In this video, I respond to The Babylon Bee’s video: If Jesus’ Resurrection were a Hoax.
Video 1: A Babylon Bee video which, in my view, strawmans naturalist explanations of the alleged Resurrection.
Below is Part 1 of my video response:
Video 2: This is my video-response to the Babylon Bee’s video, above.
In video 2, I examine the claims that the Apostles were “brutally murdered” for professing belief in the Resurrection. The latest scholarship—indeed the latest Christian scholarship—suggests that they were not. At best, there is some historical evidence that Saint Peter and Saint Paul were martyred.
In video 2, I ponder whether or not stealing the body was even necessary for a belief in the Resurrection to crop up, naturalistically, amongst the Early Church. The latest Scholarship suggests that there was no empty tomb. Even Bart Ehrman[1] has abandoned belief in the ‘honorable burial’ of Jesus. I suggest that—in the unlikely event that it ever even existed!—Jesus’s tomb was so luxurious, that it would have been reused after His death. If we ever did find Jesus’s tomb, there would, in all likelihood, be a corpse interred there. It would then be impossible for us to determine whether or not this corpse would be Jesus’s or the later tomb-occupant’s.
In video 2, I also stress that History is about ascertaining what probably happened in the past, and not about ascertaining what absolutely happened in the past. History has no way of ascertaining what absolutely happened in the past.
As Bart Ehrman stresses, given that History proceeds via methodological naturalism, the silliest and most ad hoc Naturalist explanation for the Resurrection is still going to be much much much more likely than a supernaturalist explanation that entails a man rising from the dead.
Ehrman posulates, for example, that Jesus might have had a twin, and whenever Jesus died, then Jesus’s twin came back on the scene, and began to tell everybody that he was the risen Jesus. This explanation is silly and absurd, and yet, according to Ehrman, it is much more likely than the postulation that a man rose from the dead.
Bart Ehrman does not say that miracles do not happen. As an ontological naturalist, this is, indeed what he privately believes, but this is not something that he can assert as an historical fact. However, what Ehrman does say is that if miracles do happen, then the Historical Method has no means of detecting them.
The Historical Method can only detect natural occurrences proceeding from natural causes. If miracles occur in the past, then the Historical Method is incapable of detecting them. Even then, the Historical method can only detect some natural events proceeding from some natural causes. The Historical Method is far from error-free. Sometimes it fails to detect phenomena that actually occurred in the past. Sometimes the Historical Method detects an occurrence that never occurred in the past.
I think that some Christian Apologists, like Frank Turek, have a hard time understanding this.
If there be an 80% chance that an event occurred in the past, then there is also a 20% chance that this same event did not occur in the past. Sometimes phenomena occur in the past—or, indeed, fail to occur—in the past, against the odds.
[1] The following quote is from Bart Ehrman Blog: ‘One of the most pressing historical questions surrounding the death of Jesus is whether Jesus really was given a decent burial, as the NT Gospels indicate in their story of Joseph of Arimathea. Even though the story that Joseph, a member of the Jewish Sanhedrin, received permission to bury Jesus is multiply attested in independent sources (see, e.g., Mark 15:43-47; John 19:38-42), scholars have long adduced reasons for suspecting that the account may have been invented by Christians who wanted to make sure that they could say with confidence that the tomb was empty on the third day. The logic is that if no one knew for sure where Jesus was buried, then no one could say that his tomb was empty; and if the tomb was not empty, then Jesus obviously was not physically raised from the dead. And so the story of the resurrection more or less required a story of a burial, in a known spot, by a known person. For some historians, that makes the story suspicious.
CIARAN: “Is Inspiring Philosophy a secret Inerrantist? Well, let us take a look at this video, and see.”
ZAC SECHLER: “How
do you go about the Inerrancy of Scripture, is that an idea that you have?”
CIARAN: “The
correct answer to this question is ‘no’. That’s it! ‘No. I do not hold to the
idea of the Inerrancy of scripture.’ This is the correct answer but let us see
what Michael Jones says.”
