanity.

If supersessionism is wrong, the theological repercussions could be vastly deleterious, since a major theological entity (Israel), seemingly central to God’s programme, would be erroneously displaced.

Our thesis is that the hermeneutics of supersessionism is the cause of widespread exegetical issues, which lead to a theological avalanche affecting several areas of systematic theology. In order to show this, we shall divide our work in three major sections: first, we shall introduce the foundation of supersessionism, namely its hermeneutics; second, we shall analyse their exegesis of passages commonly used as prooftexts; third, we shall outline the wider theological implications. 

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KEDS Essays — Introduction to Philosophy and Apologetics

The problem of evil is not a defeater for the Christian faith. Discuss. 


The epistemic question posed by evil is whether the world contains unfavourable states of affairs that provide the basis for an argument that makes it unreasonable or outright inconsistent to believe in the existence of an omnipotent, omniscient and omnibenevolent God (Tooley, 2019). It is customary to quote Hume’s formulation of the atheistic argument from evil: 

    “Is [God] willing to prevent evil, but not able? then is he impotent. Is he able, but not willing? then is he malevolent. Is he both able and willing? Whence then is evil?” (Hume, 1779, p. 186)

Scholars such as Mackie (1955) and McCloskey (1960) concurred with this traditional understanding of the problem, arguing that all forms of theism holding to the omnipotence and omnibenevolence of God succumb before the Epicurean trilemma cited above (Feinberg, 2004, p. 17). The problem of evil allegedly exposes an unsolvable internal inconsistency of the theistic beliefs; in other words—says the atheist—theists must believe not that which cannot be proven, but that which can be disproven by their own beliefs (Mackie, 1955, p. 200).

In contrast, we maintain that not only does evil not constitute a problem for the Christian faith, but it provides a positive case for it.

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KEDS Essays — Biblical Exegesis: Theory and Practice

Application of Exegesis Methods to Disputed Biblical Passages

Matthew 24:15

Text. Modern English translations (ESV, HCSB, NASB, NET, NIV) as well as major modern Italian ones (CEI, LND, NR2006), reveal no significant variation in the rendering. NET provides extensive translations notes, and no particular dispute in translating this passage is reported. Davies & Allison (2004) agree. 

Paralles are found in Mark 13:14 and Luke 21:20.

Historical BackgroundChrist’s discourse is set around forty years prior to AD 70, during His final week before the crucifixion (Kostenberger, Stewart, & Makara, 2018). In Roman-controlled Israel, the messianic expectation was that “Messiah would lead the nation to throw off Gentile domination” (Myers, 2006, p. 42). Thus, Jesus’ statement in 24:2 puzzles the disciples, who then ask for clarifications in 24:3 regarding three things: the events about to happen; His coming into His Kingdom; and the end of the age (Walvoord, 1971).

Literary AnalysisSimilar to ancient Greco-Roman biographies, Gospels uniquely combine teaching and action in a preaching-based document (Carson & Moo, 2005), whilst still comprising of various familiar genres: parable, discourse, dialogue, biography, etc. (Magnum, 2020). In Matthew’s chiastic structure, the Olivet Discourse is situated at the antipodes of the Sermon on the Mount (Mt 5-7), the latter laying down the qualifications to enter the Kingdom, and the former explaining when it will actually come (Derickson, 2006).

The word for “standing” is neuter (ἑστὸς) in Matthew, whilst in the Marcan parallel it is masculine (ἑστηκότα), suggesting a personification of the abomination, lending support to the “future Antichrist” view (Davies & Allison, 2004). See also 2 Thessalonians 2:3-4; Dydache 16; Apoc. Elijah 2:41; 4:21. 

Theological Analysis. The crucial theological element is the explicit reference to Daniel and his ‘abomination of desolation’ (cf. Dan 9:27; 11:31; 12:11), thus it is interesting that no references to the ‘abomination’ or the prophet Daniel are found in the Lucan parallel, whilst the Marcan parallel does not mention the ‘holy place’ explicitly, and does not directly attribute the ‘abomination of desolation’ to Daniel.

