FORMAL LOGIC -- Justifying that Initial Premises are TRUE

[2PhiloVoid]

Then, we have accomplished SOMETHING.

We have identified a possible source (a methodology) that makes us
come to different Conclusions.

This is important, in Christian Apologetics, in which some discussions
never identify why 2 people are coming to different Conclusions.

The problem here is that there is no "one, singular" epistemic method emerging by way of some implicit necessity in any of this. It seems you allude to the notion that there is such a singular method to be discovered, but I don't think there really is one. In fact, my original question in my previous post was given to imply that there are mulitiple methods, frameworks, worldviews, and praxes which all vie for a place at the table of conversation.

And, what's more, I'll aver that none of these can systematically and decisively take us directly to God. There is no "Path of Pure Logic" by which to recognize and thereby reach God.

There is only human Being and Exploring ... and we each to this as best we can.

THEN, we can argue the reasons why we hold to the method of justifying
what is True. And this, is making progress.

I don't know about how much progress is being made. On my part, I'm going to agree with Ralph Baergen's general conclusions in his book, Contemporary Epistemology, (1995). In other words, while I certainly respect those who attempt a sort of modernized Cartesian approach to the Christian Faith, I lean much more toward the notions bound up in a modernized version of Blaise Pascal and Soren Kierkegaard, one which takes into account the fragmentary, partial, and imperfect historical delivery of the Gospel message of Jesus.

And this is where I think we are at: in the mire of life, attempting to pull ourselves up out of the mire by our own thick lock of logical hair (ala Baron Munchausen).

 

[Stephen3141]

Example 4: Camels and Definitions

Arguments may include multiple definitions and justifications, that
different people may NOT agree on. Consider...

Dood1: "Today is Wednesday, so it is hump day"
"A camel has 1 hump, in the middle of its back, so Wednesday is
the hump day of the week."
Dood3: "If it were Thursday, then your statement would be false.
Your statement is not globally True, through all time.
Dood1: "I'm only addressing Wednesdays, so my statement is globally True."

Dood2: "Every week has 2 hump days.
So you're both wrong."

Dood1: "And so, how is my assertion wrong?"
Dood2: "My camel is a Bactrian camel with 2 humps"
"So, Tuesdays and Thursdays are hump days"

So, I guess that "Either Tuesday, Wednesday, or Thursday is hump day"
should be the global rule.

 

[partinobodycular]

A rule with embedded exceptions, is a rule.
It's not (by some definition) a faulty rule.

It's the difference between saying
"Every human being is not ME."
and
"Every human being without my unique definition of personhood, is not me."

The first is a flawed rule.
The second rule, that includes 1 exception, is a True rule.

I agree that a rule with embedded exceptions is a rule. It just seems to render the whole concept of rules useless, because one can embed a rule with as many exceptions as they want. I think that we should have a rule that states that rules can't have exceptions, and if a rule can't be formed in any other manner then it's not a True rule, and one would need to restate it in a manner that didn't require exceptions.

So, rule No. 1: Rules can't have exceptions, because to allow exceptions is to render rules useless.

 

[essentialsaltes]

So, rule No. 1: Rules can't have exceptions, because to allow exceptions is to render rules useless.

Oh, but these clever philosophers will just start making new definitions.

A squobble is a mammal that is not a monotreme.

P: All squobbles bear live young.

 

[partinobodycular]

A squobble is a mammal that is not a monotreme.

I don't have a problem with this. It's like differentiating between alligators and crocodiles. They're demonstrably different, but they're both crocodilians. You just start by defining crocodilians such that they both qualify, and then subdivide from there. In the case of the platypus the problem would seem to lie in the definition of a mammal... the platypus doesn't fit, so rather than make an exception for it simply redefine what it means to be a mammal, removing the reference to live young, and then subdivide from there into those that give birth to live young and those that don't. Problem solved, the platypus fits naturally into the category of mammals with no need for exceptions.

 

[Stephen3141]

I agree that a rule with embedded exceptions is a rule. It just seems to render the whole concept of rules useless, because one can embed a rule with as many exceptions as they want. I think that we should have a rule that states that rules can't have exceptions, and if a rule can't be formed in any other manner then it's not a True rule, and one would need to restate it in a manner that didn't require exceptions.

