Showing posts with label ontology. Show all posts
Showing posts with label ontology. Show all posts

Monday, November 22, 2010

The Trinity, Marriage, and Relative Identity

Submitted for your reading pleasure, for Thanksgiving break...



So, let’s go back to two earlier issues that have arisen in this blog. Let’s also do this by way of a common path in addressing the matter of relative identity. Because if it is true that the relation of identity is not absolutely subject to the rule of transitivity, and if it is true that it is possible for objects X and Y to be the same object F but not same object G, then certain matters of Christian and biblical theology just became that easier to grasp.

To establish some context, the reader may recall the following past blog entries:

Monday, April 19, 2010
“Challenge for Trinitarians”
http://bright-idea.blogspot.com/2010/04/challenge-for-trinitarians.html

(Cf. Monday, April 26, 2010
“Challenge for Anti-Trinitarians, Part 1”
http://bright-idea.blogspot.com/2010/04/challenge-for-anti-trinitarians-part-1.html

Monday, May 03, 2010
“Challenge for Anti-Trinitarians, Part 2”
http://bright-idea.blogspot.com/2010/05/challenge-for-anti-trinitarians-part-2.html)

Saturday, October 02, 2010
“About David's Census”
http://bright-idea.blogspot.com/2010/10/about-davids-census.html

Linked to:
SEP: “Relative Identity¨
First published Mon Apr 22, 2002; substantive revision Mon Nov 5, 2007
http://plato.stanford.edu/entries/identity-relative/

Wednesday, October 27, 2010
“A Difficult Teaching”
http://bright-idea.blogspot.com/2010/10/difficult-teaching.html

The two issues in question are: 1) the supposed logical and metaphysical impossibility of the biblical teaching of the divinity and co-distinctiveness of God the Father, the Son, and the Holy Spirit; and 2) the bodies of a man and his wife being one in number. The would-be downfall of the doctrine of the Trinity and of the difficult marital teaching was this: the Rule of Transitivity of the relation of identity.

The Scriptures apparently hold that each of the Father, the Son, and the Holy Spirit (the names of whom we will abbreviate as F, S, H, respectively) is distinct from the other and that each is God, where the noun phrase “God” is a subject complement and not a camouflaged adjective of any sort. What do we know about identity? If an A is C, and if B is C, then A is B. Again, if les États-Unis are the United States and if los Estados Unidos are the United States, then les États-Unis are los Estados Unidos: this is something which is perfectly clear to see. So where we abbreviate the name “God” with “G,” if F is G and if S is G--and don’t lie to yourself--then F is S according to the transitivity rule of identity.

The same problem arises with married couples. Christ said that a man and wife are no longer two but one, and if we are to take the words of Christ at face value or are to take his words literally--as is required in any hermeneutic enterprise until the possibilities that words were meant to be taken literally are exhausted--then we have a problem. For it is clear that when the body of Barack Obama stands behind a teleprompter to give a speech while the bodies of wife and children have every appearance of being located elsewhere on the stage or on the earth, there are two distinct objects involved, even two distinct bodies. Leibniz’s Law of the Indiscernibility of Identicals creates the problem, because if Barry is Michelle and if Barry is behind the teleprompter, then according to the rule it must be that Michelle is behind the teleprompter. However, we will see later that the law is quite possibly defeasible in instances of this sort if we want to hold to the idea that the bodies of a man and his wife are one in number and not two.

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So once again, what are some facts of identity or something’s being identical with something else?

(1) A is A.
(In other words, everything is identical with itself.)

(2) If A is identical with B, then every property of A is a property of B, and vice versa.
(In other words, if A and B are the same thing, then whatever is true of A is true of B, and vice versa; likewise, whatever quality A possesses is also possessed by B, and vice versa.)

(3) (Except where subject to qualification) The relation of identity is transitive. If A is C, and if B is C, then A is B.
(In other words, if Jesus’ Father is God, and if Jesus is God, then apparently Jesus is Jesus’s Father.)

