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- 1. © Art Traynor 2011
Logic
Nomenclature
Definitions
Logic
The field of inquiry ( discipline/science )
which evaluates arguments
Argument
A Set of Statements
composed of a Conclusion
and evidentiary Premises
from which it is claimed to logically follow
Statement
A declarative sentence ( a sentence which declares a Fact )
that is either True or False
but not both
Truth Value
The attribute by which a statement can be evaluated
to be either True or False
Sometimes “proposition”
“ that ” something is the case….
Purports to demonstrate a conclusion
on the basis of evidence
Hurley Section 1.1, ( Pgs. 1 – 2 )
A system of inquiry addressed to
gauging the validity of Arguments
Wiki: “ Logic ”
“ Inquiry ” because Logic is
a process directed toward
discovery
“ Expression ” and “ Statement ” are
essentially synonymous , with
“ Expression ” preferred in Symbolic
Logic contexts
The terms “ Fact ” , “ Information ” ,
or sometimes “ Meaning ” are
synonymous in this context
The Expression or Statement
encodes a “ Fact ” or “ Information ”
- 2. © Art Traynor 2011
Logic
Nomenclature
Definitions
Hurley Section 1.1, ( Pg. 5 )
As in Inferential Nexus ( InfNex )
Inference
A process of Reason
supplying the Structure
by which the Validity
of an Argument or Conditional Statement
can be gauged
That component of a Statement
encoding Information
about which a Truth Value can be ascertained
Proposition
“ Expression ” and “ Statement ” are
essentially synonymous , with
“ Expression ” preferred in Symbolic
Logic contexts
The terms “ Fact ” , “ Information ” ,
or sometimes “ Meaning ” are
synonymous in this context
The Expression or Statement
encodes a “ Fact ” or “ Information ”
- 3. © Art Traynor 2011
Logic
Argument
Definition
Argument
A prefatory composition
of Propositions ( i.e. Declarative Statements ) ,
or Premises ,
the Truth Value of which can be reckoned ,
and by which the application of Inference
will permit a Conclusion to be gauged
Wiki: “ Argument ”
A group of Statements
the Conclusion of which
is claimed to follow from its Premises
“ that ” something is the case….
Purports to demonstrate a conclusion
on the basis of evidence
Hurley Section 1.1, ( Pgs. 2 – 3 )
An Argument expresses an Inference
in a special way, in terms of one or
more premises that present Evidence
and a Conclusion that is claimed to
follow from that Evidence.
Hurley Section 1.2, ( Pg. 15 )
An Inferential Nexus ( InfNex )
- 4. © Art Traynor 2011
Logic
Argument
Statements
Argument
A group of Statements
the Conclusion of which
is claimed to follow from its Premises “ that ” something is the case….
Purports to demonstrate a conclusion
on the basis of evidence
Premises
One or more Statements
asserted as Evidence
Conclusion
A singular Statement
from which the Premises
are asserted to follow
Hurley Section 1.1, ( Pgs. 2 – 3 )
Follow: to implicate with Necessity
Argument
conclusion
statement
statement
statement
premises
statement
- 5. © Art Traynor 2011
Logic
Statement
Premise
Argument
A group of Statements
the Conclusion of which
is claimed to follow from its Premises “ that ” something is the case….
Purports to demonstrate a conclusion
on the basis of evidence
Premises
One or more Statements
asserted as Evidence
Hurley Section 1.1, ( Pgs. 2 – 3 )
Argument
statement
statement
statement
premises
May be inferred from…
Seeing that…
For the reason that…
Inasmuch as…
As indicated by…
Premise Indicators
Given that…
Since…
Owing to…
Because…
In that…
For…
As…
- 6. © Art Traynor 2011
Logic
Statement
Conclusion
Argument
A group of Statements
the Conclusion of which
is claimed to follow from its Premises “ that ” something is the case….
Purports to demonstrate a conclusion
on the basis of evidence
Premises
One or more Statements
asserted as Evidence
Conclusion
A singular Statement
from which the Premises
are asserted to follow
Hurley Section 1.1, ( Pgs. 2 – 3 )
Argument
conclusion
statement
statement
statement
premises
statement
We may conclude…
It follows that…
It must be that…
We may infer…
Consequently…
Conclusion Indicators
Accordingly…
Therefore…
Implies that…
Wherefore…
As a result…
Whence…
Hence…
Thus…
So…
- 7. © Art Traynor 2011
Logic
Reason
Definition
Reason
A process of Inquiry
may be discovered and Evaluated
Wiki: “ Reason ”
populating an Ontological System ( OntSys ) or Set
“ Inquiry ” because Reason
is a process directed
toward discovery
Akin to an Algebra
by which Relations
between Class Equivalent Elements
“ Evaluate ” to reduce an
indeterminant to determinacy
Etymology
λóγος or “ logos ” , is the root of the English word “ Logic ” which also had a
connotation of “ speech ” or “ explanation ” or an “ account ” ( as of money )
Translated into Latin as “ ratio ” , from which its synonymous correspondence
with “ Rationality ” emerged
There is thus a pleasing sense in which Rationality or Reason connotes
the abstract evaluation of Ratios or Proportions
nn
- 8. © Art Traynor 2011
Logic
Reason
Definition
Reason
A process of Inquiry
may be discovered and Evaluated
Wiki: “ Reason ”
populating an Ontological System ( OntSys ) or Set
“ Inquiry ” because Reason
is a process directed
toward discovery
Akin to an Algebra
by which Relations
between Class Equivalent Elements
“ Evaluate ” to reduce an
indeterminant to determinacy
Domain of Discourse
Whereas Logic lies within Reason ,
Reason unconstrained by Logic supplies extra-logical processes of Inquiry
Skipping Steps
Working Backward
Diagraming
Exemplifying ( Exampling or Modeling )
Axiom Transformation ( changing the Laws of Composition – LOC’s )
Processes that lie outside of
the OntSys and Logic
- 9. © Art Traynor 2011
Logic
Reason
Logic
Logic Wiki: “ Reason ”
which evaluates arguments Hurley Section 1.1, ( Pgs. 1 – 2 )
A system of inquiry addressed to
gauging the validity of
Arguments
Wiki: “ Logic ”
“ Inquiry ” because Reason
is a process directed
toward discovery
The field of Inquiry ( discipline/science )
That species of Reason
which is applied within an Ontological System ( OntSys )
Inference Hurley Section 1.1, ( Pg. 5 )
A process of Reason
supplying the Structure
by which the Validity
of an Argument or Conditional Statement
can be gauged
Wiki: “ Logic ”
Observation Hurley Section 1.1, ( Pg. 5 )
A process of Reason
applied to a Phenomenological System ( PhenSys )
by which the state of that system
can be characteristically quantified
Wiki: “ Logic ”
Good PhenSys make Good Neighbors
A PhenSys is thus a
subspecies of an OntSys
- 10. © Art Traynor 2011
Logic
Reason
Logic
Logic Wiki: “ Reason ”
which evaluates arguments Hurley Section 1.1, ( Pgs. 1 – 2 )
A system of inquiry addressed to
gauging the validity of
Arguments
Wiki: “ Logic ”
“ Inquiry ” because Reason
is a process directed
toward discovery
The field of Inquiry ( discipline/science )
That species of Reason
which is applied within an Ontological System ( OntSys )
- 11. © Art Traynor 2011
Logic
Reason
Statement
Proposition
Hurley Section 1.1, ( Pg. 5 )
“ Expression ” and “ Statement ” are
essentially synonymous , with
“ Expression ” preferred in Symbolic
Logic contexts
A single Statement or expression can
exhibit more than one Proposition…
a Compound Proposition
A Declarative Expression
That component of a Statement
asserting a Fact
the Truth Value of which can be ascertained
encoding a Fact
about which a Truth Value can be ascertained
Identical Information can be expressed in a multiplicity of Statements
A single Statement may express a multiplicity of Propositions
The terms “ Fact ” , “ Information ” ,
or sometimes “ Meaning ” are
synonymous in this context
The Expression or Statement
encodes a “ Fact ” or “ Information ”
ExpressionStatement ↔
Proposition
Information
- 12. © Art Traynor 2011
Logic
384 – 322 B.C.