So, rule No. 1: Rules can't have exceptions, because to allow exceptions is to render rules useless.

The problem with what you want, with human language, is that we sometimes do not have
human words to describe all the sets of things that we wish to talk about.

What we are doing, in writing rules, is asserting that some "outcome" (at the tail
of a rule) follows logically whenever the input conditions (in the head of a rule)
are met. That is, rules are conditional assertions. The tail of the rule is
asserted, if the condition(s) in the head of a rule are met.

The same is true in conditional statements in a computer language. We do not
demand that these computer "rules" must have a conditional expression that
only includes one simple group description. Conditions may include logical ANDs, ORs and NOTs,
in order to specify very precise sets of things to which the rule applies.

the Bible includes many statements that include exceptions. A common way
of defining an exception is human language is by using "... and not ...."

 

[Stephen3141]

(By the way, I am using an informal label of "rule" for a material implication.
Material implications can have complex parts, both in their head, and in
their tail.

The head and the tail of a material implication, can be any valid proposition
that is expressed in logical notation.

Whether or not a specific material implication is globally True, or not,
does not depend on whether the head or the tail of the implication
is Simple.

Some groups of things, require complex expression to define.)

 

[SavedByGrace3]

I propose a thread that will discuss ways to "justify" (the philosophical term)
that the initial premises used in an argument, are TRUE.

I propose this subject, because ...

1 Most of what I would call errors in arguments used by Christian
involve differences in basic definitions (premises).

2 The way in which we try to justify our initial premises, often
include appeals to authorities. What authorities we are appealing
to, is often left out of the arguments.

3 The anti-intellectual Christian traditions appeal to VERY different methods
of identifying authorities, than the Christian groups that are assuming that
formal reasoning methods are part of our shared reality (and so should be
used in Christian apologetics.

4 In Christian apologetics, we should try to explain WHY Christians hold
certain premises, in their arguments. This is part of explaining the
Christian faith.


I think that this topic would be VERY interesting, and reveal VERY different
approaches to dealing with the topic of truth, among different Christian
groups.

Your list is correct. No progress can be made unless all participants agree on a set of foundational truths. When it comes to matters of faith, this is impossible. Why? Because faith is the evidence of things not seen. There will be no agreed-upon foundational truth because it cannot be seen and, hence, is unprovable to your opponent. I have ceased trying to convince an unbeliever using "scientific" truth. They will not be convinced. People are saved by faith, that is, belief in the unprovable. So, while I enjoy discussing these things with anyone who wants to, I never expect them to be convinced using debatable logic.

 

[Stephen3141]

Your list is correct. No progress can be made unless all participants agree on a set of foundational truths. When it comes to matters of faith, this is impossible. Why? Because faith is the evidence of things not seen. There will be no agreed-upon foundational truth because it cannot be seen and, hence, is unprovable to your opponent. I have ceased trying to convince an unbeliever using "scientific" truth. They will not be convinced. People are saved by faith, that is, belief in the unprovable. So, while I enjoy discussing these things with anyone who wants to, I never expect them to be convinced using debatable logic.

I think, in this thread, that I am presenting information that is a bit different than what you are talking about.

The initial definitions/rules in a proof, must be "justified" (demonstrated to be True)
or else, the proof will be about "some other world" than the one we live in.

We DO reason about systems of beliefs (initial premises) that are NOT the way our
shared reality works, in order to reason about alternative possibilities (than the reality that
we observe).

It is POSSIBLE, sometimes, for people who start with different sets of information,
to end up at the same conclusion. for example, 2 different police detectives, starting
with different sets of evidence, finding the same person who committed a crime.

BUT, among Christians (this is a christian apologetics site), the Bible presents a
coherent and unified picture of our shared reality. And so, all Christians, if they
want to be reasoning within a Christian worldview, SHOULD BE starting with the
same initial premises.

