Logic supplement 3:
Credit to J Wagemans of the grandly-named "Periodic Table of Arguments". A modified version follows:
1. Unit: subject(a,b,c..) and predicate(x,y,z..)
Basic units are taken to be the linguistic subject and predicate of a sentence. The subject is what the sentence is about. The predicate is everything else that is about the subject of the sentence. In the sentence, "
the subject is what the sentence is about", the subject is underlined, and the predicate isn't. Another example. "
You are browsing thephilosophyforum.com." One last example. "Any
x subject does, can, or must, have y status relative to z system of y2 qualities". Computationally, this framework can admit strings of infinite length.
Sentence = Subject + Predicate
2. 'Id-op': 'is'(=) [or "do","can","will"(=)]
Next we define our operation of identity. At the formal level, this is just 'is'. Unfortunately natural language is multivalued and 'is' has many specific definitions. This is unhelpful. But as mentioned in my first post, discourse can be divided into descriptive, evaluative, and prescriptive claims in which people attribute a level of factivity to their claims which is supposed to carry their rhetorical force. Accordingly:
substance: attitude / reference / cognate
Is1: 'Descriptive' / Fact / "Do"
Is2: 'Evaluative' / Value / "Can"
Is3: 'Prescriptive' / Method / "Must"
In reality there are a limitless number of verbs that my be appropriated for formal use.
Determining attitude is obviously a subjective matter of interpretation that will relate to a personalized ontology. There is no real solution for 'correctly' pinning the correct attitude to the respective sentence. Intuition is involved, and this can be especially true when meaning shifts to what has not been said, as with speech acts, messages-by-omission, and whatever other interactive nuance that is partially obscured by the 'code of discourse'. My suggestion -- if in doubt, assume evaluation.
3. 'Prop': subject(a,b,c..) and 'is' and predicate(x,y,z..)
A proposition is a declarative sentence that can be true or false because it contains an 'is' with the following form:
As I would like propositions to become a universal unit of discourse I will define them no further, other than that they
must be true or false. A proposition that can bear no value is a sentence, not a proposition.
4. 'Di-op': 'because'(<),'therefore'(>) [or 'if-then'(>)]
The operation of direction indicates the causal, consequential, or relative direction of two propositions adjoined by a 'because' or similar cognate. 'Direction' is my nonstandard term that is just a general logical entailment as dictated by the grammar. Metaphysically, the direction always points away from the most original or prior epistemic source in the formula (or 'formulate').
Here is the definition of the classical conditional, 'therefore':
p q p>q
t t t
t f f
f t t
f f t
Which we can use to define a 'because':
p q p<q
t t t
f t f
t f t
f f t
We can define any operator we please by using a truth table to define the logical properties of the informative throughput. Tables like these define the basis of logical systems. If their functions are sufficiently complicated, and their definitions sufficiently well-defined, objects like these can constitute the basis of abstract machines.
5. 'Arg': proposition(p,q,r..) and 'because'(<) and proposition(p,q,r..)
Here are two generic forms of argument:
Argument = 'a is x' because 'a / x is b / y'
Argument = if 'a is x' then 'a / x is b / y'
Once we identify the two component propositions of the argument we're trying to analyze, whatever terms they have in common is the rhetorical action that links them and creates the force of the argument. By squaring and comparing the components we arrive at the following, where p means 'same proposition', p~= means 'different proposition', s= means 'same subject', and s~= means 'different subject':
s= s~=
p= Be1 Be2
p~= Be3 Be4
These are traditionally valid arguments:
Be2 in which two subjects are linked to a single predicate. a=x<a=y. ('Placing').
Be3 in which two predicates are linked to a single subject. a=x<b=x. ('Classing').
These are traditionally invalid arguments:
Be1 in which propositions are linked to themselves or virtually equivalent propositions. a=x<a=x.
Be4 in which propositions have no obvious link. a=x<b=y.