History
Milestones
Aristotle
Syllogistic Logic
279 – 206 B.C.
Crysippus
Propositional Logic
Co-Founder of Stoic
School of Philosophy
129 – 199 A.D.
Galen
Compound Categorical
Syllogistic Logic
480 – 524
Boethius
Commentator on
Aristotle & Crysippus
1079 – 1142
Peter Abelard
Theory of Universals
Mental Constructs v. Platonic Forms
Formal Validity v. Content Validity
1285 – 1349
William of Occam
Modal Logic Comprising
Possibility, Necessity,
Belief, Doubt
Metalanguage & Linguistics
1646 – 1716
Gottfried William Leibniz
Symbolic Logic
1781 – 1848
Bernard Bolzano
Expanded Leibniz’s
Symbolization of Logic
1806 – 1871
1815 – 1864
George Boole
Symbolic Logic
Augustus DeMorgan
Symbolic Logic
1835 – 1882
William Stanley Jevons
Symbolic Logic
1834 – 1923
John Venn
Symbolic Logic
Hurley Section 1.1, ( Pgs. 5 – 7 )
1806 – 1871
1806 – 1873
John Stuart Mill
Inductive Logic
Gottlob Frege
Symbolic Logic
1861 – 1947
Alfred North Whitehead
Betrand Russell
Mathematical Logic
1872 – 1970
- 13. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators
2 Form of Argumentation
3 Character of the Link between Premise & Conclusion
Evaluate ASC Satisfaction: Argument or Non-Argument
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Do we have an Argument ?
Deductive or Inductive
If we have an Argument, what Form does it assume ?
Inferential Morphism: G ⋀ P ↔ P ⋀ G
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Evaluation Standards
- 14. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators Evaluate ASC Satisfaction: Argument or Non-Argument
Do we have an Argument ?
Argument
A group of Statements
the Conclusion of which
is claimed to follow from its Premises
Premises
Conclusion
Hurley Section 1.1, ( Pgs. 2 – 3 )
Is understood to assert a Claim
Explicit : often preceded by an Indicator word
Implicit : can be rendered explicit
by restatement including an Indicator
Tantamount to the grammatical test
for the object of a (transitive) Verb
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
- 15. © Art Traynor 2011
Logic
Non-Arguments
Taxonomy
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 11 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Warning
Advice
Belief / Opinion
Description
Report
Exposition
Illustration
Conditional
Explanation
- 16. © Art Traynor 2011
Logic
Non-Arguments
Warning
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 11 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Warning
A proto-command or precautionary statement
tantamount to a claim lacking evidence
to which a progression of consequence is minimally implicit Wiki: “ Precautionary Statement ”
Warning…
Notice…
Danger…
Caution…
Hazard…
Warning Indicia
- 17. © Art Traynor 2011
Logic
Non-Arguments
Advice
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 11 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Advice
A proto-conditional
tantamount to a claim lacking evidence
to which a progression of consequence is explicitly asserted
Advise…
Invite…
Suggest…
Prefer…
Recommend…
Advice Indicia
Consider…
- 18. © Art Traynor 2011
Logic
Non-Arguments
Belief or Opinion
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 12 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Belief / Opinion
Assertion of a Conclusion
in the absence of Evidentiary Premises
about which a Truth Value might be ascertained
Believe…
Offer…
Trust…
Aver…
Vouchsafe…
Belief / Opinion Indicia
Suspect…
- 19. © Art Traynor 2011
Logic
Non-Arguments
Description
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 12 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Description
A Set of Statements
in which the Evidentiary Premises
are merely evocative ( as of imagery )
and which fail to assert a Conclusion
for which a Truth Value might be ascertained
Imagine…
Picture…
Descriptive Indicia
One of the four Rhetorical Modes
or Modes of Discourse
- 20. © Art Traynor 2011
Logic
Non-Arguments
Report
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 12 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Report
A Set of Statements
with otherwise well-formed Premises ,
tantamount to a congeries of information
about which a Truth Value can indeed be ascertained ,
but which however fails to include a Conclusion
Concerning…
Rumored…
Reportorial Indicia
Authorities…
Participants…
Beware of Reports about
Arguments !