Differences in theologies among Christian groups, may be due to many reasons...
1 Different concepts of authority (and so, different appeals to what is an authority)
2 Different concepts of how the Bible is to be interpreted
3 Theologies that are built from partial biblical foundations (instead of on the
entire witness of Scripture, on a topic)
4 Theologies that extend the teaching of Scripture, to form theologies that may
be coherent to an individual, but overstate what Scripture teaches
5 Theologies that are built on dysfunctional interpretations of Scripture
6 theologies that are forced on Scripture, because of a person's idea of
who God OUGHT to be, instead of Scriptural evidence about who God IS
(hard determinism in Calvinism, that erases human free will, is one of these:
God is LOVE, he is only LOVE is another: another weird expectation is that
God only is concerned with forgiving our sins, and not saving our entire life
and being).

As for faith, anti-intellectual Christian groups (and individuals) like to define
"faith" in an anti-intellectual way. That is, trust without evidence for that trust.
But "faith" in the Bible, has always included the evidence that we can directly
and indirectly observe. The faith once for all delivered to the saints, is a body
of evidence. Some have faith/trust in God with little evidence. Some have faith
in God with a lot of evidence. Trying to characterize "faith" as a response that
is without evidence, is a mistake. It is not biblical.

1 What was from the beginning,
what we have heard,
what we have seen with our eyes,
what we looked upon
and touched with our hands
concerns the Word of life—
2 for the life was made visible;
we have seen it and testify to it
and proclaim to you the eternal life
that was with the Father and was made visible to us—
3 what we have seen and heard
we proclaim now to you,
so that you too may have fellowship with us;
for our fellowship is with the Father
and with his Son, Jesus Christ.
New American Bible, Revised Edition. (Washington, DC: The United States Conference of Catholic Bishops, 2011), 1 Jn 1:1–3.

 

[essentialsaltes]

(this is a christian apologetics site)

You've said this a couple times now, but you might consider going easier on the A word. Although there used to be forums on Philosophy, Formal Debate and Christian Apologetics, they have all been shut down by the Powers That Be (although they exist in Read Only mode). (see also item #3 in the Guidelines)

 

[Stephen3141]

You've said this a couple times now, but you might consider going easier on the A word. Although there used to be forums on Philosophy, Formal Debate and Christian Apologetics, they have all been shut down by the Powers That Be (although they exist in Read Only mode). (see also item #3 in the Guidelines)

What "A" word are you referring to?
I have no idea what you are asserting, if you start to use some sort of custom shorthand.

 

[essentialsaltes]

A nod's as good as a wink to a blind horse.

 

[Stephen3141]

Because of some unexpected comments that I am getting on this thread,
that seem to hint that Christian apologetic content is not appreciated on
a philosophical thread, I will clearly repeat what I have said before in the
2 Formal Logic threads that I am writing...

1 Valid Reasoning methods are part of our shared reality
2 Deductive logic is a subset of valid reasoning methods
3 Modern Formal Logic sums up all previous valid deductive logic operations
(modern formal logic is "complete", in logical language)
4 Modern Formal Logic rules of inference address ONLY the syntax of
arguments/proofs. There is nothing radical in this truth.

However,

5 In previous centuries, back to the original Greek philosophers,
there was a big concern over using initial premises in an argument/proof,
that were justified as being True.
6 Christians, in their use of formal logic, MUST be concerned about
using initial premises that are justified as being TRUE.
7 Non-Christians, in their use of formal logic, MUST be concerned with
using initial premises that are justified as being TRUE.
8 Formal Logic arguments/proofs that use False initial premises,
produce Conclusions that are Unsound. These proofs are useless.

Therefore, it is vital for both Christians and non-Christians to carefully
examine their initial premises (assertions, and rules) in order to justify
them as being True. This is not a uniquely Christian concern.

9 One common approach for trying to justify initial premises as True,
is to demonstrate that they work in "our shared reality" (my wording).
10 Models in the hard sciences, MUST work in our shared reality.
11 Moral-ethical assertions MUST work in our shared reality.
12 A fair rule of law, and concepts of evidence, and the definition of
Justice, must work in our shared reality.
13 Further, the Bible presents a picture of our shared reality, that is
very consistent. This concept of reality and evidence and how we perceive
evidence, is not particularly "theology". This picture of our shared reality
is upstream of formal theology.
Therefore, discussing aspects of our shared reality, that are important
for justifying whether or not initial premises are TRUE, I do not consider
to be theology.
14 Therefore, I do not consider that what I am doing in the Formal Logic
thread (on justifying whether initial premises are True), to be theology.