Interpretation. The verse is part of the Olivet Discourse (Mt 24-25). Some scholars rightly observe that Daniel’s prophecy seems fulfilled in history by Antiochus IV Epiphanes in 167 BC (1 Maccabees 1:54, 59; 6:7; 2 Maccabees 6:1–5), yet Jesus clearly intends a future fulfilment for it. This first puzzle is solved by noting that not all of Daniel’s abomination passages refer to the same event. Daniel 11:31 (11:20-35) is about Antiochus (Walvoord, 1971), but 11:36-45 refer to an eschatological future (so Daniel 9:27), the one Jesus refers to (also Paul in 2Th 2:3). The debate regarding whether Matthew 24:15 refers to a historical future or an eschatological one (Theophlos, 2009) is resolved similarly, through the early Jewish hermeneutical idea of ‘patterns of fulfilment’ (Haug, 2003), though we favour the “law of double reference” rather than that of “double fulfilment” (Fruchtenbaum, 2003, p. 4-5). Preterists (Bigalke, 2008) use the Lucan parallel to support the idea that the siege of Jerusalem (AD 70) was the historical fulfilment of the passage, since Luke explicitly mentions Jerusalem surrounded by armies and its desolation being near. However, we must observe that Luke (21:7) only reports the first of the disciples’ three original questions that we find in Matthew (24:3); and that first question is what is answered in Luke 21:20-24. Christ’s prophecy, as a whole, contains multiple references, some to the events of AD 70, some to an eschatological future; the latter is what is addressed in the Matthean account, which links the ‘abomination’ to Daniel and to the ‘holy place’. This agrees with Matthew’s chiastic centre being the postponement of the Kingdom (Derickson, 2006, p. 429).

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KEDS Essays — Exegesis and Bible Polemics: Free Will

Do Christians exercise free will? 


The nature of free will is “the most contentious question of metaphysics” (Hume, 2007). Without free will—Kreeft (2012) argues—all moral language would become meaningless, and justice with it. Meaningless justice would frustrate mercy, grace and love, and ultimately render human life itself meaningless (p. 113-114).

The matter does indeed have repercussions on how adequately we are able to address issues such as God’s goodness (Flowers, 2019), moral responsibility (Moreland, 1988), the problem of evil (Scott, 2015), the origin of sin (Crisp, 2017), the tension between foreknowledge and free will (Swartz, 2020)and between God’s sovereignty and free will (Lemke, 2013), the function of evangelism (Packer, 1961), the roles of man and God in salvation, sanctification, and works (Hankins, 2012; Harwood, 2012; Horn, 2013; Reynolds, 2012; Rogers, 2012).

The topic is vast, thus we shall focus on the question “do Christians exercise free will?” by looking at the most controversial issue: are all men free to believe the gospel? and are believers free to forfeit eternal life? We shall select relevant texts for exegesis, with a more detailed focus on the first of the two questions.

Free will: a definition

Views on free will stem from the answer to the question: if determinism were true, could we still have free will (Timpe, 2020)? Incompatibilism[1] answers in the negative, compatibilism[2] in the affirmative. 

We shall define “free will” as an individual’s ability to make self-determined choices that select one option out of genuine alternatives. This is a form of libertarianism that stands in contrast to all forms of determinism.

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KEDS Essays — Exegesis and Bible Polemics: Apologetics

How central was apologetics to the teaching and preaching of the early apostles? Discuss, with reference to both Acts and any one of the Pauline epistles.


Modern apologetics may be defined as the rational justification of Christian truth claims against relevant questions, objections and alternatives (Dahle, 2002, p. 313); it encompasses topics such as arguments for God’s existence and the reliability of Scriptures, as well as refutations of unbiblical worldviews. However, biblical apologetics seems primarily concerned with the defence of the Gospel (Bruce, 1981) in response to unbelievers slandering and persecuting Christians (Boa & Bowman, 2006). Is this apologetics at the heart of apostolic preaching and teaching? Prophets of old defended the faith (Bennetch, 1941), Jesus Himself employed apologetics (Bruce, 1981),[1] thus it is only natural that apostles such as Peter (Barnard, 2014), Paul (Comfort, 1984), and John (Geisler, 1979), for example, did too.

Though many today draw various distinctions between apologetics and evangelism (Hanegraaff, 2016; Howe, 1978; Montgomery, 2004), we agree with McGrath (1998) that apologetics is integral to evangelism, and shall argue from the book of Acts that this is indeed the case in the apostolic era. We shall then use the epistle to the Romans to show how apologetics was part of the teachings, too.

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