- 21. © Art Traynor 2011
Logic
Non-Arguments
Exposition
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 12 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Exposition
A Set of Statements
typically commencing with a well formed opening ,
satisfying the evidentiary requirement of a proper Premise ,
but which then merely expands, elaborates,
or offers supplemental evidence to an implied ,
or previously established Conclusion
Moreover…
Furthermore…
Expository Indicia
Nevertheless…
In addition to which…
One of the four Rhetorical Modes
or Modes of Discourse
A Logical Conjunction ,
akin to “ And ”
- 22. © Art Traynor 2011
Logic
Non-Arguments
Illustration
Argument Recognition
An Argument can be difficult to recognize
Hurley Section 1.2, ( Pg. 12 )
The presence of Indicators
does not necessarily render a Set of Statements into an Argument
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Akin to Equivalence Classes
Illustration
A Set of Statements
in which the Evidentiary Premises
are a congeries of existential instantiations
exemplifying the Conclusion
which however fail to satisfy a Proof of the Proposition
Illustrating…
Defining…
Illustrative Indicia
Showing…
For example…
For all…
There exists…
- 23. © Art Traynor 2011
Logic
Conditional Statement
A two-part Statement wherein
an Antecedent Proposition, prefaced typically by “ if ”
inferentially posits a Consequent Proposition , prefaced typically by “ then ”
If antecedent then consequent
consequent if antecedent
Hurley Section 1.2, ( Pg. 14 )
In an Argument a True Conclusion is
Inferred to follow from True Premises, yet
in a Conditional neither the Antecedent nor
the Consequent are necessarily True
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
can be characterized into distinct classifications
Conditional
Not equivalent to an Argumentnn
Does not necessarily posit a Causal Relationship between propositionso
Asserts no pretense of Evidence or Truth Value of propositionso
Posits an Inference between Propositionso
Non-Arguments
Conditional Structure Criteria ( CSC )
1. Antecedent proto-Premises
And an Inferentially connected
A Set of Statements composed of
2. Consequent
Of no particular Truth Value
The Inferential content of a Conditional may be restated to satisfy ASCo
- 24. © Art Traynor 2011
Logic
Conditional Statement
Hurley Section 1.2, ( Pg. 14 )
Akin to an Existential Instantiation
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
Conditional
Not equivalent to an Argumentnn
Non-Arguments
Conditional Structure Criteria ( CSC )
1. Antecedent proto-Premises
And an Inferentially connected
A Set of Statements composed of
2. Consequent
Of no particular Truth Value
Sufficiencynn
A Condition “ A ” is a Sufficiency if some
Condition “ B ” may arise in its presence ,
but not exclusively so
Akin to an Independent Variable
Necessitynn
Conjunctive Necessity & Sufficiencynn
A Condition “ A ” is a Necessity if some
Condition “ B ” may not arise in its absence
Sufficient But Not Necessaryo
Sufficient And Necessaryo
- 25. © Art Traynor 2011
Logic
Conditional Statement
Hurley Section 1.2, ( Pg. 16 )
Akin to an Existential Instantiation
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
Conditional
Not equivalent to an Argumentnn
Non-Arguments
Conditional Structure Criteria ( CSC )
1. Antecedent proto-Premises
And an Inferentially connected
A Set of Statements composed of
2. Consequent
Of no particular Truth Value
Sufficiencynn
Akin to an Independent Variable
Necessitynn
Conjunctive Sufficiency & Necessitynn
Sufficient But Not Necessaryo
Sufficient And Necessaryo
Condition “ B ” may arise in the presence of “ A ” ,
but not exclusively so
Condition “ B ” may not arise in the absence of “ A ”
On closer inspection the Conjunction
is superfluous…Necessity certainly
entails Sufficiency ( redundant )
whereas Sufficiency is something
far less restrictive than Necessity
“ A ” is not the only thing that might
occasion “ B ”
No “ A ” … No “ B ”
- 26. © Art Traynor 2011
Logic
Explanation
“why” something is the case…
Non-Arguments
Hurley Section 1.2, ( Pg. 17 )
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
can be characterized into distinct classifications
A group of Statements, comprised of at least two salients
purporting to describe or otherwise account for an event or phenomena
Explanation
The Explandum , describing the event or phenomenann
The Explanans , providing the causal or precipitating conditionsnn
Not asserting to offer proof, as in argument
Argument Explanation
conclusion explanandum
more
obvious
less
obvious
less
obvious
more
obvious
proof elucidation
An Argument however may also
serve as an Explanation answering
“ why ” something is the case as well
as offering proof that it is the case…
Explanation + Proof = Argument
- 27. © Art Traynor 2011
Logic
Explanation
“why” something is the case…
Non-Arguments
Hurley Section 1.2, ( Pg. 17 )
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
can be characterized into distinct classifications
A species of proto-Argument
Explanation
Like Conditionals , an Explanation proceeds by Inferencenn
Where the Explanans exhibit proof the Explanation will satisfy ASCnn
i.e. : Explanation + Proof = Argument
Problematic Indicatorsnn
Becauseo
May ambiguously preface either a Premise or an Explanans
Thuso
May ambiguously preface either an Conclusion or an Illustration
- 28. © Art Traynor 2011
Logic
Explanation
“why” something is the case…
Non-Arguments
Hurley Section 1.2, ( Pg. 17 )
Argument Recognition
An Argument can be difficult to recognize
Non-Arguments ( NonArg )
can be characterized into distinct classifications
A species of proto-Argument
Explanation
Like Conditionals , an Explanation proceeds by Inferencenn
Where the Explanans exhibit proof the Explanation will satisfy ASCnn
i.e. : Explanation + Proof = Argument
Problematic Indicatorsnn
Sinceo
Promise to Preface your Premise…
In its Temporal sense is merely a species of narrative ( i.e. Report ? )
In its Logical sense it can preface a Premise
- 29. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators
2 Form of Argumentation
Evaluate ASC Satisfaction: Argument or Non-Argument
Do we have an Argument ?
Deductive or Inductive
If we have an Argument, what Form does it assume ?