(1) is the Law of Identity and its validity is incontrovertible. (2) is pretty much Leibniz’s Law of the Indiscernibility of Identicals and it supports (3). (3) is the rule of transitivity which is thought to bind or govern the identity relation.

The validity of the transitivity rule is to be granted. For starters, remember that language is a matter of the signifier and the signified. With that said, consider the statement “A is B.” If the name “A” refers only and precisely to an object φ and if the name “B” refers only and precisely to an object φ, then there just is only one denotation of the two names: φ. In other words, A necessarily is B and B necessarily is A since A and B are I-related (i.e., identity-related) in that there is precisely, only, and commonly one object which they denote.

Because the transitivity rule of identity is to be granted, guess what you get with the following sentences:

(4) The Father is God.
(5) The Son is God.
(6) The Spirit is God.

Or if any trinitarian will not admit that there is trouble for trinitarianism here, let’s reduce those sentences to symbolic logic, with the attendant reminder, for example, that the Bible apparently affirms not merely that Jesus and the Spirit of Jesus are equal with God but identical, as in John 1.4 or Acts 5.3-4:

(4') F = G
(5') S = G
(6') H = G

On the transitivity rule, F = S = H, which clearly is not orthodox.

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In philosophy it is often useful to examine language and the ways in which we speak of different matters of ontology, mereology, epistemology, and so forth. In fact, it is useful to think of the identity relation as being a linguistic or semiotic relation, but only up to a certain point. The foregoing account of trinitarian doctrine and the transitivity of identity is a semiotic one, and there are shortcomings in a mere semiotic account of identity.

[DB, Semiotics contrasts with semantics in being the study of the words and such that convey meanings or connotations. ;) ]

Number one, how does a mere semiotic account explain the Law of Identity? After all, when we stop to contemplate the Law of Identity and affirm it we are not asserting that a name, N, refers to what it refers to. To the contrary, it is clear that in those instances what we have in mind is that an object, φ, is φ--our concern is one of raw metaphysics and not language.

Number two, suppose you point at two physical objects (such as two coffee mugs) resting on your desktop and assert that one is the other. Regardless of whether your assertion is veridical or jibes with reality, it is clear that your concern in this case is not a semiotic one and also that you are not employing any novel or unconventional concept of identity in the process.

Number three, a mere semiotic account of identity reduces the Father, Jesus, and the Holy Spirit to mere names of a common object, something which is hardly supported by the entirety of the Scriptures.

Having considered these problems, what would it mean to point to a physical object with your right hand and to assert that it is another physical object that you point out with your left hand? Transitivity could not begin to apply to the two physical objects, as it were, or to any additional and third object if the assertion were true. This is because Leibniz’s law, which is metaphysical and concerned with the properties of objects, still holds true such that you have no diversity or plurality of objects to which transitivity could apply.

What all of this means is that the transitivity rule of identity apparently holds in language and symbolic logic, but not beyond language and symbolic logic. In terms of the realities of raw metaphysics or ontology, which are the foundation of language in the first place, the rule binds nothing.

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So the transitivity rule of identity apparently cannot rightly be used to deny the doctrines of the Trinity. It remains entirely possible that F = G and S = G while F ≠ S. Of course, if one affirms that F = G and S = G while F ≠ S then he affirms the idea of relative identity, according to which X and Y can be the same φ though not the same ψ. Someone might invoke Occam’s razor to claim that the Scriptures themselves are proof that relative identity exists, at least in the case of the Father, Son and the Holy Spirit. Apart from that, strong proofs of the existence of relative identity seem rather elusive. However, a tentative case can be made with the paradox of constitution.

Take a piece of clay that has no remarkable or special shape or form. Now take that entire quantity of clay and fashion it such that the piece of clay that now has a shape exactly like that of a man, with various constituent atoms or matter in various locations relative to one another: the piece of clay is now a statue. Now take a mallet and smash the statue. By doing so, you will have destroyed the statue, but it bears noting that at the same time you have not destroyed the piece of clay.