MICHAEL JONES: “I
don’t even know what that means, anymore.”
CIARAN: “Ok, so Michael
Jones supposedly does not know what ‘inerrancy’ means anymore so let us explain
it to him: if we come into CodePen, here. The term, ‘inerrancy’, comes from the
Latin word, ‘errāre’, and ‘errāre’ means ‘to err’; ‘to go astray’; ‘to
make a mistake’; ‘to wander away from the truth’. That is what the ‘errāre’
part of ‘inerrant’ means. That is what the ‘errant’ part of ‘inerrant’ means. And
then we have… then we have have the word, ‘in-’, and what does ‘in-’ mean? Well…
I apologise, this is my first time using streamyard. Eh, so ‘in-’ is is Latin
for ‘privative’ and so ‘in- ’ ‘ means ‘not’. ‘in-’ is a prefix. ‘in-’ is a
privative prefix that means ‘not’ so ‘inerrant’ quite simply means ‘not errant’.
‘inerrant’ quite simply means ‘not having any mistakes’. ‘inerrant’ means ‘not
having
any errors’ and I
find it hard to believe that Inspiring Philosophy does not know the definition
of the word ‘inerrant’. This is a tactic[1]
of Greg Koukl’s.
When one is to ask
an apologist for the evangelical Christian Faith a difficult question, they
say: “What do you
mean by that?” and so here Inspiring Philosophy has essentially said: What do
you mean by that?” in the vein of Greg Koukl’s Tactics. And so this is
what I mean by that: Does the Bible have errors? Does the Bible go astray? Does
the Bible make a mistake? Does the Bible wander away from the truth? And the
honest answer to that is ‘yes! It does!’ and if you want a list of all errors
in the Bible than this right here (pointing to Skeptic’s Annotated Bible)
is a great way to start and the list of errors in the Bible presented by this
book is by no means exhaustive. And so let us get back to our friend, here. Inspiring
philosophy.”
MICHAEL JONES: “I
don’t even know what that means, any more.”
CIARAN: “This is a
dodge! This is a shuffle! This is an evasion! The honest answer is: ‘No! I do
not hold to the idea of Biblical Inerrancy.’ But inspiring Philosophy, instead,
just simply sidesteps the question.”
INSPIRING
PHILOSOPHY: “I remember I was at ETS…”
CIARAN: “Evangelical
Theological Seminary. Michael Jones arguing towards academia. He brings the
PhD, Mike Licona, into it, which is simply an ‘argūmentum ex
auctōritāte’ or ‘an argument from authority’.
INSPIRING
PHILOSOPHY: “… last year, and I attended a lecture by Mike Licona, and he said
the same thing: ‘depending on who you talk to, what does “inerrancy” mean?’”
CIARAN: “Well, depending upon whether the person is intellectually honest or not, ‘inerrant’ means ‘does it have errors?’; ‘Does it have historical errors?’; ‘Does it have scientific errors?’; ‘Does it have moral errors?’; ‘Does it errors, in Math?’; ‘Does it add things up, wrong?’ And the answer and the answer to all of this is ‘yes, it does! The Bible has all of these errors in it.’ And so, if you ask an intellectually honest person what ‘inerrancy’ means, they will give you an honest answer. However, if you ask a Christian fundamentalist apologist what ‘inerrancy’ means, then they will try to muddy the waters by bringing in concepts such as ‘functional inerrancy’. You know the Bible is only inerrant essentially where it doesn’t make a mistake and all the places where the Bible does not make a mistake. Eh, well… that is not covered by ‘functional inerrancy’[2], because God really has nothing to say about these issues. So, it depends: if you ask an intellectually honest person what ‘inerrancy’ means they will give you an intellectually honest definition. I think this is an extremely intellectually honest definition of what ‘inerrancy’ means.”
INSPIRING
PHILOSOPHY: “… I don’t think that we should even use the term, anymore.”