15 Although the discussion of topics vital to "Our shared reality" is VERY
relevant to Christian belief and practice, and although my discussion of this
topic is very compatible with Christianity, this approach to describing our
shared reality is not uniquely Christian. It is the approach of the philosophical
school that is often called the "Scottish Realists". I am following the thinking
of Thomas Reid, who was a mild foundationalist. Reid is used as an example
of the Scottish Realists in the book "Epistemology: Becoming intellectually
Virtuous" by W. Jay Wood, InterVarsity Press Academic, 1998. Find Reid's
approach discussed in this book, in pages 96-.

For those who are offended that I DO mention some topics that are part
of Christian belief, I point out that there are "highways" of connections
between the concept of our shared reality, and moral-ethical systems.

Such as...

There are multiple components in our shared reality (I assert). And the Bible
presents bearing false witness (misrepresenting our shared reality) as
LYING. This is a serious sin in Christianity.

Abstract concepts are part of our shared reality. "Ownership" is an abstract
concept that is part of our shared reality. But "ownership" is not something that
can be identified by the hard sciences. However, God commands "You shall not
steal", so we see that God affirms that there are abstract concepts in our
shared reality.
---------- ----------

Although it is possible that ANYONE may claim that this thread is infringing
on theology, I am writing this thread dealing with a common view of our
shared reality. And this view, while compatible with Christianity, is not
particularly uniquely Christian. And most of my considerations, even if I
do quote Scripture, are upstream of formal theology.

Perhaps those who do not read philosophical books on Epistemology, or who
come from an anti-intellectual background, may misunderstand this thread
as infringing on theology.

Also, I add, that arguments for Christianity that come from non-uniquely
Christian subject matter, should not be excluded from discussion, in
the philosophical part of this web site.

 

[public hermit]

Because of some unexpected comments that I am getting on this thread,
that seem to hint that Christian apologetic content is not appreciated on
a philosophical thread, I will clearly repeat what I have said before in the
2 Formal Logic threads that I am writing...

1 Valid Reasoning methods are part of our shared reality
2 Deductive logic is a subset of valid reasoning methods
3 Modern Formal Logic sums up all previous valid deductive logic operations
(modern formal logic is "complete", in logical language)
4 Modern Formal Logic rules of inference address ONLY the syntax of
arguments/proofs. There is nothing radical in this truth.

However,

5 In previous centuries, back to the original Greek philosophers,
there was a big concern over using initial premises in an argument/proof,
that were justified as being True.
6 Christians, in their use of formal logic, MUST be concerned about
using initial premises that are justified as being TRUE.
7 Non-Christians, in their use of formal logic, MUST be concerned with
using initial premises that are justified as being TRUE.
8 Formal Logic arguments/proofs that use False initial premises,
produce Conclusions that are Unsound. These proofs are useless.

Therefore, it is vital for both Christians and non-Christians to carefully
examine their initial premises (assertions, and rules) in order to justify
them as being True. This is not a uniquely Christian concern.

9 One common approach for trying to justify initial premises as True,
is to demonstrate that they work in "our shared reality" (my wording).
10 Models in the hard sciences, MUST work in our shared reality.
11 Moral-ethical assertions MUST work in our shared reality.
12 A fair rule of law, and concepts of evidence, and the definition of
Justice, must work in our shared reality.
13 Further, the Bible presents a picture of our shared reality, that is
very consistent. This concept of reality and evidence and how we perceive
evidence, is not particularly "theology". This picture of our shared reality
is upstream of formal theology.
Therefore, discussing aspects of our shared reality, that are important
for justifying whether or not initial premises are TRUE, I do not consider
to be theology.
14 Therefore, I do not consider that what I am doing in the Formal Logic
thread (on justifying whether initial premises are True), to be theology.