The piece of clay is the piece of clay. The statue is the piece of clay. The piece of clay is the statue. The statue is an object, O, which the piece of clay is not. Stated in another way:

C = C
S = C
S = O
C ≠ O

Compare:

F = G
S = G
H = G
F = O1 (“O1” meaning an object which S and H are not)
S = O2
H = O3
F ≠ S; S ≠ H; F ≠ H

Notice that the thought experiment of the piece of clay is carefully worded. The piece of clay does not merely take the form of a man or of a statue. To the contrary, in virtue of the piece of clay’s having a shape exactly like that of a man it just is a statue. Meanwhile, it is clear that a statue is destroyed when it is smashed with a mallet. At the same time, it bears noting that in the thought experiment the piece of clay begins as an object which has no remarkable or special shape or form and persists even after it obtains a special shape. Therefore, the piece of clay is not destroyed by any stroke of a mallet, though the statue is. Consequently, it seems difficult to conceive that the thought experiment or its conclusions suffer from some sort of language defect or some sort of “vague” or “misleading” use of vernacular speech. No, the vernacular means of speaking of destruction and constitution seems quite straightforward in this instance, and so there seems to be at least one intuitive example of relative identity.

So with a dismissal of the transitivity rule of identity in matters of metaphysics or ontology, we discovered what we already knew to begin with: that it is entirely possible that each of F, S, H is G while F, S, H are distinct from each other. With the would-be paradox of constitution, we see again that it is entirely possible that each of F, S, H is G while F, S, H are distinct from each other. Of course, no one believes that either F, S, or H is a physical or mental construct of any sort, yet the paradox only bolsters and supports the re-evaluation of the transitivity rule.

Now let’s see what happens if we try to account for trinitarian proof texts by means of the concept of relative identity. In the ontological realm, when two objects are I-related--and let’s stop right there, because there can be no naïve relation of identity between two distinct objects in extra-linguistic world; instead, identity by definition means having only one object in question though it may carry two different names. Then again, in the ontological realm when objects are R-related (i.e., when the relation of relative identity obtains between the objects) A and B will be the same X, but not the same Y. Again, A and B will be the same X, but not the same Y.

A and B will be identical with some common object (this object perhaps being either A, or B, or some third object), though at the same time there is at least one object A is though B is not or at least one object B is though A is not. In the case of the piece of clay, the piece of clay was the statue and vice versa, though apparently the statue was something which the piece of clay was not, for one object was destroyed while the other was not destroyed. Therefore, the piece of clay and the statue are R-related to each other while there is yet a third object somewhere in the picture, regardless of whether or not it is readily discernible. In the case of F, S, and H, it is likewise the case that certain objects (e.g., S and G) apparently are identical while there is a third object which one of the two is while the other is not (cf. the doctrines that G is F though F is not S).

So, relative identity is possible, and it appears to support the propositions that each of God the Father, the Son and the Holy Spirit is the one god that exists while each is also distinct from each other.

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If a piece of clay and a statue are R-related in the paradox of constitution, then it follows that such may well be the case with human beings. Consider a human body for example. It seems entirely fair (though every matter of philosophy is doomed to remain forever controversial to some degree) to say reductionistically that a zygote is a particular amount or body of matter, regardless of its being a vessel of a soul or spirit. This zygote, or rather this body of matter, will undergo radical changes in its career. If all goes normally, the body of matter will increase in size over the course of nine months and its shape will undergo radical changes of shape, but the body of matter persists nonetheless as opposed to ceasing to exist upon any would-be change that it undergoes.

Now suppose the worst and that this body of matter perishes at an age of ten months and is later incinerated. The human being is destroyed in the process, but that particular amount or body of matter is not. Come rain or shine or fire or any other condition, all the constituent atoms of that body of matter persist, even if their locations relative to one another become as counterintuitive or as strange as the relative locations of the United States or the minuscule letter “i,” which both consist of disparate parts. What follows from our thought experiment is that the body of each of us is never alone; instead, it may well be that we have two of them even if one of them is not readily discernible.