CIARAN: “No, the
term is accurate. And this is a very Orwellian part of Michael Jones. He
redefines words. He discards words. You know, ‘inerrancy’ is a good term. Is… Does
the Bible make mistakes? In the genealogy of Jesus Christ, Matthew can’t even
add up the generations right… He makes a mistake in arithmetic. So, there are
arithmetical errors in the Bible. So, it is not the term that is at fault: it
is the fact that the Bible fails the inerrancy test. So, let us keep the term,
‘inerrancy’. Let us keep the term, ‘inerrancy’, so that we can say of this
book: ‘no, it is not inerrant!’”
INSPIRING
PHILOSOPHY: “I don’t know what it means!”
CIARAN: “You don’t
know what ‘inerrancy’ means!? I mean, I am … This is why I think that Michael
Jones is the most intellectually dishonest apologist on the internet… because
he says wild stuff, like this.”
INSPIRING
PHILOSOPHY: “And everyone pretty much agrees…”
CIARAN: “Michael
Jones here, is about to make the question-begging fallacy, here. He is going to
beg the question that there were perfect originals… and, in begging the
question, here, he actually gives the proper answer! The proper answer… you
know, we have to deduce this out of him. The proper answer is that he thinks
that the originals were inerrant but the copies… we only have copies of the
Bible, and so the copies of the Bible: they aren’t inerrant. So so on the one
hand he says: “I don’t know what inerrancy means”, but, here, he essentially
says, well yes the autographa[3],
the autographs, the Ausgangtexte[4],
the originals: they were inerrant, so… in this, in the first, in the first few
seconds of the video, he says: ‘I don’t what it means.’ And then, in the last
seconds of the video he says: ‘Well, I kind of think that the originals were
inerrant.’ So, let us go back to see Michael Jones commit the question-begging
fallacy:”
INSPIRING
PHILOSOPHY: “I mean everyone pretty much agrees, there are scribal errors.”
CIARAN: “This is
begging the question: ‘scribal errors’: ‘scribes’ copy texts, they don’t write texts.
So, here he is begging the question that the originals were perfect. So, I
mean, in this… you know, we can kind of, you know extract, from him here what
he actually thinks: he kind of actually thinks that the originals
were perfect; that the originals were inerrant.
INSPIRING
PHILOSOPHY: “… like in Ezra or if you compare lists between Chronicles or Kings: there is going to be a little bit of discrepancies there.”
CIARAN: “‘discrepancies’,
you know, if a document is ‘discrepant’, I mean, this is a synonym for ‘error’,
so he will use the word ‘discrepancy’; he won’t use the word ‘error’. He’s… ha
ha ha! he’s tap-dancing around the word, ‘error’!
INSPIRING
PHILOSOPHY: “I don’t see that as much of an issue.”
CIARAN: “Ha ha ha!
Well, it’s evidence against your religion! It might not be conclusive evidence,
but it is evidence against your religion, because for, until roughly the time
of Spinoza, the Christian Church did hold to inerrancy, but then Spinoza
began to notice mistakes and errors in the Bible, in The Age of Enlightenment, and
since then there has been a slow retreat from the Doctrine of Biblical
Inerrancy. And it’s evidence against your religion, eh, I mean, this is a
tactic of his friend, Testify’s, as well. Testify will say: ‘Oh well that
doesn’t disprove Christianity!’ No, okay, it doesn’t disprove it
but it is evidence against it. If your God actually inspired a perfect
and inerrant book, then that would be evidence in favour of
Christianity. So, the fact that this book, supposedly written by God is saturated
with errors is, in my view, evidence against it, so, it is an issue. It
is an issue, but, you know, here is Michael Jones hand-waving the issue away.”
INSPIRING
PHILOSOPHY: “I am more interested in talking about reliability[5]…”
CIARAN: “The Bible
is not reliable. Genesis to the Book of Ruth is pure fiction, and if you read The
Oxford Bible Commentary they’ll even say that 1st and 2nd
Samuel: it’s fiction, but some of the characters in there like Saul and David
actually existed. Eh, the New Testament is full of forgeries. Read Bart Ehrman.