15 Although the discussion of topics vital to "Our shared reality" is VERY
relevant to Christian belief and practice, and although my discussion of this
topic is very compatible with Christianity, this approach to describing our
shared reality is not uniquely Christian. It is the approach of the philosophical
school that is often called the "Scottish Realists". I am following the thinking
of Thomas Reid, who was a mild foundationalist. Reid is used as an example
of the Scottish Realists in the book "Epistemology: Becoming intellectually
Virtuous" by W. Jay Wood, InterVarsity Press Academic, 1998. Find Reid's
approach discussed in this book, in pages 96-.

For those who are offended that I DO mention some topics that are part
of Christian belief, I point out that there are "highways" of connections
between the concept of our shared reality, and moral-ethical systems.

Such as...

There are multiple components in our shared reality (I assert). And the Bible
presents bearing false witness (misrepresenting our shared reality) as
LYING. This is a serious sin in Christianity.

Abstract concepts are part of our shared reality. "Ownership" is an abstract
concept that is part of our shared reality. But "ownership" is not something that
can be identified by the hard sciences. However, God commands "You shall not
steal", so we see that God affirms that there are abstract concepts in our
shared reality.
---------- ----------

Although it is possible that ANYONE may claim that this thread is infringing
on theology, I am writing this thread dealing with a common view of our
shared reality. And this view, while compatible with Christianity, is not
particularly uniquely Christian. And most of my considerations, even if I
do quote Scripture, are upstream of formal theology.

Perhaps those who do not read philosophical books on Epistemology, or who
come from an anti-intellectual background, may misunderstand this thread
as infringing on theology.

Also, I add, that arguments for Christianity that come from non-uniquely
Christian subject matter, should not be excluded from discussion, in
the philosophical part of this web site.

I hear you saying we can secure the truth of premises in a "shared reality." What are the main features of this reality that we share? Are they primarily transcendent features like *justice* and *ownership* (your examples)? You seem to be saying there is a pragmatic aspect to justification related to how our shared reality works so that it allows for widespread agreement (so long as we're honest?).

Can you label this approach to justification? Is it a soft form of foundationalism with pragmatic sprinkles? Is it grounding the justification of premises in the coherence of our shared reality?

Pragmatically speaking, when it comes to the truth of premises, what matters is agreement. Agreement is the indication of a sound premise. And, if we all agree the premises are true, then so long as the argument is valid, we are likely all going to agree on the conclusion. Agreement does all the heavy lifting. Unfortunately, agreement does not secure the truth of p if we assume a correspondence view of truth or want some chain of inference/justification, but perhaps widespread agreement makes p more likely than not.

Maybe pragmatic indicators of our shared reality and the true premises it might entail are those areas where there is widespread agreement? The likelihood of p is proportional to the widespread agreement that p enjoys among the relevant epistemic agents. Certainly, the less the agreement, the less it is a feature of our shared reality.

 

[zippy2006]

I agree that a rule with embedded exceptions is a rule. It just seems to render the whole concept of rules useless, because one can embed a rule with as many exceptions as they want. I think that we should have a rule that states that rules can't have exceptions, and if a rule can't be formed in any other manner then it's not a True rule, and one would need to restate it in a manner that didn't require exceptions.

So, rule No. 1: Rules can't have exceptions, because to allow exceptions is to render rules useless.

The first thing to note is that rules do not have embedded exceptions. If a rule accounts for an outlier case, then that outlier case is not an exception to the rule. Rules and exceptions are inherently contrary, as you have noted. If something does not conflict with a rule, then it is not an exception.

The second thing to note is that the meaning of a proposition derives from the intention of the speaker. When a mathematician says that "2 + 2 = 4," he is positing an exceptionless rule. When a legislator says, "You cannot perform medical operations on another person without their consent," he is positing a rule with exceptions, for we allow exceptions to this rule in certain cases, such as when the person is unconscious and in dire need of aid.

 

[Stephen3141]

I hear you saying we can secure the truth of premises in a "shared reality." What are the main features of this reality that we share? Are they primarily transcendent features like *justice* and *ownership* (your examples)? You seem to be saying there is a pragmatic aspect to justification related to how our shared reality works so that it allows for widespread agreement (so long as we're honest?).

Can you label this approach to justification? Is it a soft form of foundationalism with pragmatic sprinkles? Is it grounding the justification of premises in the coherence of our shared reality?