With that said, let’s revisit some texts that we earlier looked at. It is written:

1 And he arose from thence, and cometh into the coasts of Judaea by the farther side of Jordan: and the people resort unto him again; and, as he was wont, he taught them again. 2 And the Pharisees came to him, and asked him, Is it lawful for a man to put away [his] wife? tempting him. 3 And he answered and said unto them, What did Moses command you? 4 And they said, Moses suffered to write a bill of divorcement, and to put [her] away. 5 And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept. 6 But from the beginning of the creation God made them male and female. 7 For this cause shall a man leave his father and mother, and cleave to his wife; 8 And they twain shall be one flesh: so then they are no more twain, but one flesh. 9 What therefore God hath joined together, let not man put asunder. 10 And in the house his disciples asked him again of the same [matter]. 11 And he saith unto them, Whosoever shall put away his wife, and marry another, committeth adultery against her. 12 And if a woman shall put away her husband, and be married to another, she committeth adultery. (Mark 10.1-12)

Again:

3 The Pharisees also came unto him, tempting him, and saying unto him, Is it lawful for a man to put away his wife for every cause? 4 And he answered and said unto them, Have ye not read, that he which made [them] at the beginning made them male and female, 5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? 6 Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder. 7 They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away? 8 He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so. 9 And I say unto you, Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery. 10 His disciples say unto him, If the case of the man be so with [his] wife, it is not good to marry. 11 But he said unto them, All [men] cannot receive this saying, save [they] to whom it is given. 12 For there are some eunuchs, which were so born from [their] mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive [it], let him receive [it]. (Matthew 19.3-12)

So Matthew 19 and Mark 10 speak of acts of remarriage which constitute acts of adultery. The texts also raise the following question: How does remarriage constitute adultery since the divorced person presumably is no longer married? For the time being, let’s try to answer this question with the naïve set of assumptions which most of us have concerning the texts: that the identity relation is always transitive and that the word “one,” as used in the texts above of a man and his wife, is merely figurative in meaning.

On the naïve view, remarriage or acts resulting from remarriage can be adultery only in virtue of the following: either a divinely irrevocable married status or a divinely irrevocable oneness of married couples. The former disjunct seems not to be an option, since it seems as though people who divorce do end their marriages and are unmarried right after they obtain a divorce. John 4.1-18 also seem to support this assessment (just as it is entirely unlikely that the Samaritan’s five former husbands were all dead at that time).

So marriages apparently end even when neither a husband nor a wife dies, and that means that adultery in this case must be a violation of oneness of an earlier marriage, which is a problem. It is a problem because the naïve view treats the word “one” in this case as being figurative in meaning: it ends up meaning close instead of one. Yet people who divorce each other clearly are no longer close in the sense of the Mt 19 and Mk 10 passages; they are neither physically nor emotionally nor sociologically close in whatever sense could exist in these passages. So the naïve view on the one hand must treat the adultery problem as a violation of erstwhile oneness while on the other hand it cannot possibly affirm that such oneness is possible. Therefore, the naïve view must be incorrect and cannot account for all the details of Mt 19.3-12 and Mk 10.1-12.

However, you get a solution to the problem if you assume that some particular relation of relative identity exists between married couples. The piece of clay and the statue overlapped in space and time, and perhaps two bodies for every human person also overlap in space and time. When someone marries, one of those two bodies ceases to be distinct in quality or in number from a body of another person who has just experienced an analogous change of being. In the case of the piece of clay and the statue, there turned out to be a third object which one object was while the other was not and which was meanwhile more or less indiscernable. In the case of married couples, some more or less indiscernable objects are those which become one in number while the two distinct bodies which we all see with our own two eyes are analogous to the piece of clay and the statue which we likewise see with our own two eyes. Consequently, it would have to be the case that the kind of people that Christ speaks of in Mt 19.3-12 and Mk 10.1-12 is not that which we see with our own eyes but rather the “hidden” physical bodies; otherwise, the appeal to relative identity is thus far ineffective.

So there it is: a bunch of things to consider, along with possible implications of 1 Corinthians 6.15-17. Food for thought and grounds for further research, to borrow from Emory.