The Gospels are anonymous novels that are full of contradictions. The synoptics
and the Gospel of John have Jesus crucified on different days. So, again, he is
side-stepping the issue. The question was: ‘Do you hold to the idea of
inerrancy?’ but Michael Jones shuffles towards the totally different question:
‘Do you think that the Bible is historically reliable?’ Well, that’s not the
question, Michael Jones: The question is: ‘Do you think that the Bible is
inerrant?’ and you’ve totally dodged and evaded this question.”
INSPIRING
PHILOSOPHY: “… than inerrancy, because I don’t even know what ‘inerrancy’ means,”
CIARAN: “You don’t
know what ‘inerrancy’ means. You know I find that… That’s staggering to me!”
INSPIRING PHILOSOPHY:
“… anymore.”
CIARAN: “‘anymore’
So you once knew what it meant. So, have you become more ignorant? Ha ha ha! Have
you… Usually, people acquire and augment their knowledge as they go on: they
don’t get more and more ignorant. So you used, so you used to know what
‘inerrancy’ meant, back when you probably believed in it, but now that you kind
of pretend that you don’t believe in it, anymore, you don’t. You’ve suddenly
lost the ability to discern what the term, ‘inerrancy’, means.”
INSPIRING PHILOSOPHY:
“It is different depending on who you talk to.”
CIARAN: “‘depending
upon who you talk to’ yes! If you ask an intellectually honest person what
‘inerrancy’ means, then they will define it, thusly. They will define it thus: ‘Does
it contain errors?’ ‘Is it not-errant?’ ‘in-’ means ‘not’; ‘errāre’ means
‘to make a mistake’. ‘Does the Bible contain a mistake?’ So, yes, it does
depend on who you talk to: if you talk to an intellectually honest person, they
will define it, something like this.”
CIARAN: “If you ask a Christian fundamentalist apologist, then they will try to redefine ‘inerrancy’ so as to account for all the errors. And this is why I call Michael Jones a Gish-galloper extraordinaire. This video has been a few seconds, and yet it has been full of errors. I don’t know how long this video I’m recording is[6], but it is significantly longer, than this video here. And, as I often think to myself: ‘one could just have an entire counter-apologetics channel devoted to critiquing Inspiring Philosophy, because he puts out so much error.”
[1]Koukl, Greg (2019). Tactics: A Game Plan for Discussing Your Christian
Convictions, 10th Anniversary Edition. Grand Rapids, Michigan:
Zondervan.
[2]Robert M. Price PhD discusses ‘functional inerrancy’ in Inerrant the Wind. The
function of Scripture is arbitrarily defined to be ‘The Good News of
Salvation’, and so innerancy only covers what is deemed to be ‘The Central
Gospel Message’ of Salvation through the atonement and Resurrection of Jesus
Christ. This allows the Bible to be saturated with errors in History, Science,
morality, and arithmetic, whilst remaining ‘functionally inerrant’.Cf.Price, Robert McNair. (2009). Inerrant the wind: The evangelical crisis
of biblical authority. Amherst, N.Y, New York: Prometheus Books.
[3]‘autographa’ is derived from
Latinised Greek. ‘autós’, in Ancient Greek means ‘himself’. ‘graphein’, in
Ancient Greek means ‘to write’. Thus, etymologically, the ‘autographa’ are ‘the
original manuscripts as handwritten by the original authors’.
[4] German for: ‘texts as they left
[the hands of the original authors when they were finished writing them].’ ‘aus’
is German for ‘out’. ‘gehen’ is German for ‘to go’. ‘ausgehen’ is German for ‘go
out’. ‘der Text’ is German for ‘the text’. Thus, ‘der Ausgangtext’,
etymologically, is ‘the text as it went out from [the original author when he/she
had completed writing it]’.
[5] Michael Jones is more interested
in talking about Biblical Reliability, because this is a much easier tenet of
Evangelical Christianity to defend than Biblical Inerrancy. If we take Licona’s
and Habermass’s approach, then what we can say is that, at a minimum, the Bible
gets a number of facts correct! These are the much-vaunted “minimal facts”! I
side with Pine Creek Doug: the best way to counter-apologise is simply to laugh
at Apologetics.