Pragmatically speaking, when it comes to the truth of premises, what matters is agreement. Agreement is the indication of a sound premise. And, if we all agree the premises are true, then so long as the argument is valid, we are likely all going to agree on the conclusion. Agreement does all the heavy lifting. Unfortunately, agreement does not secure the truth of p if we assume a correspondence view of truth or want some chain of inference/justification, but perhaps widespread agreement makes p more likely than not.

Maybe pragmatic indicators of our shared reality and the true premises it might entail are those areas where there is widespread agreement? The likelihood of p is proportional to the widespread agreement that p enjoys among the relevant epistemic agents. Certainly, the less the agreement, the less it is a feature of our shared reality.

Good questions.

I will repeat what I wrote on another apologetics site, with some modifications. I believe that I list some components of our shared reality, in the thread Formal Logic.

---------- ----------
July 10th, 2023 (c)

I would assert that the Bible (and Church doctrine) strongly connects the Bible's concept of what "our shared reality" is, and the concept of bearing true witness, or the opposite, of bearing false witness (lying).

What is it that we bear false witness about? Our shared reality.

What is it that we could bear FALSE witness about? Our shared reality.
LYING is important in the Jewish and Christian moral-ethical system, BECAUSE lying can get us condemned at the final judgment. (!!!)
Lying is a false representation of our shared reality. This means that Christians need to be VERY clear about what our shared reality, is.

Because God holds us responsible for lying, this means that it was possible for us to observe accurately what our shared reality is.

North American Christians have not done a good job of teaching about our shared reality, from the biblical point of view. Some of the parts of our shared reality are:

-- the physical universe
-- biological life
-- valid reasoning methods
-- God
-- abstract ideas (such as ownership)
-- God's moral-ethical code
-- virtues and vices
...

Note that some people are not careful about carefully observing what our shared reality is. We see this is a lot of activities:

-- slander: speaking lies about someone
-- gossip: passing on information that we do not know is true (this is what a lot of talk shows do)
-- accepting speculation or guessing, without carefully searching out whether the speculation is true. This is what passing on conspiracy theories, does.
-- Not accepting the methods of valid reasoning. This is what the anti-intellectual Christian groups do. They reject formal logic, and call it "vain philosophies". But, careful thinking has always been promoted by the Bible.
-- Not accepting valid methods of reasoning, also undercuts the study of how the biblical authors use human language. And how human language can express many different things, using different styles of writing.
-- Not accepting that there can be accurate historical writing.
-- Not accepting that there can be a fair rule of law. Note that a fair rule of law is based on evidence, which is observations about our shared reality, and honest testimony from people who observed this reality.
-- Without a fair rule of law, and strict rules on evaluating evidence, we can never have justice, from a legal process.
---------- ----------

As far as Epistemology, I am attracted to the soft Foundationalism. But,
I sympathize with Coherentism, but not as standing alone as a principle to justify
beliefs as True. (see the quotes from Wood). One truth cannot be contradictory to
another truth (formal logic is based on this), so truths in our belief system should
cohere together.

I also agree with Wood that the intellectual virtues are needed, in order to
have sound thinking. Without developing the mind, we will not properly
grasp "valid reasoning" methods. which I think are a component in our
shared reality.

NOTE: I explicitly point out the relevance of this approach to our shared
reality, by pointing out that the biblical sin of LYING, must be misrepresenting
SOMETHING dealing with our shared reality (unless we are lying to god, about
some event that only I perceived). So, the biblical concept of bearing false witness,
requires Christians to deal with the concept of our shared reality (even though
many Christians, have blown off this logical requirement).

Also, the concept of Ownership is an abstract concept (that is undetectable by
the hard sciences, in the object being owned). And because ownership is a
big thing in a fair rule of law, and the 10 Commandments, this means that
Christians must EXPLICITLY include "abstract concepts" in the components of
our shared reality.

I include the concept of "justice", because it is grounded in a fair rule of law,
God's moral-ethical law, and a shared concept of what reality is.


So, when I address how to justify our personal beliefs as True, I MUST
deal with topics that tie directly to core Jewish and Christian beliefs,
about reality. This is not "doing theology", but the nature of reality
impacts all sorts of disciplines, for Christians and non-Christians.