Deduction
Induction
Evaluation Standards
- 30. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
That a Conclusion does not follow with Necessity from the Premises
does not conclusively indicate that an Argument is Inductive
It could be a poorly executed Deductive Argument
Necessarily…
Certainly…
Deductive Indicia
Absolutely…
Definitely…
Problematic Indicatorsnn
Musto
Can ambiguously indicate either Probability or Necessity
- 31. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Necessarily…
Certainly…
Deductive Indicia
Absolutely…
Definitely…
Morphism
The Aristotelian convention holds that Deduction
proceeds canonically from Generalized class Premises to a
Conclusion directed toward Particular class elements
General → Particular
General → General
Particular → Particular
Deduction
conclusion
statement
statement
statement
premises
statement
General
Particular
This need not necessarily be the case as it is valid for the
argument to assume the following alternate Morphisms
Canonic
Particular → General
This is easy to recall as “ Deduct ”
suggests a subtractive morphism
- 32. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Necessarily…
Certainly…
Deductive Indicia
Absolutely…
Definitely…
Form
Certain Formal constructions indicate Class inclusion in Deduction
Mathematics
Definitions
Categorical Syllogism
Hypothetical Syllogism
Disjunctive Syllogism
Deduction
conclusion
statement
statement
statement
premises
statement
General
Particular
- 33. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Necessarily…
Certainly…
Deductive Indicia
Absolutely…
Definitely…
Form
Certain Formal constructions indicate Class inclusion in Deduction
1 Mathematics
Exclusive of subject matter lodged in Probability Theorynn
Beware of the inaptly named “ Mathematical Induction ”
it is in point of fact Deductive
nn
- 34. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Defined…
Means…
Definitional Indicia
Connotes…
Tantamount…
Form
Certain Formal constructions indicate Class inclusion in Deduction
2 Definitions
Identifies the Term by non-tautological correspondencesnn
Isolates the Term as a proper subset from its constituent correspondencesnn
Terminologynn
Examplesnn
Maximal parsimonyo
Maximal syntactic generalityo
Trivialo
Superficialo
- 35. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
All…
No…
C-Syll Indicia
Some…
Form
Certain Formal constructions indicate Class inclusion in Deduction
3 Categorical Syllogism
All professors are academicians
Syllogism Structure Criteria ( SSC )
1. Exactly two Premises
And
An Argument consisting of exactly
2. A singular Conclusion
Example:
No academicians are headhunters
Therefore , no professors are headhunters conclusion
premises
Essentially a notion of
Transitivity
- 36. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Form
Certain Formal constructions indicate Class inclusion in Deduction
4 Hypothetical Syllogism
If Tony is convicted of a felony,
then he will go to jail
Syllogism Structure Criteria ( SSC )
1. Exactly two Premises
And
An Argument consisting of exactly
2. A singular Conclusion
Example:
If he goes to jail,
then his wife will divorce him
Therefore , if Tony is convicted of a felony ,
then his wife will divorce him
conclusion
premises
Essentially a notion of
Transitivity
A Syllogism wherein the Premises include a Conditional
- 37. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.2, ( Pg. 25 )
Deduction
An Argument is Valid
only if its Conclusion follows Necessarily
from its Premises
Nothing to do with Taxes !
Presuming the Truth of the Premises ,
it is impossible for the Conclusion to not be True
Either…
Or…
Dj-Syll Indicia
Form
Certain Formal constructions indicate Class inclusion in Deduction
5 Disjunctive Syllogism
Either the battery is charged
or the car won’t start
Syllogism Structure Criteria ( SSC )
1. Exactly two Premises
And
An Argument consisting of exactly
2. A singular Conclusion
Example:
The battery is not charged
Therefore , the car won’t start conclusion
premises
Essentially a notion of
Transitivity
A Syllogism wherein the Premises include a Disjunction
- 38. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators
2 Form of Argumentation
Evaluate ASC Satisfaction: Argument or Non-Argument
Do we have an Argument ?
Deductive or Inductive
If we have an Argument, what Form does it assume ?
Deduction
Induction
- 39. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.3, ( Pg. 25 & 27 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude…
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
Induction has been conventionally ( i.e. historically )
regarded to proceed from Particular Premises to a
more generalized Conclusion
The Conclusion Content conspires to “ go beyond ”
the Premises Content
- 40. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.3, ( Pg. 25 & 27 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude…
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
Morphism
The Aristotelian convention holds that Induction proceeds canon-
ically from Particularized class Premises to a Conclusion directed
toward the entirety of the Generalized class elements or Set
This need not necessarily be the case as it is valid for the
argument to assume the following alternate Morphisms
Particular → General
General → General
Particular → Particular
Canonic
General → Particular
- 41. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 26 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
Prediction
Analogy
Inductive Generalization
Authority
Signs
Casual Inference
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 42. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
1 Prediction
Premises assert Temporal Claims
about the state of an Ontological system
nn
Conclusion avers a speculative Claim about the
resulting state of the Ontological system at
some point ensuing
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 43. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
1 Prediction
There is an implicit Claim that the state of an
Ontological system is parameterized by time
nn
The Claim however is not deterministic and thus
its Truth Value is necessarily associated with a
Probability distribution
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 44. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
2 Analogy
Premises assert a Claim of Similarity
( i.e. Congruence ? ) between one
Ontological system ( OntSys ) and another
nn
The Analogy is implicitly postulated to obtain
from a Claim about a better known Ontsys
exhibiting a similar Claim about a less
familiar OntSys
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 45. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
2 Analogy
Premises assert a Claim of Similarity
( i.e. Congruence ? ) between one
Ontological system ( OntSys ) and another
nn
Conclusion avers a speculative Inference about
the consequent claim of the lesser known
OntSys by reference to the consequent claim of
the better-known OnsSys
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 46. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
3 Inductive Generalization
Premises assert Claims about a Quantitative or
Qualitative state of some attribute characteristic
of a sample or Subset of an OntSys
nn
The inductive proposition suggests that the pre-
valence or state of this characteristic attribute in
the sample or Subset will exhibit in similar
fashion in some larger population or Superset of
the Ontsys toward which the Claim is directed
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 47. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
3 Inductive Generalization
Premises assert Claims about a Quantitative or
Qualitative state of some attribute characteristic
of a sample or Subset of an OntSys
nn
Conclusion avers a speculative Inference that
some larger universe or Superset populating the
sample or Subset will exhibit the characteristic
attribute in similar fashion in that larger Set
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 48. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
4 Authority
Premises assert Claims arising from the expertise
of a learned or informed figure or found in a
canonical text addressing the OntSys
nn
Conclusion avers a speculative Inference that the
validity of the resulting claim is thus free from
mistake , error , or prevarication
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 49. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
5 Signs
Premises assert a Claim arising from the
declarative or admonitory exhortation of a
symbolic representation
nn
A “sign” is not usually produced by the
phenomena it signifies
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 50. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
5 Signs
Premises assert a Claim arising from the
declarative or admonitory exhortation of a
symbolic representation
nn
Conclusion avers a speculative Inference urging
as an advisory or precaution that certain action
be taken or avoided
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 51. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
6 Causality
Premises assert a Claim proceeding from
knowledge of a Cause to knowledge of its
Effects or vice-versa
nn
Sometimes conflated with Arguments based on
Signs , as an Effect can often be interpreted as
a “sign” of a Cause…
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
An Effect , unlike a Sign , is evolved from its correlative cause
( i.e. a Sign does not produce an effect )
nn
- 52. © Art Traynor 2011
Logic
Taxonomy
Arguments
Hurley Section 1.2, ( Pg. 28 )
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Presuming the Truth of the Premises ,
it is possible , but not probable that the Conclusion is not True
Probable…
Improbable…
Inductive Indicia
Plausible…
Implausible…
Likely…
Unlikely…
Reasonable to conclude… Form
Certain Formal constructions indicate Class inclusion in Induction
6 Causality
Premises assert a Claim proceeding from
knowledge of a Cause to knowledge of its
Effects or vice-versa
nn
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
Conclusion avers a speculative Inference positing
a nexus between Cause and Effect that is less
than wholly deterministic
nn
- 53. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators
2 Form of Argumentation
3 Character of the Link between Premise & Conclusion
Evaluate ASC Satisfaction: Argument or Non-Argument
Do we have an Argument ?