[6] It turned out to be sixteen
minutes and fifty-five seconds long.
Figure 1: The Latin Alphabet. The word ‘abecedarium,’ in English, can mean ‘an alphabet inscribed into stone.’ Hence, this portico, with the Latin alphabet inscribed onto its frieze, is a diagram of an ‘abecedarium,’ in the English sense of the word, as well.
Introduction:
In beginning our study of the Classical Latin language, we shall begin with its alphabet. We shall learn the Latin name of its letters, and how these letters ought to be pronounced.
The Latin word for ‘alphabet’ is ‘abecedārium.’[i]
Body:
Classical Latin possesses an alphabet that contains twenty-three letters. These letters are as follows:
The Classical Latin Alphabet:
Latin Lowercase Letter:
Latin Uppercase Letter:
Letter Name in Latin:
How to Pronounce the Letter’s Name in Phonemic Transcription:
Table 1: The Classical Latin Alphabet. The diligent student will pronounce the letters of this alphabet, aloud, over and over again; and shall write them out, over and over again; until he/she will have committed this alphabet, and the names of its letters, to memory.
Conclusion:
In this chapter have examined the alphabet of the classical Latin language. We have committed the knowledge:
that the Latin word for ‘alphabet’ is ‘abecedārium;’
that the Latin Alphabet comprises twenty-three letters;
which letters comprise the Latin Alphabet;
the names of the Latin letters;
how the names of the Latin Letters are pronounced in Latin.
to memory. Our now having acquired the above-listed knowledge, we can now move forth to following chapters that will treat of the pronunciation of Latin in greater detail.
Endnotes for the Chapter, ‘The Classical Latin Alphabet:’
[i] The Latin, ‘abecedārium,’ genitive singular: ‘abecedāriī,’ is a 2nd-declension neuter noun. The first four letters of the Latin alphabet are:
‘ā,’ ‘bē,’ ‘cē,’ ‘dē
.
Hence from the first four letters of the Latin alphabet we derive the word:
‘“ā,”-“bē,”-“cē,”-“d’”-“-ārium.”’
The 2nd-declension neuter nominal suffix: ‘-ārium,’ genitive singular: ‘-āriī,’ denotes ‘a place where things are kept.’ Where do we keep our letters? We keep our letters in an ‘alphabet,’ or, in Latin, in an ‘abecedārium.’
Hence, etymologically, in Latin, an ‘abecedārium,’ can be defined as: ‘a place where we keep the Latin letters, “ā,” “bē,” “cē,” “dē,” etc.’
[ii]Properly speaking, there is no ‘j’ or ‘J’ in Latin. However, one will often see this character’s being employed—usually in Church texts and other works composed later than the Classical epoch—to denote a consonantal ‘i,’ or ‘I.’ In Latin, ‘i,’ as a vowel, is pronounced, when short, as /ɪ/ or /i/; and when long as /iː/.
In Latin, consonantal ‘i’ can be represented by the IPA symbol, /j/. The consonantal ‘i,’—or ‘j,’ as one sometimes sees (in Church texts)—represents this very /j/ sound. The consonantal ‘i’ in the Latin word, ‘iugum,’ or ‘jugum,’ /ˈjʊ.ɡʊm/ that means ‘yoke,’ is pronounced as the ‘y’ in the English word, ‘yurt,’ i.e. as: /jεːt/.