Also, thinking in a focussed way about the particular COMPONENTS
of our shared reality, starts to point out why some denominational theologies
or "trends" are dysfunctional. (Although this is a subject that can be seen
as emotionally explosive, it is a necessary follow-on to debating what our
shared reality is. And, I discuss the topics, philosophically.) Especially,
if we agree that "valid reasoning methods" are part of our shared reality,
THEN we must say that being systematically anti-intellectual is a form
of lying about our shared reality. This directly connects dysfunctional
reasoning, and the perpetuation of dysfunctional reasoning, with the
Christian sin of lying.

I do not know how much thinking it will take, for a younger generation
American Christian to put together this approach to our shared reality, with
formal logic rules of inference, and the justifying of initial premises as
True. It may take a year. I wrote an entire book about it, and published it in
2020 with Dorrance Publishing. And I have been studying systems of logical
notation for 35 years, so this sort of synthesis of formal logic and philosophy
and moral theory is not new to me. BUT, I admit, that this synthesis (which
I present in the book) does not come easily. Because American Christians
have not cultivated a renewed mind, as the Apostle Paul commands.

Think about these ideas for a month.

 

[Stephen3141]

The first thing to note is that rules do not have embedded exceptions. If a rule accounts for an outlier case, then that outlier case is not an exception to the rule. Rules and exceptions are inherently contrary, as you have noted. If something does not conflict with a rule, then it is not an exception.

The second thing to note is that the meaning of a proposition derives from the intention of the speaker. When a mathematician says that "2 + 2 = 4," he is positing an exceptionless rule. When a legislator says, "You cannot perform medical operations on another person without their consent," he is positing a rule with exceptions, for we allow exceptions to this rule in certain cases, such as when the person is unconscious and in dire need of aid.

You're wrong on this.

In formal logic, a rule (material implication) defines 2 sets of things
(the Head of the rule, and the Tail of the rule).

In defining sets, we can use any simple or complicated condition we
wish.

You may not be familiar with a formal logic concept of a rule/material implication.
But for those who are, this definition of "rule" is not novel or objectionable.

(I think that you are arguing, using the English sense of "rule", not the formal
logic concept of a material implication.

 

[partinobodycular]

North American Christians have not done a good job of teaching about our shared reality, from the biblical point of view. Some of the parts of our shared reality are:

-- the physical universe
-- biological life
-- valid reasoning methods
-- God
-- abstract ideas (such as ownership)
-- God's moral-ethical code
-- virtues and vices

I would grant you the first two, (With a caveat) but not a single one of the others. Yes, we all understand the concept behind the others, but we don't share a universal viewpoint on what the others entail. For example, to some people God is an actual being, but to others He's just a myth. Two completely different things.

 

[2PhiloVoid]

I would grant you the first two, (With a caveat) but not a single one of the others. Yes, we all understand the concept behind the others, but we don't share a universal viewpoint on what the others entail. For example, to some people God is an actual being, but to others He's just a myth. Two completely different things.

And sometimes, even among Christians who supposedly share a reality, God is still the proverbial Elephant in the Room.

Somehow, "Logic" is going to help us sort out which parts of the Elephant are which. I guess the effectiveness of this expectation depends on the extent to which we think our analogies, like our proverbs, are substantive enough for Logic to actually make clear and distinct incisions so we can parcel God out like so much meat to the market.

Epistemology is a wonderful thing, ain't it?

 

[zippy2006]

You're wrong on this.

In formal logic, a rule (material implication) defines 2 sets of things
(the Head of the rule, and the Tail of the rule).

In defining sets, we can use any simple or complicated condition we
wish.

You may not be familiar with a formal logic concept of a rule/material implication.
But for those who are, this definition of "rule" is not novel or objectionable.

(I think that you are arguing, using the English sense of "rule", not the formal
logic concept of a material implication.

I am not unfamiliar with it, you are. The parts of a consequence are not called "the head of the rule" and "the tail of the rule," they are called the antecedent and the consequent (or in more antiquated language, the protasis and apodosis). A material implication is simply one kind of consequence.

You are making things up again, but the things you are making up have no bearing on the issue at hand. A condition that is added to a rule is not an exception (to the rule).