Although we can make them valid with:
Be5 in which propositions are linked to themselves or virtually equivalent propositions but are also linked to 'is true'. a=x<a=x=y. ('Sensing').
Be6 in which propositions have no obvious link but are each also linked to 'is true'. a=x=z<b=y=z. ('Fielding').
Hence:
form: formula / formulate / cognate
Be5: 'a=x<a=x=y' / If subject1 is predicate1 then subject1 is predicate1 (is predicate3) / "Sense"
Be2: 'a=x<a=y' / If subject1 is predicate1 then subject1 is predicate2 / "Place"
Be3: 'a=x<b=x' / If subject1 is predicate1 then subject2 is predicate1 / "Class"
Be6: 'a=x=z<b=y=z' / If subject1 is predicate1 (is predicate3) then subject2 is predicate2 (is predicate3) / "Field"
Again, in all of these arguments, "(is predicate3)" stands for "is true", and 'true' can be any arbitrary value.
6. List of sample arguments
In Wagemans' original framework, a list of prototypal arguments is given as follows:
A majore (greater to lesser) A minore (lesser to greater) Ad baculum (force) Ad carotam (coax) Ad hominem Ad populum Axiologic argument (value) Case to case Deontic argument (duty) Ethotic argument (personal credibility) From analogy From authority From beauty From cause From character From commitment From comparison From consistency From correlation From criterion (ie. metalinguistic eg. definitions) From disjunctives From effect From emotion From evaluation From example From genus From opposites From parallel From sign From similarity From standard From tradition From utility Petitio principii (circularity) Pragmatic argument (convenience-practicality).
How these arguments have been chosen and why they have their factive properties is not explained. Originally they're given a more structured form, where individual propositions have individual factivities. Here they're presented in a more leniant, linear form. The difference is that in my framework, whole sentences are given a factivity in order to facilitate greater interpretive flexibility.
7. Args by validity/form:
So then, a small miracle happens and then arguments can be ranked according to distinct criteria as pertaining to subject-predicate relations:
- Be5 a is x because a is x is y: authority,character,populum / utility,beauty / baculum,carotam / character,ethotic,hominem / emotion.
- Be2 a is x because a is y: cause,correlation,effect,sign / criterion / axiology,standard / pragmatic / deontic,evaluation.
- Be3 a is x because b is x: case,example,genus,similarity / analogy,majore,minore / parallel / comparison.
- Be6 a is x because b is y: consistency / disjunctives,principii,opposites / tradition.
8. Args by identity/substance:
Or graded according to the more indistinct and personal criteria mentioned at the start:
- Pure fact: cause,correlation,effect,sign / case,example,genus,similarity.
- Mixed fact: authority,commitment,populum / criterion / parallel / consistency.
- Pure value: / beauty,utility / axiologic,standard / analogy,majore,minore / disjunctives,principii,oppositions.
- Mixed value: authority,baculum,carotam,character,commitment,ethotic,hominem,populum / evaluation,deontic.
- Pure method: emotion / comparison.
- Mixed method: baculum,carotam,character,ethotic,hominem / deontic,evaluation / parallel / consistency.
It's possible to conjecture that the game of factivity ends when a disputant successfully changes the acceptability of their thesis using a sequence of dialectical moves in which a value is transformed, ultimately via a chain of analogies that may take minutes or decades, into an accepted fact or into an accepted method. Whatever evidence is available to a disputant will not in itself persuade without an explanatory
logos relating the object of dispute to the
situation of dispute. However, any given situation is a dynamic object that is constantly undergoing change, meaning that, as I mentioned, any given logical endeavor is also a
logistical endeavor.
Analysis of individual arguments and why they have their factive properties is something that is possible, though I will leave this aside as there is enough literature on the topic. Presumably, all that remains is a list of universal objects along with their representative factivites that settles the ontological details and fixes the objective criteria about which an argument is supposed to be about.
:)