[iii]In Classical Latin, properly, ‘u,’ and ‘v’ are the same letter. Properly, a ‘V’ is nothing more than the capital form of the lowercase ‘u.’ Therefore, strictly speaking, the presence of a lowercase ‘v,’ in a classical Latin text, is an aberration. Oxford University Press wishes, eventually, to strike this aberration from all of its Latin publications, and I wish them well with this endeavour. Hence, the word ‘verbum,’ that one may observe in present O.U.P. Latin texts will eventually become ‘uerbum.’ However, this practice, today, is far from standard. I prefer this practice, and this is the practice that is employed by Peter V. Jones and Keith C. Sidwell’s Reading Latin: Text Cambridge, Cambridge University Press, 1986. However, these texts—although I deem them more correct—are still in the minority. At present, in most Latin texts, a ‘u,’ or a ‘U,’ is employed to represent the letter ‘u,’ as a vowel; and a ‘v’ or a ‘V’ is employed to represent the letter ‘u,’ as a consonant. Hence, the letter ‘u,’ or ‘U,’ when short, can be said to represent the phonemes: /ʊ/ or /u/ and, when long it can be said to represent the phoneme /uː/. The letter ‘v’ or ‘V’ can be said to represent the phoneme /w/. This will be the practice employed in this present work. Although not our focus, in Church texts, the letter ‘v,’ or ‘V’ can be said to represent the phoneme /v/.
The technical name for the phoneme, /v/, is ‘voiced labiodental fricative.’
The Phonetics term, ‘voiced,’ informs us that vibrating air from the vocal chords is involved in the pronunciation of /v/.
The Phonetics term, ‘labiodental,’ informs us that both the lips and the teeth are involved in the pronunciation of /v/.
The English adjective, ‘labiodental’ is derived from the New Latin 3rd-declension adjective, ‘labiōdentālis, labiōdentāle,’ genitive singular: ‘labiōdentālis,’ genitive plural: ‘labiōdentālium,’ base: ‘labiōdentāl-.’ This New Latin word is derived from the Classical Latin 2nd-declension neuter noun, ‘labium,’ genitive singular: ‘labiī,’ which means ‘lip;’ and from the Classical Latin 3rd-declension masculine noun, ‘dēns,’ genitive singular: ‘dentis,’ genitive plural: ‘dentium,’ which means ‘tooth;’ and from the 3rd-declension adjectival suffix, ‘-ālis, -āle.’
Hence, etymologically, in this instance, the English adjective, ‘labiodental’ denotes ‘the use of the lips and the teeth in the articulation of a phoneme.’
The Phonetics term, ‘fricative,’ informs us that turbulence, caused by the air escaping from a narrow channel—in this instance, the mouth and lips—is involved in the pronunciation of /v/.
[iiii]As with ‘i,’ the Latin letter, ‘y,’ can function as a vowel or as a consonant. Its name in Latin is ‘ī Graeca’ which means ‘Greek “i.”’ When the character, ‘y,’ functions as a consonant, it is said to represent the phoneme, /j/, and on the occasions that ‘y’ functions as a vowel, when short it can be said to represent the phonemes: /ɪ/ or /i/ and when long—i.e. when a macron should appear above it, as: ‘ȳ’—it can be said to represent the phoneme: /iː/.
The Ancient-Greek word, τὰ στοιχει̃α or, when transliterated ‘tà stoicheĩa,’ is a plural form of the 2nd-declension neuter verb, τὸ στοιχει̃ον genitive: του̃ στοιχείου or, when transliterated: ‘tò stoicheĩon,’ genitive: ‘toũ stoicheíou.’
The Ancient-Greek word, ‘tò stoicheĩon,’ can mean ‘an element in a set.’
Figure 1: The elements of this set are alpha, beta, gamma and delta.
The Ancient-Greek word, ‘tò stoicheĩon,’ is formed from the Ancient-Greek masculine noun, ὁ στοι̃χος genitive: του̃ στοίχου or, when transliterated, ‘ho stoĩchos,’ genitive: ‘toũ stoíchou,’ which means ‘steps,’ or ‘a flight of stairs;’ and the Ancient-Greek 2nd-declension neuter nominal suffix, ‘-eĩon,’ genitive: ‘-eíou’ which denotes ‘a means (of),’ ‘an instrument of;’ etc.
Figure 2: a ‘stoĩchos’ or ‘series of steps.’
The term, ‘stoĩchos,’ according to Wiktionary, may be traced back to the indo-european word:
*steigʰ
, which means:
‘climb.’