Monday, April 19, 2010

Challenge for Trinitarians

Christians tend to be behind the curve on different things. Yet as soon as Christian apologists figured out that the law of transitivity of identity and/or Leibniz’s Law of the Indiscernibility of Identicals proves what we all knew in our hearts to be true, many of these apologists came up with a quick answer.

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If A = C, and if B = C (where “=” signifies the relation of identity), then A = B. For example, if Samuel Clemens is the one man who invented Huck Finn, and if Mark Twain is the one man who invented Huck Finn, then Samuel Clemens is Mark Twain.

On a different yet related note, if A = B, then whatever is true of A is true of B. For example, if Y'shua is Jesus, and if Y'shua is the Messiah, then Jesus is the Messiah; and if Y'shua is Jesus and if Jesus is the Messiah, then Y'shua is the Messiah--no exceptions.

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Now, Christian apologists know this rule, and many of them have been confronted with the true (!) statement that if F = G and S = G, then F = S --or rather that if the Father is identical with the one god that exists and if the Son is identical with the one god that exists, then the Father is (identical with) the Son. One thing they have done in response is to take a sentence on the order of “The Word was God”--as in John, chapter one and as in common Christian parlance--and then have the boldness to treat the noun “God” as if it is a predicate noun both in Koine Greek John 1.1 and in common parlance. Translation: they take the noun “God” and they treat it like an adjective, all such that John’s sentence “The Word was God” may as well be rendered as the sentence “The Word was divine.”

And that’s supposed to be their solution to the problem: to boldly make a noun to be an adjective. Now, let’s assume for a moment that this analysis of “theos” is faithful to Greek grammar and that this analysis of Modern English “God” is faithful to English grammar and pragmatics. Okay, so John 1.1 may as well be rendered “...The Word was divine”--but so what? One could also aptly use the word “divine” in speaking of the attributes or properties that God has--God has divine properties of omniscience, omnipotence, etc. Those properties are divine, yet those properties’ being divine do not make them to be as great as the Father; so what follows is that Jesus’ being divine (in the sense of the word in question) do not necessarily make him to be equal with the Father or as great as the Father, despite the whole intention of Christian apologists in drawing attention to the idea of a predicate noun in the first place. What this means, in turn, is that the possibility that John expresses the proposition in John 1.4 that the Word is the one god that exists does remain; likewise, it follows that Christians perhaps unwittingly and unintentionally do contradict themselves with regard to the doctrine of the Trinity.

Yet there is another attempt at a solution to the problem raised by the nature of the identity relation. I have actually seen people equivocate and use four-term fallacies in order to save face for popular, contemporary emphases on the doctrine of the Trinity which revolve around sentences like “The Father is God, the Son is God...but the Father is not the Son.” I have actually seen people argue like this:

(1) I am human.
(2) Billy Graham is human.
(3) But I am not Billy Graham.
(4) So it is possible for two distinct objects to be human.
(5) So by analogy, it is possible for two distinct objects to be God.


The argument involves and depends on equivocation. It’s understood by rules of common parlance that “to be God” is a grammatical construction formed with the equative copula “be” and the noun “God.” Yet it is also understood that “to be human” involves the use of an adjective (not to mention the predicate “be”). (Compare: “To err is human.”) So the argument depends on a false analogy.

Yet there is a similar argument:

(1) I am a human.
(2) Billy Graham is a human.
(3) But I am not Billy Graham.
(4) So it is possible for two distinct objects to be a human.
(5) So by analogy, it is possible for two distinct objects to be God.


More or less of a four-term fallacy. One knows good and well for there to be an analogy, the contestant has to go all the way to say what he did not have the courage to say; if premise (4) is to stand, and if the argument is to be valid, then premise (5) must be changed as follows:

(5′) So by analogy, it is possible for two distinct objects to be a god.

So what the argument would end up suggesting, in a modified form, is that the Father is a god, the Son is a god, and that the Father is not the Son. Okay, so how many gods are there, anyway? Answer: one. But that means that the Father is the one god that exists, and that the Son is the one god that exists, and consequently that the Father is the Son, a proposition which Christian apologists try avoid.