Deductive or Inductive
If we have an Argument, what Form does it assume ?
Inferential Morphism: G ⋀ P ↔ P ⋀ G
Morphism
General → General
Particular → Particular
General → Particular
Particular → General
- 54. © Art Traynor 2011
Logic
Classification Criteria
Arguments
Classification Criteria
1 Indicators
2 Form of Argumentation
3 Character of the Link between Premise & Conclusion
Evaluate ASC Satisfaction: Argument or Non-Argument
Do we have an Argument ?
Deductive or Inductive
If we have an Argument, what Form does it assume ?
Inferential Morphism: G ⋀ P ↔ P ⋀ G
Morphism
Particular → General
General → General
Particular → Particular
General → Particular
- 55. © Art Traynor 2011
Logic
Statement
Arguments
Hurley Section 1.3, ( Pg. 25 & 27 )Quantification
Addresses the inherent Cardinality of An
Argument is Valid
if its Conclusion follows with Probability
from its Premises
A Statement that asserts a Claim about one or
more members of a Class or Elements of a Set
Particular Statement
A Statement that asserts a Claim about every or
all members of a Class or Elements of a Set
General Statement
- 56. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 34 )Validity
Every Deductive Argument is either
Valid or Invalid
An Argument in which the Conclusion
follows necessarily from the Premises
If the Premises are assumed True , it is
impossible that the Conclusion be false
An Invalid Deductive Argument is thus one in which the
Conclusion does not follow with necessity from the premises
If the Premises are assumed True , it is
possible that the Conclusion be false
There is thus no middle ground between Validity and Invalidity A Binary State
There are no Arguments that are “ almost ” Valid or Invalid
- 57. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 34 )Validity
Every Deductive Argument is either
Valid or Invalid
There is thus no middle ground between Validity and Invalidity A Binary State
There are no Arguments that are “ almost ” Valid or Invalid
There is only an indirect relation between Validity and Truth
If the Premises
are assumed True ,
the Conclusion is True
on the basis of that assumption alone !
For an Argument to be Valid it is not necessary that either the
Premises or the Conclusion be True !
It is sufficient for Validity to obtain
merely IF the Premises
are assumed True ,
the Conclusion is rendered True on the basis of that assumption alone !
- 58. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 34 )Validity
Every Deductive Argument is either
Valid or Invalid
There is thus no middle ground between Validity and Invalidity A Binary State
There are no Arguments that are “ almost ” Valid or Invalid
There is only an indirect relation between Validity and Truth
For an Argument to be Valid it is not necessary that either the
Premises or the Conclusion be True !
Just as a False Premise and a False Conclusion does not preclude Validity ,
so too a True Premise and True Conclusion does not vouchsafe Validity !
The probative test for Validity is that the Conclusion
follow with Necessity from the Premises
If it is possible that the Conclusion may be False , a
Deductive Argument fails Validity
- 59. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 34 )Validity
Every Deductive Argument is either
Valid or Invalid
There is thus no middle ground between Validity and Invalidity A Binary State
There are no Arguments that are “ almost ” Valid or Invalid
There is only an indirect relation between Validity and Truth
For an Argument to be Valid it is not necessary that either the
Premises or the Conclusion be True !
Just as a False Premise and a False Conclusion does not preclude Validity ,
so too a True Premise and True Conclusion does not vouchsafe Validity !
The Truth Value of the Premises and Conclusion thus tell us nothing ,
cannot tell us anything , about the Validity of a Deductive Argument
Any Deductive Argument exhibiting True Premises
and a False Conclusion is thus necessarily Invalid
- 60. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Every Deductive Argument is either
Valid or Invalid
Premises Conclusion
T T
T F
Validity
F T
F F
?
Invalid
?
?
Soundness
A Deductive Argument that is Valid and exhibits True Premises
is regarded as a Sound Argument
In the absence of the satisfaction of these two conjunctive
conditions the Deductive Argument is rendered Unsound
- 61. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Every Deductive Argument is either
Valid or Invalid
Soundness
A Deductive Argument that is Valid and exhibits True Premises
is regarded as a Sound Argument
In the absence of the satisfaction of these two conjunctive
conditions a Deductive Argument is rendered Unsound
All the Premises must be True
Satisfying ASC , a Sound Argument will always feature
a True Conclusion
Deductive Argument
Structure Criteria ( DASC )
1. If the Premises are assumed True
Then
An Argument ( Satisfying ASC )
for which
2. The Conclusion follows Necessarily
A Sound Argument is a species of
Argument featuring additional
structure… i.e.: True Premises
Sound Argument = Valid Argument + True Premises
The Deductive analogue of a
Cogent Inductive Argument
- 62. © Art Traynor 2011
Logic
Induction
Arguments
Hurley Section 1.4, ( Pg. 36 )Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Strong Inductive Argument
The Conclusion follows with probability presuming True premises
The relative Strength of an
Inductive Argument is
thus not a Binary State ,
but more akin to a
continuum
Induction
( Strong )
conclusion
True
True premises
True ?Probable
This barrel contains 100 apples
Example:
Eighty apples randomly
chosen were confirmed ripe
Therefore , probably all 100
apples are ripe
Particular
General
- 63. © Art Traynor 2011
Logic
Induction
Arguments
Hurley Section 1.4, ( Pg. 36 )Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Weak Inductive Argument
The Conclusion does not follow with probability
presuming True premises
The relative Strength of an
Inductive Argument is
thus not a Binary State ,
but more akin to a
continuum
Induction
( Weak )
conclusion
True
True premises
True ?Not
Probable
This barrel contains 100 apples
Example:
Three apples randomly
chosen were confirmed ripe
Therefore , probably all 100
apples are ripe
Particular
General
- 64. © Art Traynor 2011
Logic
Induction
Arguments
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Inductive Arguments can be strengthened or
weakened by modifications to their Premises
Strength or Weakness are only indirectly
related to Truth and Falsity
Induction
( Less Weak )
statement
Induction
( Weak )
True
True
True ?Not
Probable
Induction
( Less Strong )
statement
Induction
( Strong )
True
True
True ?Probable
Probable
True ? True ?
