FORMAL LOGIC

[Stephen3141]

On Logical Causation, and Conspiracy Theories
---------- ----------

Note that there are common trends in American society, that
tend to raise our gullibility to Conspiracy Theories. Such as...

1 All those nature videos, that show videos of animal behavior,
and "explain" it as if the animals were human beings, making the
best rational choices that any human being could make.

Much of this animal behavior, is presented as much more intelligent than
the behavior of most human beings.

The "explanations" of this animal behavior, is often VERY specific to the
behavior that is being filmed. BUT, while this explanation may fulfill the
concept of Modus Ponens, it does not explore all alternate animal behaviors, in the
same situation, in which other outcomes happen. The Modus Tollens test of
animal behavior "rules" is not examined. And so, the behavior is not logically
being proven to follow logical causality.

2 We know that there are hundreds of characteristics that an individual human
being can have. And yet, it is common in many situations (such as news stories),
to act as if only a very limited list of possible characteristics are determining the
outcome of the story. And this limited list is VERY biased: race, sex, culture, and
"minority" or "majority" group membership.

This is like dictating that only a few facts, can be used in the Assumptions
part of a proof. This is a serious misunderstanding of the complexity of
our shared reality.

3 There is a trend that given a specific action by someone, they MUST have had
a very specific motivation/purpose. In reality, for a single action, there could
potentially be hundreds of individual motivations possible. This is another
misunderstanding of CAUSALITY.

4 Note that those doing the "explaining" in American society, often
ARBITRARILY change their assumed list of relevant characteristics, or
short list of possible causes of an event, or their assumed motivation
that is imputed to someone doing an action.

These modern "explanations" of why someone did something, often is
more like a Conspiracy Theory, than a logical presentation of the complexity
of human behavior.
---------- ----------

As an exercise, go to the Google news page, and read multiple news
stories about the same event, from different news sources (this is
how the Google news site is organized). Do the descriptions of the
event match each other? Do the writers about the same event, think
that the relevant topics associated with the event are the same? With
a lot of these stories, you may think that they are trying to describe
different events? Do the authors of these stories, explain what their
own interests are, in promoting?

---------- ----------

In contrast to the Google news page, think about how the Bible
presents our shared reality...

1 We all live in the same shared reality
2 bearing false witness about this shared reality, is called "lying"
3 Lying is a very serious sin, in Christianity
4 Lying, in Christianity, can keep us out of the kingdom of heaven.

Consider how the Christian definition of lying, requires a view of our shared reality
that is VERY different than the modern American approach of creating some
"Explanation" that is emotionally appealing, includes arbitrary aspects of reality,
and is cut free of a rigorous justification of assertions that form the "explanation".

Note how the Christian concept of lying, is much more compatible with the
formal logic approach of trying to justify a personal opinion (using our
shared reality), than are the spinners of Conspiracy Theories.

Note that the Christian moral-ethical model is MUCH more interested in
determining real logical CAUSALITY, than is the modern culture of
Conspiracy Theories.

 

[Stephen3141]

On Logical Causation, and the logical "fallacy" "Appeal to Authority"

---------- ----------

(This is a thread on Formal Logic...)

"Appeal to Authority" is an ancient "logical fallacy".
To rephrase it in modern symbolic logic, reveals that it is not a precise fallacy.

A modern proof has different sections to it:

1 Assumptions: statements of assumed facts and causal relationships
2 Body of the proof: each step must be justified by a formal Rule of Inference (listed above in the thread)
3 Conclusion: If the Conclusion (logically) follows from the Assumptions,
then the proof in "logically valid".
---------- ----------

The "Appeal to Authority" is usually invoked, when a person thinks
(asserts) that one or more go the Assumptions (a supposed fact, or a
supposed causal relationship) is NOT authoritative.

This is an assertion that the definition in the Assumptions part of the proof, is NOT
from a justified authority (who knows the subject matter).

If this objection is true, then the proof is "logically unsound".

Appealing to Appeal to Authority (asserting that it applies to some proof/
argument) has a problem. That is, the definition of the "fallacy" does not
include a "decision algorithm" that clearly lays out the process by which
all can decide whether or not one or more of the Assumptions is NOT
warranted.