Yeah, such are the pitfalls of trying to mix and dabble with all the different functions and meanings of the verb be (which are listed in any decent dictionary, though perhaps not the more recent usage which even makes “be” to mean cost in certain contexts). The attempts really do not seem to work.

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Finally, one last problem with the attempt to render “God” as a predicate noun when Christians say “The Father is God, the Son is God...but the Father is not the Son.” Presumably, they base their believe that F and S = G on the Scriptures themselves. Well, guess the Scriptures have to say about this matter of predicate nouns: they suggest that the premise of the predicate noun cannot save the day. Consider the following:

26 And after eight days again his disciples were within, and Thomas with them: [then] came Jesus, the doors being shut, and stood in the midst, and said, Peace [be] unto you. 27 Then saith he to Thomas, Reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust [it] into my side: and be not faithless, but believing. 28 And Thomas answered and said unto him, My Lord and my God. 29 Jesus saith unto him, Thomas, because thou hast seen me, thou hast believed: blessed [are] they that have not seen, and [yet] have believed. (John 20.26-29, KJV)

Simon Peter, a bondservant and apostle of Jesus Christ, To those who have obtained like precious faith with us by the righteousness of our God and Savior Jesus Christ: (2 Peter 1.1, NKJV)
Apparently, Jesus is denoted by the word “God” in each passage. And the word “God” in these passages clearly are neither adjectives nor predicate nouns. To the contrary, this word is clearly used as a token of the identity relation in these passages.

So, score one for the Oneness Pentecostals or other naysayers in this case, because up to a certain point they are correct on this issue: contemporary expressions of the doctrine of the Trinity do have a problem. Of course, that is not to say that the problem cannot be explained away, but equivocation, four-term fallacies, and false analogies are no legitimate means of making the problem go away.

Saturday, October 10, 2009

Powerless Powerful People

2 Timothy 2:13: “If we believe not, [yet] he abideth faithful: he cannot deny himself.”

If it is fair for the apostle Paul to blur identities here, as if the Head of the body of Christ were identical with the parts of the body, then up to a point perhaps it is fair for us to do the same. That is, if Christ cannot deny himself, then his self probably cannot deny him. Consequently, particular apostasy--in this case, a repudiation of Christianity--probably is not possible for those in whom the seed of God and the Spirit of God dwells.

Meanwhile, even if one can produce biblical exhortations or warnings that one not succumb to even this sort of apostasy, this doesn't necessarily prove that such apostasy is possible of believers. I go back to what Dr. John Martin Fischer was telling us once in class. Someone once explained to him (and I paraphrase): Look, even if determinism is true and your visiting a particular restaurant later tonight is determined, it’s still not going to happen unless you (intentionally) get up and go there.

God keeps his people safe, but God is also a God of means. And this means that you should not be surprised if God were to accomplish his ends through reminders of what would happen if two links in the causal chain were to be removed.

Friday, October 02, 2009

Second Juxtaposition

The following set harkens back to http://bright-idea.blogspot.com/2009/09/juxtaposition.html, but it also presents its own challenge:

Revelation 2.20: “Notwithstanding I have a few things against thee, because thou sufferest that woman Jezebel, which calleth herself a prophetess, to teach and to seduce my servants to commit fornication, and to eat things sacrificed unto idols.”

1 John 3.9: “Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.”

The challenge for biblical inerrantists is to come up with a truly plausible explanation of the seeming contradiction. The challenge for errantists includes this and their civil obligation to give the benefit of the doubt and not to jump the gun. Any thoughts?

Friday, September 18, 2009

Juxtaposition

Regeneration does not guarantee instant moral infallibility. Nevertheless, it apparently does come with limits:

1 John 3.15: “Whosoever hateth his brother is a murderer: and ye know that no murderer hath eternal life abiding in him.”

Revelation 2.20: “Notwithstanding I have a few things against thee, because thou sufferest that woman Jezebel, which calleth herself a prophetess, to teach and to seduce my servants to commit fornication, and to eat things sacrificed unto idols.”

More could be said on this subject.