True
True
True
True
Not
Probable
- 65. © Art Traynor 2011
Logic
Induction
Arguments
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Example:
This barrel contains 100 apples
Eighty apples randomly
chosen were confirmed ripe
Therefore , probably all
100 apples are ripe
This barrel contains 100 apples
Eighty apples randomly
chosen were confirmed ripe
Therefore , probably all
100 apples are ripe
Induction
( Less Strong )
statement
Induction
( Strong )
True
True
True ?Probable
Probable
True ?
True
True
One unripe apple found
earlier had been removed
Inductive Arguments can be strengthened or weakened
by modifications to their Premises
- 66. © Art Traynor 2011
Logic
Induction
Arguments
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Example:
Of the many U.S. Presidents
Therefore , probably the next American
President will be a Federalist
Induction
( Strong )
False
False
False ?Probable
Strength or Weakness are only indirectly related to
Truth and Falsity
The vast majority have been
Federalists
conclusion
premises
A Strong IA ( SIA ) cannot
render a Conclusion
probably True
If these False Premises
however were considered
True , a True Conclusion
may probably follow
- 67. © Art Traynor 2011
Logic
Induction
Arguments
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Example:
During the past fifty years
Therefore , industrial productivity will
probably increase in the years ahead
Strength or Weakness are only indirectly related to
Truth and Falsity
Inflation has consistently reduced
the value of the American dollar
conclusion
premises
Induction
( Weak )
True
True
True ?Not
Probable
The Truth of the Premises
and probable Conclusion
cannot render a weak IA
( WIA ) Strong
- 68. © Art Traynor 2011
Logic
Induction
Arguments
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
Induction
( Weak )
True
True
False ?Not
Probable
Any SIA featuring True
Premises but with a
probably False
Conclusion is Ipso Facto
rendered into a WIA
Strong Inductive Argument ( SIA )
The Conclusion follows with probability presuming True premises
Weak Inductive Argument ( WIA )
The Conclusion does not follow with probability presuming True premises
Inductive Arguments can be strengthened or weakened
by modifications to their Premises
Strength or Weakness are only indirectly related to
Truth and Falsity
- 69. © Art Traynor 2011
Logic
Induction
Arguments
Hurley Section 1.4, ( Pg. 36 )Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
The Conclusion follows with probability presuming True premises
The Conclusion does not follow with probability presuming True premises
The relative Strength of an
Inductive Argument is
thus not a Binary State ,
but more akin to a
continuum
Inductive Arguments can be strengthened or weakened
by modifications to their Premises
Strength or Weakness are only indirectly related to
Truth and Falsity
Strong Inductive Argument ( SIA )
Weak Inductive Argument ( WIA )
- 70. © Art Traynor 2011
Logic
Induction
Arguments
Hurley Section 1.4, ( Pg. 36 )Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
The relative Strength of an
Inductive Argument is
thus not a Binary State ,
but more akin to a
continuum
Strength or Weakness are only indirectly related to
Truth and Falsity
Induction
conclusion
statement
statement
statement
premises
statement
Particular
General
- 71. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 38 )
Premises Conclusion
T Probably T
T
Validity
F
F
?
Weak
?
?
Probably F
Probably T
Probably F
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
Inductive Arguments are either Strong or Weak
The relative Strength of an
Inductive Argument is
thus not a Binary State ,
but more akin to a
continuum
Strength or Weakness are only indirectly related to
Truth and Falsity
- 72. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 38 )
Cogency
A Inductive Argument that is Strong and exhibits True Premises
is regarded as a Cogent Argument
In the absence of the satisfaction of these two conjunctive
conditions an Inductive Argument is rendered Uncogent
All the Premises must be True
Satisfying ASC , a Cogent Argument will always feature
a Conclusion that is True with Probablity
Inductive Argument
Structure Criteria ( IASC )
1. If the Premises are assumed True
Then
An Argument ( Satisfying ASC )
for which
2. The Conclusion Probably follows
A Cogent IA ( CIA ) is a species
of Argument featuring additional
structure… i.e.: True Premises
Cogent Argument = Strong Argument + True Premises
Induction
An Argument is Valid
if its Conclusion follows with Probability
from its Premises
The Inductive analogue of a
Sound Deductive Argument
- 73. © Art Traynor 2011
Logic
Classification
Arguments
Hurley Section 1.4, ( Pg. 38 )
Statements Deductive Arguments
FalseTrue
Truth Value
InvalidValid
Validity
Unsound
Sound Unsound
Inductive Arguments
WeakStrong
Strength
Uncogent
Cogent Uncogent
- 74. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The validity of an Argument arises from the Form or Structure of the Argument
The Argument is valid because of the way in which the terms of the Premises are arranged
We can substitute any terms we choose in the form of the argument and obtain a Valid Argumentnn
Depending on what terms we substitute for “ A ” , “ B ” , and “ C ”
the Conclusion will sometimes evaluate to True or False truth values
nn
Example:
All Adlers are Bobkins
Therefore , all Adlers are Crockers
All Bobkins are Crockers
conclusion
premises All A are B
All B are C
All A are CParticular
Essentially Transitive!
General
Valid
Deduction
- 75. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The validity of an Argument arises from the Form or Structure of the Argument
The Argument is valid because of the way in which the terms of the Premises are arranged
We can substitute any terms we choose in the form of the argument and obtain a Valid Argumentnn
Nevertheless if we assume the Premises True we obtain a True Conclusionnn
Example:
All Adlers are Bobkins
Therefore , all Adlers are Crockers
All Bobkins are Crockers
conclusion
premises All A are B
All B are C
All A are CParticular
Validity is not affected
by Truth !
General
Valid
Deduction
- 76. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The validity of an Argument arises from the Form or Structure of the Argument
The Argument is valid because of the way in which the terms of the Premises are arranged
We can substitute any terms we choose in the form of the argument and obtain a Valid Argumentnn
A False Conclusion however can never arise from True Premises
within an otherwise Valid form
nn
Example:
All Adlers are Bobkins
Therefore , all Adlers are Crockers
All Bobkins are Crockers
conclusion
premises All A are B
All B are C
All A are CParticular
Validity is not affected
by Truth !
General
Valid
Deduction
- 77. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Premises Conclusion
T T
T F
Validity
F T
F F
V
I
V
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Validitynn
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
Deductive Argument
Structure Criteria ( DASC )
1. If the Premises are assumed True
Then
An Argument ( Satisfying ASC )
for which
2. The Conclusion follows Necessarily
A Sound Argument is a species of
Argument featuring additional
structure… i.e.: True Premises
V
- 78. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The validity of an Argument arises from the Form or Structure of the Argument
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Example:
All Adlers are Bobkins
Therefore , all Adlers are Crockers
All Crockers are Bobkins
conclusion
premises All A are B
All C are B
All A are CParticular
The Form fails
Transitivity…
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
Validity is not
Commutative…
General
Invalid
Deduction
- 79. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Example:
conclusion
premises All A are B
All C are B
All A are CParticular
The Form fails
Transitivity…
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
Validity is not
Commutative…
This is problematic however because it is mathematically valid !