This means that every Christian (and non-Christian) group that appeals to
this logical fallacy, may assume a different list of who is (or is not) an
authority in the subject matter area that the proof/argument deals with,
and so THERE IS NO AGREEMENT ON WHO IS AN AUTHORITY.

This means that the Appeal to Authority "fallacy" will only be accepted
as a "fallacy", among a homogenous group that completely agrees on who
is an authority, in every possible area of subject matter. Even the Christian
denominational groups, do not have this agreement.

Many different Protestant denominations have their "favorite" commentary,
by their favorite "biblical scholar", that they quote as an "authority" in
some subject matter area. Note that the denominational theologies differ,
as to who is an authoritative biblical scholar. So this approach still has no
decision algorithm.

Note that many Christian groups accept the early creeds of the united Church, as
authoritative statements of Christian doctrine. But some do not. (Obviously,
non-Christians may not accept creeds such as the Nicene Creed, as authoritative.)

Note that a direct appeal to a text of Scripture, in the Assumptions area of a proof,
also has its problems. Some of these problems are...

1 most American Christians don't know the original biblical languages
2 most American Christians who "quote" the Bible, are quoting translations
3 there is the embedded problem of which Bible translations are authoritative,
and so the question of authority is buried and not addressed
4 Most American Christians cannot go to the original language of Scripture, and
justify their initial Assumptions
5 Many American Christians do not use the old-class biblical lexicons, to
quote THEIR definitions of biblical language. They quote their favorite
commentary (which does not solve the authority problem), or a non-professional
definition of a verse (which does not address the authority problem), or they
quote some favorite pastor or teacher (which does not address the authority
problem. Even Christians who appeal to "biblical scholarship" to establish
the assertions in their Assumptions part of a proof, often are NOT quoting authoritative
sources.
6 Many Christians appeal to the direct guidance of the Holy Spirit.
Note that this appeal, also does not include a decision algorithm. All sorts of people
who appeal that the Holy Spirit has guided them in their definitions, will still disagree
in their Conclusions.

It would be better if Christians would appeal directly to the critical Bible study skills,
that deal with the original language of the Scriptures. (This is not demeaning the
guidance of the Holy Spirit, but acknowledging that the Spirit of God normatively
guides us in the study of Scripture, through the critical Bible study skills -- not by
a mystic feeling that we have gotten the right interpretation of a text.)
---------- ----------

It used to be, historically, that the Christian groups that were historically
anti-intellectual had the most problems with (wrongly) applying the Appeal
to Authority fallacy claim. But now, in 2023, most North American Christians
have ditched formal logic, and the critical Bible study skills (Hebrew/Aramaic/koine Greek),
and have replaced them with emotional feelings and rants, or by appeals to the
"diverse" "authority" of native cultures, to serve as the decision algorithm as to
what a valid assertion is in the Assumptions part of a proof.

Although it may seem a bit abrupt, for me to criticize an argument (that appears on a
Christian apologetic site) by saying that the basic definition are wrong, this is necessary
for Christians. We cannot allow ad hoc definitions to be used, as if they were
authoritative.

 

[Stephen3141]

Examples of arguments/proofs that use defective authorities...
---------- ----------

1 Definitions of modern "science" that do not understand what the
scientific definition of terms, are.
2 The use of the word "evolution", without realizing that the modern
scientific definition is based on random mutation, and then
natural selection. All other definitions (or lack of definitions),
are not dealing with scientific concepts of evolution.
3 The confusion of religious theological slogans, with authoritative
facts or causes in the Assumptions part of a proof.
4 The quoting of biblical (English) passages, without a statement
of what you think they MEAN.
5 The use of one biblical passage, as if it represented the combined
testimony of the entire Bible, on a specific topic.
6 The assumption that a biblical text, is in the form of a modern style
of writing (such as history, or science).
7 The assumption that biblical writers MUST HAVE BEEN WRITING in the
modern styles of writing, that we are used to.
8 Deriving meaning s from the Bible, only through translations of the Bible,
without checking out the original biblical language.
9 Picking the WRONG biblical texts, to try to argue about a certain topic.
This is trying to apply a WRONG biblical authority, to a subject.
10 Trying to use a biblical text that asserts "NOT <whatever>" to reason
that the "alternative" option (that the Scriptures do not mention) must be
true. This is an appeal to the modern American expectation of what could
be authoritative options, and is a form of logical fallacy dealing with
believing a wrong authority.
11 Arguments that appeal to emotions, as if they had logical force.
12 Arguments that appeal to native cultural norms, as if they had
authoritative force.