Hence, etymologically, the Ancient-Greek term, ‘stoicheĩa,’ can be said to mean: ‘the means of climbing up;’ ‘the means of stepping up;’ ‘the means of ascent;’ etc.
This is highly instructive, as, in truth, Elements is a book that is a Jacob’s ladder, of sorts, by which one can ascend, element by element, into the heavens of mathematical knowledge.
Figure 3: With The Elements of Euclid, we advance in our mathematical knowledge element by element. Each element is, conceptually, like a rung, heaving us upwards to Mathematical prowess; to an implicit knowledge of Euclidean Geometry.
Conventional Arithmetic possesses rules for the order of operations. Which operations ought we to evaluate first? In what order ought we to evaluate operations? This is the topic that this chapter wishes to address. ‘Precedence,’ is also sometimes referred to as ‘the order of operations.’
Body:
The Etymological Definition of ‘Precedence:’
Our English noun, ‘precedence,’ is derived from the Latin substantive participle, ‘praecēdentia.’[3] ‘Praecēdentia,’ in Latin, means ‘the abstract concept of which things go before [other things].’
Figure 2: The English arithmetical term, ‘precendence,’ is derived from a compund of the Latin verb ‘cēdēre,’ which means ‘to go.’ Go, or Golang, as a language, is—syntactically—very like the C Programming Language.
Within the context of Arithmetic, ‘precedence,’ etymologically, means ‘the science of determining which operations go before [other operations];’ ‘the science of determining which operations should be evaluated before [other operations].
The Acronym, ‘P.E.M.D.A.S:’
The acronym, ‘P.E.M.D.A.S.,’ stands for:
Parenthesis;
Exponentiation;
Multiplication and Division;
Addition and Subtraction.
The Acronym, ‘P.E.M.D.A.S.,’ can be easily remembered with the Mnemonic phrase:
As we can observe from the above ordered list, some operations share the same level of precedence. For example, the operation, multiplication, and the operation, division, have the same level of precedence. Multiplication and Division share the third level of precedence, in the above list. When we are confronted with an expression or an equation that contains operations at the same level of precedence, seeing that in Anglophone countries, we read from left to right, then we evaluate operations that possess the same level of precedence from left to right. Hence, when two or more operations—within an equation or an expression—share the same level of precedence, then we evaluate them from left to right. Concerning operations at the same level of precedence, we evaluate from beginning at the leftmost operation, and work our way rightwards.
An Example of Precedence:
In the expression:
2 ÷ 1 + 3 × 42 – 5 + ( 3 – 2 )
, we first evaluate the operation in parenthesis, i.e.:
( 3 – 2 )
. When we evaluate:
( 3 – 2 )
, then we obtain the difference:
1
.
This renders the original expression as:
2 ÷ 1 + 3 × 42 – 5 + ( 1 )
or as:
2 ÷ 1 + 3 × 42 – 5 + 1
.
Second, we evaluate the exponentiation operation i.e.:
42
. When we evaluate:
42
, then this obtains for us the power:
16
. This renders our original expression as:
2 ÷ 1 + 3 × 16 – 5 + 1
.
The operations, Multiplication and Division, share the same level of precedence. However, given that the division operation is further to the left, on the page, than the multiplication operation, then we evaluate the division operation before we evaluate the multiplication operation.
Given that the division operation:
2 ÷ 1
is further to the left, on our page than the multiplication operation:
3 × 16
, then we evaluate:
2 ÷ 1
before we evaluate:
3 × 16
.
When we evaluate:
<!–
2\div1
–>
2 ÷ 1
, then we obtain the quotient:
2
. This renders our original expression as:
2 + 3 × 16 – 5 + 1
. Then we proceed to evaluate:
3 × 16
, and this obtains for us the product:
48
. This renders our original expression as:
2 + 48 – 5 + 1
.