All Adlers are Bobkins
Therefore , all Adlers are Crockers
All Crockers are Bobkins
General
Invalid
Deduction
- 80. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Example:
All Cats are Animals
Therefore , all Cats are Dogs
All Dogs are Animals
conclusion
premises All C are A
All D are A
All C are D
General
Particular
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
This substitution however yields a manifestly False Conclusion
The Class Equivalency here
is valid by Union but does
not obtain as Intersection
Invalid
Deduction
- 81. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Example:
All Cats are Animals
Therefore , all Cats are Earthlings
All Animals are Earthlings
conclusion
premises All C are A
All A are E
All C are EParticular
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
Class Equivalency is somehow implicated in the Argument Form
General
Valid
Deduction
- 82. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Premises Conclusion
T T
T F
Validity
F T
F F
I
I
I
I
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
The possibility of Invalidity
violates the DASC
Deductive Argument
Structure Criteria
Validate or Vitiate
Invalid
Deduction
All A are B
All C are B
All A are CParticular
General
- 83. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Premises Conclusion
T T
T F
Validity
F T
F F
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
Deductive Argument
Structure Criteria ( DASC )
1. If the Premises are assumed True
Then
An Argument ( Satisfying ASC )
for which
2. The Conclusion follows Necessarily
A Sound Argument is a species of
Argument featuring additional
structure… i.e.: True Premises
I
I
I
I
- 84. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Premises Conclusion
T T
T F
Validity
F T
F F
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
The mere arrangement of terms can render a Valid form Invalid …o
If we assume the Premises True , it is not Necessarily the case
that the Conclusion is True !
o
I
I
I
I
An Argument is Invalid if and only if its form allows for a substitution instance having
True Premises and a False Conclusion
- 85. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.4, ( Pg. 36 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
If an Argument is Invalid, it will exhibit an Invalid Form ( e.g. Formally Invalid )o
However if the Form is Invalid (e.g. Formally Invalid ) , there is at least one
conjunctive Substitution instance featuring True Premises and False Conclusion
o
An Argument is Invalid if and only if its form allows for a substitution instance having
True Premises and a False Conclusion
Premises Conclusion
T T
T F
Validity
F T
F F
I
I
I
I
- 86. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
If an Argument is Invalid, it will exhibit an Invalid Form ( e.g. Formally Invalid )o
However if the Form is Invalid (e.g. Formally Invalid ) , there is at least one
conjunctive Substitution instance featuring True Premises and False Conclusion
o
An Argument is Invalid if and only if its form allows for a substitution instance having
True Premises and a False Conclusion
Otherwise every substitution featuring True Premises would exhibit a True
Conclusion , as required by the Valid Deductive Argument ( VDA ) form
o
Conversely if a substitution were to yield an Argument featuring True
Premises and exhibiting a False Conclusion , that substitution violates
VDA Structure Criteria ( VDASC ) and is thus evaluates Invalid
- 87. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Otherwise every substitution featuring True Premises would exhibit a True
Conclusion , as required by the Valid Deductive Argument ( VDA ) form
o
Conversely if a substitution were to yield an Argument featuring True
Premises and exhibiting a False Conclusion , that substitution violates
VDA Structure Criteria ( VDASC ) and is thus evaluates Invalid
This constructive Invalidation of an otherwise Valid Deductive form admits
an alternate, direct definition of Invalidity ( i.e. a means to Prove Invalidity )
Counter Example Method ( CEM )o
The Argument is thus Proven Invalid !
A Deductive form of Argumentation is Isolated – Evaluated by Inspection
A Substitution is constructed featuring True Premises and a False Conclusion
- 88. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 45 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
The Argument is thus Proven Invalid !
A Deductive form of Argumentation is Isolated – Evaluated by Inspection
A Substitution is constructed featuring True Premises and a False Conclusion
Example:
Since some employees
are not social climbers
We may conclude that some VP’s
are not Social Climbers
And all Vice Presidents
are Employees
conclusion
premises
→
Some E are not S
Therefore Some V are not S
All V are E
- 89. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
The Argument is thus Proven Invalid !
A Deductive form of Argumentation is Isolated – Evaluated by Inspection
A Substitution is constructed featuring True Premises and a False Conclusion
Example:
conclusion
premises
→
Some E are not S
Therefore Some V are not S
All V are E
All V are E
Therefore Some V are not S
Some E are not S
BUT…Some E not S are Not V
i.e. We lose some “ E ”
along the way here…
i.e. There are some “ E ”
that are “ Not S ” and
“ Not V ”
- 90. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 45 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Example:
conclusion
premises
→
Some Animals are not Mammals
Therefore Some Dogs are not Mammals
All Dogs are Animals
E = Animals
S = Mammals
V = Dogs
Particular
General
Invalid Categorical Syllogism
- 91. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 45 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Example:
conclusion
premises
Some Animals are not Mammals
Therefore Some Dogs are not Mammals
All Dogs are Animals
Particular
General
Invalid Deductive Argument
1. True Premises
2. False Conclusion
Invalid Categorical Syllogism
- 92. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 46 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Example:
conclusion
premises
→
If the Government imposes import restrictions
Therefore since the Government will not
impose import Restrictions
( then ) the price of Automobiles will rise
If G then P
Not G
Therefore, not P
Particular
General
Invalid Hypothetical Syllogism
It follows that the price of Automobiles
will not rise
This is an Invalid Deductive Argument ( IDA )
because the price of Automobiles may rise
notwithstanding Government inaction
- 93. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 46 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Example:
conclusion
premises
→
If G then P
Therefore , not P
Not G
If G then P
Not G
Therefore, not P
Particular
General
Invalid Hypothetical Syllogism This is an Invalid Deductive Argument ( IDA )
because the price of Automobiles may rise
notwithstanding Government inaction
- 94. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 46 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Example:
conclusion
premises→
If Abraham committed suicide,
Therefore , Abraham Lincoln is not Dead
Then Abraham Lincoln is dead
G = Abraham Lincoln committed suicide
P = Abraham Lincoln is dead
Particular
General
Invalid Hypothetical Syllogism This is an Invalid Deductive Argument ( IDA )
because the price of Automobiles may rise
notwithstanding Government inaction
Abraham Lincoln did not commit suicide
- 95. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 46 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
conclusion
premises
If the Government imposes import restrictions
Therefore since the Government will not
impose import Restrictions
( then ) the price of Automobiles will rise
Particular
General
Invalid Hypothetical Syllogism
It follows that the price of Automobiles
will not rise
The Form of the Argument is revealed
by substitution ( i.e. Counter Example )
to be invalid – one exhibiting True
Premises and a False Conclusion
If Abraham committed suicide,
Therefore , Abraham Lincoln is not dead
Then Abraham Lincoln is dead
Abraham Lincoln did not commit suicide
↔
- 96. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 46 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
conclusion
premises
If the Government imposes import restrictions
Therefore since the Government will not
impose import Restrictions
( then ) the price of Automobiles will rise
Particular
General
Invalid Hypothetical Syllogism
It follows that the price of Automobiles
will not rise
Applying CEM to a Conditional, it is best
to construct a Substitution expressing a
Necessary hypothetical nexus: e.g. as
between suicide and death
If Abraham committed suicide ,
Therefore , Abraham Lincoln is not dead
Then Abraham Lincoln is dead
Abraham Lincoln did not commit suicide
↔
- 97. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Only useful for Proving Arguments Invalid
The only arrangement of Truth & Falsity that Proves anything in
Deductive Argumentation is True Premises with a False Conclusion
Premises Conclusion
T T
T F
Validity
F T
F F
V
I
V
V
- 98. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Invaliditynn
Counter Example Method ( CEM )o
Only applicable to Deductive Argumentation
Only useful for Proving Arguments Invalid
A VDA featuring True Premises and a True Conclusion Proves nothing
The only arrangement of Truth & Falsity that Proves anything in
Deductive Argumentation is True Premises with a False Conclusion
The relative Strength or Weakness of Inductive Argumentation is only
tenuously dependent on the Form of the Argument
No method that relates exclusively to the form of an Inductive Argument
can be used to prove the Argument Weak
- 99. © Art Traynor 2011
Logic
Deduction
Arguments
Hurley Section 1.5, ( Pg. 42 )Validity
Every Deductive Argument is either Valid or Invalid
The validity of an argument has nothing to do with its specific subject matter
The Argument is valid because of the way in which the terms of the Premises are arranged
Formal Validitynn
For a Deductive Argument, Subject Matter is irrelevant to a determination of Validity
Deductive Argument Form
InvalidValid
Subject MatterIrrelevant Germaine
- 100. © Art Traynor 2011
Logic
Extended Arguments
Arguments
Hurley Section 1.6, ( Pg. 49 )Extended Arguments ( ExArg )
A composite Argument, satisfying ASC comprised of :
one or more Standards of Evaluation , ( i.e. Deduction and/or Induction )
and possibly featuring numerous Non-Arguments ( NonArg )
The process by which extraneous subject matter is eliminated from the ExArg ,
and Premises and a Conclusion are isolated / identified
Warning
Advice
Non-Arguments
Belief / Opinion
Description
Report
Exposition
Illustration
Conditional
Explanation
Hurley Section 1.2, ( Pg. 25 )
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Hurley Section 1.2, ( Pgs. 11 – 18 )
Logical Analysis
A Conclusory Statement must be associated
in a well-ordered fashion
to its Premises
by positing its Inferential Nexus ( InfNex )
- 101. © Art Traynor 2011
Logic
Extended Arguments
Arguments
Hurley Section 1.6, ( Pg. 49 )Extended Arguments ( ExArg )
A composite Argument, satisfying ASC comprised of :
one or more Standards of Evaluation , ( i.e. Deduction and/or Induction )
and possibly featuring numerous Non-Arguments ( NonArg )
Warning
Advice
Non-Arguments
Belief / Opinion
Description
Report
Exposition
Illustration
Conditional
Explanation
Hurley Section 1.2, ( Pg. 25 )
Argument Structure Criteria ( ASC )
1. Evidentiary Premises
And
A Set of Statements composed of
2. A single Conclusion
Arising Logically from the
Premises
Hurley Section 1.2, ( Pgs. 11 – 18 )
Logical Analysis
Inferential Nexus ( InfNex )
Vertical Inferential Nexus ( VIN )nn
Horizontal Inferential Nexus ( HIN )nn
The process by which extraneous subject matter is eliminated from the ExArg ,
and Premises and a Conclusion are isolated / identified
- 102. © Art Traynor 2011
Logic
Extended Arguments
Arguments
Hurley Section 1.6, ( Pg. 49 )Extended Arguments ( ExArg )
A composite Argument, satisfying ASC comprised of :
one or more Standards of Evaluation , ( i.e. Deduction and/or Induction )
and possibly featuring numerous Non-Arguments ( NonArg )
Warning
Advice
Non-Arguments
Belief / Opinion
Description
Report
Exposition
Illustration
Conditional
Explanation
Hurley Section 1.2, ( Pgs. 11 – 18 )
Logical Analysis
Inferential Nexus ( InfNex )
Vertical Inferential Nexus ( VIN )nn
The process by which extraneous subject matter is eliminated from the ExArg ,
and Premises and a Conclusion are isolated / identified
conclusion
premises
The contamination of underground aquifers
represents a pollution problem
of catastrophic proportions
Half the nation’s drinking water ,
which comes from these aquifers ,
is being poisoned by chemical wastes
dumped into the soil for generations
↔
1
2
[ if ] Half the nation’s drinking water ,
comes from aquifers ,
being poisoned by chemical wastes
dumped into the soil for generations
2
[ Then ] contamination of underground aquifers
represents a pollution problem
of catastrophic proportions
1
- 103. © Art Traynor 2011
Logic
Extended Arguments
Arguments
Hurley Section 1.6, ( Pg. 49 )Extended Arguments ( ExArg )
A composite Argument, satisfying ASC comprised of :
one or more Standards of Evaluation , ( i.e. Deduction and/or Induction )
and possibly featuring numerous Non-Arguments ( NonArg )
Warning
Advice
Non-Arguments
Belief / Opinion
Description
Report
Exposition
Illustration
Conditional
Explanation
Hurley Section 1.2, ( Pgs. 11 – 18 )
Logical Analysis
Inferential Nexus ( InfNex )
Vertical Inferential Nexus ( VIN )nn
The process by which extraneous subject matter is eliminated from the ExArg ,
and Premises and a Conclusion are isolated / identified
conclusion
premises
↔
[ if ] Half the nation’s drinking water ,
comes from aquifers ,
being poisoned by chemical wastes
dumped into the soil for generations
2
[ Then ] contamination of underground aquifers
represents a pollution problem
of catastrophic proportions
1
2
1
Inferential Nexus ( InfNex )