There are probably other types of error, that fall into the broad category
of appealing to "authorities", that are not really authorities.

 

[Stephen3141]

It's interesting how many Christians think that they know what Appeal to Authority
logical fallacy means.

But, when I list many different examples of this fallacy, no one has anything to say!

 

[2PhiloVoid]

It's interesting how many Christians think that they know what Appeal to Authority
logical fallacy means.

But, when I list many different examples of this fallacy, no one has anything to say!

That's "gaslighting" us to respond... it's probably not the best way in which to prompt the rest of us.

 

[Stephen3141]

If you think that I am shooting the bull, when I ask for responses to my list of defective authorities, then provide some demonstration of this.

I am presenting some basic lists of examples of dysfunctional arguments, that do
appear in our experience. I think that this is relevant. I'm surprised that almost no
one in a Christian apologetics site, is bothering to leave their thoughts on these
forms of dysfunctional arguments.

 

[2PhiloVoid]

If you think that I am shooting the bull, when I as for responses to my list of defective authorities, then provide some demonstration of this.

I am presenting some basic lists of examples of dysfunctional arguments, that do
appear in our experience. I think that this is relevant. I'm surprised that almost no
one in a Christian apologetics site, is bothering to leave their thoughts on these
forms of dysfunctional arguments.

Not many people are reading your post, Stephen. Heck, I don't expect people to read 99% of anything I ever post on here. I'm tickled if they even say something once ...

Personally, I have no problem with the use of Logic, formal or informal. I just don't agree with all you've said. I've already said a piece or two about how I view your reliance on Formal Logic earlier on in this thread. I don't think less of you as a fellow Christian, but I simply don't approach either Epistemology or Hermeneutics to Christian Apologetics (or even just the Christian faith in general) the way that you do.

But please carry on, though. Don't let me stop you.

 

[BrendanG]

I have thought of many of the topics that the original poster talked about. My background is in physics though, and I don't have as many years of experience, so it has been hard for me to try to come up with a rigorous moral system. In physics, we don't do math for its own sake; we do it to describe a physical system. We use human words and draw pictures, and then use geometry, algebra, and calculus. So, I often don't understand what mathematicians are talking about when they write full sentences using only mathematical symbols. But I recognize that it is possible to do this kind of thing.

I have only seen this post today, so I've not read many of the comments. I might come back and read more later, because I am interested in this topic.

I have thought these things before:

Logical systems can only apply to physical system when we make the correct sensory assumptions (which in science consists of experimental data). It makes sense then that logical systems can only apply to morals when we make the correct moral assumptions. I had the thought that perhaps a value-bool could be created, which can take the values "good" and "bad". If you have a value-bool, it ought to be possible to use set theory or combinatorial logic on it, right? It may also be necessary to allow the value to be empty/0, in addition to being "good"/"bad". Or maybe you could make an ordered-list of values, or make an arbitrary point system for morality.

For a while, I thought that all moral systems must depend on arbitrary moral premises, since we cannot prove moral assumptions with sense-data (Hume's is-ought) logical fallacy. I do believe I may have found 2 exceptions to this, however.

It appears that only living beings have the experience of "good" and "bad". This is a sensory observation that appears to have moral significance. We can conclude that any moral system that applies to non-living beings has no effect. This does not prove that morals exist, or that a moral system ought to have a material effect, but if we assume that morals do exist (or ought to exist), and that we are only concerned with them having an effect, then we conclude that they must apply to living beings.