The operations; addition, and subtraction; share the same level of precedence. In the above ordered list, they are at the 4th level of precedence. We evaluate these operations as we should find them, beginning at the leftmost, and working our way rightward. Hence, we evaluate:
2 + 48
first. This obtains for us the sum:
50
. This renders our original expression as:
50 – 5 + 1
. We then proceed to evaluate the operation:
50 – 5
, which obtains for us the difference:
45
. This renders our original expression as:
45 + 1
. We then proceed to evaluate the expression:
45 + 1
. This obtains for us the sum:
46
.
This renders our original expression as:
46
. We have thus simplified the expression:
2 ÷ 1 + 3 × 42 – 5 + ( 3 – 2 )
to:
46
. We have observed mathematical precedence οr the order of operations in our simplification of the expression:
<!–
2 \div 1 + 3 \times 42 – 5 + \left ( 3 – 2 )
–>
2 ÷ 1 + 3 × 42 – 5 + ( 3 – 2 )
to:
46
.
Conclusion:
In this chapter, we have endeavoured to gain for ourselves an implicit understanding of precedence as it pertains to basic or conventional arithmetic. Boolean arithmetic, an arithmetic of logic employed in Computer Science, also possesses precedence or an order of operations, which we shall examine in a subsequent chapter. In the next chapter, we shall examine precedence or the order of operations as it specifically applies to the C programming language.
Figure 1: This is the ‘Shiyn’, the 21st letter of the Hebrew abjad. Its Aramaic name is שִׁין or ‘shīyn’ or ‘shîn’. It is spelt ‘shiyn,chiriq; yod; final nun;’ I drew this shiyn with gel pens. I then scanned it into Vector Magic, and then I tweaked it in Inkscape with the Typography extension.
This is the 21st letter of the Hebrew abjad. An ‘abjad’ in linguistics is an alphabet comprising only consonants and no vowels. The word ‘shiyn,’ is Aramaic for ‘teeth.’ In Proto-Sinaitic, or “Paeleo-Hebrew” this character looks like a pair of incisors.
Figure 2: This is what a ‘shiyn’ looks like in Phoenician or Proto-Sinaitic or Pale-Hebrew.
שֵׁן or ‘shē(i)n’ is ‘tooth’ in Hebrew.
Figure 3: I drew this tooth in Assembly, an app-store app. שֵׁן or ‘shē(i)n’ is ‘tooth’ in Hebrew. It is spelt ‘shiyn,tseire; final nun;’ It is a feminine noun.
Should the dot be placed over the left horn, then this character is pronounced like a clean ‘s’ would in English. The IPA symbol that represents this sound is /s/.
Figure 4: Should we place the dot over the left horn, then we pronounce this character as a clean ‘s’ or /s/.
Should the dot be placed over the right horn, then this character is pronounced like an ‘sh’ would in English. The IPA symbol that represents this sound is /ʃ/.
Figure 4: Should we place the dot over the right horn, then we pronounce this character as a “soft-‘s’” sound; as we would pronounce the digraph ‘sh’ in ‘shop.’ The IPA symbol that represents this phoneme is /ʃ/ or ‘esh’.
One word with which this character is associated is the Hebrew word for fire, which is אֵשׁ or, when transliterated: ‘ē(i)sh.’
Figure 5: It is as though a fire bites into whatever it is consuming. Hence the shiyn, as a pictograph, is said to represent fire, or passion etc.
Figure 5: What the Hebrew word, ‘ē(i)sh’ means when spelled with Proto-sinaitic or Paleo-Hebrew characters. The pictographic meaning of this word seems to be ‘the strength of consuming,’ or ‘strong consuming,’ or ‘leading to consuming,’ etc.
The word for ‘man’ in Hebrew is אִישׁ or, when transliterated, ‘īysh,’ or ‘îsh.’ Man has, as it were, the fire of life inside of him, the götterfunken, or ‘divine spark,’ as Schiller put it. His internal body temperature is 37 degrees celsius. Also, man – if not careful – can be utterly consumed by his appetites and passions.
Figure 6: Ecce homō! Behold the man! It is as though he is animated by some divine flame. However, he is also a collection of passions and appetites, and – if not careful – he can be destroyed by these.
Maths and Comedy 