Also, it seems to be necessarily true that any moral system which causes the destruction of its adherents is self-defeating, because it will reduce the number of people who practice that moral system. Given freedom in choosing and practicing different moral systems, it makes sense that those moral systems which are best at propagating themselves and at propagating their adherents will become more numerous. Now, this does not prove that self-defeating behavior is bad, but if we assume that self-defeating behavior is bad, then we must conclude that morality must consist in doing good for those that practice the morality.

I think the above 2 observations are a very firm and objective basis for a moral system. I haven't figured out how, but it seems as if it ought to be possible to use value-bools (or some other mathematical construct made to deal with values) to build objective moral statements off this base.

 

[BrendanG]

One of the early posts talks about a basis for ontology/epistomology. I believe I went further than anybody else ever has several years ago in this regard, but I never got anybody (except for one mathematician) to even look at what I wrote.

What I came up with, in summary:

I think Descartes's famous statement, "I think, therefore, I am," is incomplete. We are more than just logic, so basing a metaphysics on our ability to reason is insufficient to build a formal system which can describe all of our experiences. Also, unless you already trust your ability to reason, then his conclusion, "I am" does not follow the premise (because if you do not have faith in logic, then nothing can be derived from anything else).

I believe you need 3 minimum articles of faith to be able to function as a human:
1. Faith that your sensory experience tells you at least some true things about reality. We derive factual information (true/false) from sensory experience.
2. Faith that we have at least some ability to judge systems of logic to be consistent/inconsistent. We judge consistency/inconsistency according to our innate reason.*
3. We must have faith that it is possible to find values that make life seem meaningful and worth living.

*Note that facts and reason are very different in this regard. A proposition could be totally consistent given what information you have (such as the proposition that I went to the movies yesterday) while not being factually true (I did not go to the movies). We can judge inconsistency a priori (without experience), but we cannot judge factual truth without experience.

I believe those are minimum and sufficient articles of faith to be able to function as a human being.

This metaphysical base can be further developed in this psychological model:

(value) + (perceived event) -> (emotion)

For instance, if you value money, and perceive that someone stole your money, you'll be angry. The logic behind this is that anger is the emotion you feel when you realize that someone is attacking something that you care about. You can change your emotional state by changing your values and your perception of events. This is why my metaphysics has no place for emotions in its base. Emotions are a derived experience. Although we experience emotions, but do not direction experience values, values are actually at the base of the emotional control system used by both animals and humans.

An idea of free will can naturally be developed from this. Free will may be thought of as the ability to choose new values. Whether or not this process is in the end, deterministic, I do not address here. I think basically if a person believes in free will, he must believe in the supernatural. If he is a materialist, he cannot believe in free will. This is because if we are composed only of deterministic or random particles, then all of our behavior must be deterministic or random. This is assuming, of course, that free will is neither deterministic, nor random (neither a computer algorithm nor a die have free will).


So far as I can tell, ALL human experience can be composed of facts, reason, and values. I have drawn neat little venn-diagrams in the past to show this. Science is the combination of sensory experience (experimental data) and logic (math). Detective work is also composed of sense-data and logic. The difference between science and detective work is that science takes the sense-data for granted, and tries to work out what the logic that governs it is, whereas detective work goes in the other direction. Detective work takes scientific principles for granted, and uses them to try to figure out what historical events may have occurred. Math is just pure logic. Philosophy consists in assuming moral premises and applying logic to them. Game theory consists in assuming logical systems and deriving effective moral choices from them. Practical decisions consist primarily in knowing what one's values are, and in observing what the opportunities are in the sensory environment. Psychology may be thought of as observing outward behavior, and trying to derive inner structure (consisting largely of values) that describes that behavior.

We may also think of psychology/introspection (Christians ought to do this a lot) as "subjective science". This is because we try to understand and modify ourselves, but the sense-data that we use is subjective. It is subjective, because only we have access to our thoughts and feelings. It is just as real to us, however, as objective data that others can also see, such as what we see or hear. So, there is objective science, and there is subjective science. I think we ought to regard subjective science as being very important, while admitting that it must remain a largely private endeavor, since our experiences/techniques may often not be perfectly reproducible in any other person.

 

[BrendanG]

I read the page where you talked about propositional logic, 1st, 2nd, & higher order logic, & I was inspired to start learning about these things.

I watched a lecture yesterday on propositional logic (very similar to what I learned once about logic gates in electrical circuits).

I can now say:

L - I love my wife
C - I cheat on my wife
G - I am a good husband

(L AND NOT C) <---> G

So I have created one of my "value-bools". I think it ought to be possible to write more moral statements or even make moral proofs with this kind of language, but I am still trying to figure this out.

 

[Stephen3141]

(I am just surprised, that on a philosophical Christian apologetics site, no one seems to have any questions about formal logic.
On Protestant Fundamentalist sites, which are quite anti-intellectual, there are many responses to topics
dealing with logic. Although, many of them don't really deal with formal logic.)

 

[Stephen3141]

One of the early posts talks about a basis for ontology/epistomology. I believe I went further than anybody else ever has several years ago in this regard, but I never got anybody (except for one mathematician) to even look at what I wrote.

What I came up with, in summary:

I think Descartes's famous statement, "I think, therefore, I am," is incomplete. We are more than just logic, so basing a metaphysics on our ability to reason is insufficient to build a formal system which can describe all of our experiences. Also, unless you already trust your ability to reason, then his conclusion, "I am" does not follow the premise (because if you do not have faith in logic, then nothing can be derived from anything else).

I believe you need 3 minimum articles of faith to be able to function as a human:
1. Faith that your sensory experience tells you at least some true things about reality. We derive factual information (true/false) from sensory experience.
2. Faith that we have at least some ability to judge systems of logic to be consistent/inconsistent. We judge consistency/inconsistency according to our innate reason.*
3. We must have faith that it is possible to find values that make life seem meaningful and worth living.

*Note that facts and reason are very different in this regard. A proposition could be totally consistent given what information you have (such as the proposition that I went to the movies yesterday) while not being factually true (I did not go to the movies). We can judge inconsistency a priori (without experience), but we cannot judge factual truth without experience.

I believe those are minimum and sufficient articles of faith to be able to function as a human being.

This metaphysical base can be further developed in this psychological model:

(value) + (perceived event) -> (emotion)

For instance, if you value money, and perceive that someone stole your money, you'll be angry. The logic behind this is that anger is the emotion you feel when you realize that someone is attacking something that you care about. You can change your emotional state by changing your values and your perception of events. This is why my metaphysics has no place for emotions in its base. Emotions are a derived experience. Although we experience emotions, but do not direction experience values, values are actually at the base of the emotional control system used by both animals and humans.

An idea of free will can naturally be developed from this. Free will may be thought of as the ability to choose new values. Whether or not this process is in the end, deterministic, I do not address here. I think basically if a person believes in free will, he must believe in the supernatural. If he is a materialist, he cannot believe in free will. This is because if we are composed only of deterministic or random particles, then all of our behavior must be deterministic or random. This is assuming, of course, that free will is neither deterministic, nor random (neither a computer algorithm nor a die have free will).


So far as I can tell, ALL human experience can be composed of facts, reason, and values. I have drawn neat little venn-diagrams in the past to show this. Science is the combination of sensory experience (experimental data) and logic (math). Detective work is also composed of sense-data and logic. The difference between science and detective work is that science takes the sense-data for granted, and tries to work out what the logic that governs it is, whereas detective work goes in the other direction. Detective work takes scientific principles for granted, and uses them to try to figure out what historical events may have occurred. Math is just pure logic. Philosophy consists in assuming moral premises and applying logic to them. Game theory consists in assuming logical systems and deriving effective moral choices from them. Practical decisions consist primarily in knowing what one's values are, and in observing what the opportunities are in the sensory environment. Psychology may be thought of as observing outward behavior, and trying to derive inner structure (consisting largely of values) that describes that behavior.

We may also think of psychology/introspection (Christians ought to do this a lot) as "subjective science". This is because we try to understand and modify ourselves, but the sense-data that we use is subjective. It is subjective, because only we have access to our thoughts and feelings. It is just as real to us, however, as objective data that others can also see, such as what we see or hear. So, there is objective science, and there is subjective science. I think we ought to regard subjective science as being very important, while admitting that it must remain a largely private endeavor, since our experiences/techniques may often not be perfectly reproducible in any other person.

Brendan,
You're on the right track, in a number of ways.

(Note that I started another thread dealing with the initial premises of a formal logic proof.
Because I discovered that many Christians cannot tell the difference between basic
"philosophic" definitions, and coming up with initial premises for a proof. The other thread is called
"Formal Logic: Justifying that Initial premises are TRUE").

Descartes, in his famous quote, was trying to come up with a way to "justify"
his belief that he existed. "I think, therefore, I am."

This is part of what philosophers would call "basic" beliefs.
These are part of the philosophical discipline called Epistemology.
Some basic beliefs that most philosophers think are True, are:
My memories are evidence that some event actually happened
My senses, are basically accurate (there are exceptions)
Some basic truths can be accepted without rigorous proof, because they are "self-evident"

I go through some of the approaches of historical thinkers (in the other thread),
on "basic" beliefs.

Descartes was a "Hard Foundationalist". He thought that EVERY basic belief must
be rigorously proven (philosophers call this "justifying" that a belief is true).

Other historical thinkers think that the hard foundationalist demand can never
be met -- attempts lead to infinite regressions of trying to prove more and
more supporting beliefs to the original "basic" belief. These thinkers are
called Soft Foundationalists. They accept that basic beliefs can be thought
of as true, if they are self-evident.

During the European Enlightenment, thinkers struggled with what emphasis
their thinking (philosophy) should have. The Rationalists believed that logic was everything.
(The problem with saying THAT, is that we have senses, by which we sense evidence
from the world, and and all this is something other that thinking about a logical proof.)

Then there were the Empiricists. They emphasized that we myst have EVIDENCE for
everything that we try to justify as being true. They had the same problem, that
sensing the evidence, involves an operation upstream of USING the evidence.
---------- ----------

The approach that I take, is from a Christian worldview. I accept the picture of
"our shared reality" and the senses and thinking, that the Bible presents. The Bible
presents a lot of things as "self-evident", and so Christians should not think that
they have to "prove" all basic beliefs.

Emotions are difficult. We can train our emotions to respond in almost ANY way.
Intuitions, are not quite emotions, but they are "sorta" conclusions that we come
to, without going through formal logical reasoning. Intuitions can be very useful
as input evidence for out thinking.
---------- ----------

In the Formal Logic thread, I try to point out that in logic, we have
-- facts: these are beliefs that have been justified as True
-- rules: these are RELATIONSHIPS of causality, between propositions
-- the rules of inference: these preserve the truth in our initial
premises, and lead to valid and sound Conclusions (if we follow them).

---------- ----------

I have found, by reading a lot of arguments on Christian apologetics sites, that
most differences in Conclusions, are caused by differences in initial Premises
(definitions/facts, and rules/relationships). This is why I started the thread on
how to justify your initial Premises as True.

---------- ----------

Formal reasoning, and thinking about "basic" beliefs, is SO important for
Christians, that I decided to write a book about the topics. It will be
published (God willing) through Christian Faith Publishing, at the end of
the year or the beginning of 2024.

It would be very helpful for you to read a book on "symbolic logic",
which is what the universities currently call formal deductive logic.
It is not easy, but the discipline of learning how to code concepts
into formal logic, is an aerobic mental exercise.

Good luck, in your pursuit of thinking and finding truth.

(By the way, in the thread on justifying initial Premises of a proof, I
do a lot of quoting from books on Epistemology. Some readers here
are a bit paranoid that I am listed as "Catholic". But my quoting is
from (mostly) a professor of Philosophy at Wheaton College, in
a book published by InterVarsity Press. This is core "Evangelical"
thinking. But the thinking is the same for all the major Christian
groups, except the anti-intellectual ones (which includes the
Protestant Fundamentalists, and much of the younger generations
in America.)

Stephen Wuest
B.A. Classical languages and Literature
M.S. Computer Science, Artificial Intelligence