qproj design docsPTA worked example: Aristotle on the motion of the earth
Worked PTA analysis of pta-test document ex03, on Aristotle’s reading. The passage is from Finocchiaro’s translation of Galileo.
Text
Who is so blind as not to see that the parts of the element earth and of the element water, being heavy bodies, move naturally downwards, namely toward the center of the universe, assigned by nature herself as the goal and end of straight downward motion… Since this can be seen clearly, and since we are sure that the same holds for the whole as for the parts, must we not conclude that the natural motion of the [whole globe] earth is straight toward the center…?
Reading
Aristotle’s, not Galileo’s. “Downwards” means toward the center of the universe, and the passage argues that the whole earth moves there: the geocentric thesis. The website follows Galileo’s critique, reading “the center” as the center of the earth, which makes the conclusion incoherent (and drops T2 and T5 below).
How it was decomposed
Working principles, ours rather than ATIP’s (ATIP types one triad at a time):
- Read the author charitably: the reading the author intends.
- One triad per reason-giving construction (“because”, “since”, “so”, “must we not conclude”, participles like “being”, appositions like “namely”).
- A stated generalisation linking two statements is a lever candidate before a premise candidate.
- Every statement that is argued for gets its own triad.
- Add implicit statements only where a triad can’t be canonicalized without them.
Structure
flowchart BT S2["S2 · heavy bodies move downwards<br/>(implicit)"] -- premise --> T1((T1)) S1["S1 · the parts are heavy bodies"] -- lever --> T1 T1 -- conclusion --> S3["S3 · the parts move downwards"] S3 -- premise --> T2((T2)) S4["S4 · downward motion is motion<br/>toward the center of the universe"] -- lever --> T2 T2 -- conclusion --> S5["S5 · the parts move toward<br/>the center of the universe"] S9["S9 · nature herself assigned that goal"] -- premise --> T5((T5)) T5 -- conclusion --> S4 S6["S6 · this can be seen clearly"] -- premise --> T3((T3)) T3 -- conclusion --> S5 S5 -- premise --> T4((T4)) S7["S7 · what holds for the parts<br/>holds for the whole"] -- lever --> T4 T4 -- conclusion --> S8["S8 · the whole earth moves toward<br/>the center of the universe"]
Five triads in one chain: T1 → T2 → T4, with T3 backing T2’s conclusion and T5 backing T2’s lever. Three levers (S1, S4, S7) are stated in the text; one of them (S4) is itself argued for.
Step 2 decisions
- Rhetorical questions become assertions. “Who is so blind as not to see that q” → q. “Must we not conclude that r” → r.
- Illocutive markers are stripped. “we are sure that” is the arguer’s stance, not part of S7.
- “downwards” and “toward the center of the universe” are kept apart. Merging them would hide T2, which is the contested step.
- “the whole earth” is universal (u), not singular (s): it stands for all its parts taken together.
Statements
S1:
span: "being heavy bodies"
subj: the parts of the element earth and of the element water
pred: are heavy bodies
role: lever of T1
S2:
span: zero-width, after "heavy bodies"
implicit: true
subj: heavy bodies
pred: move naturally downwards
role: premise of T1
S3:
span: "the parts of the element earth and of the element water, being heavy bodies, move naturally downwards"
subj: the parts of the element earth and of the element water
pred: move naturally downwards
role: conclusion of T1, premise of T2
S4:
span: "downwards, namely toward the center of the universe"
subj: downward motion
pred: is motion toward the center of the universe
role: lever of T2, conclusion of T5
S5:
span: "the parts of the element earth and of the element water … move naturally downwards, namely toward the center of the universe"
subj: the parts of the element earth and of the element water
pred: move naturally toward the center of the universe
role: conclusion of T2 and T3, premise of T4
S6:
span: "this can be seen clearly"
subj: this [= S5]
pred: can be seen clearly
role: premise of T3
S7:
span: "the same holds for the whole as for the parts"
subj: what holds for the parts
pred: holds for the whole
role: lever of T4
note: '"we are sure that" stripped as an illocutive marker'
S8:
span: "the natural motion of the [whole globe] earth is straight toward the center"
subj: the whole earth
pred: moves naturally toward the center of the universe
role: conclusion of T4
S9:
span: "assigned by nature herself as the goal and end of straight downward motion"
subj: that downward motion is motion toward the center of the universe [= S4]
pred: has been assigned by nature herself
role: premise of T5Triads
T1:
anchor: "being"
formula: "S3 ∵ S2 [L: S1]"
canonicalization: >
the parts of earth and water move naturally downwards
BECAUSE heavy bodies move naturally downwards
subjects:
delta: false
equal: false
reason: '"the parts of earth and water" != "heavy bodies"'
predicates:
equal: true
reason: '"move naturally downwards" == "move naturally downwards"'
form: beta
substance: "β pu"
substance_reason: >
conclusion: the parts of earth and water are some heavy bodies (p);
premise: heavy bodies in general (u)
lever: GENUS
lever_statement: S1
classification: "β pu G"
reconstruction: >
'the parts of earth and water move naturally downwards'
BECAUSE 'the parts of earth and water belong to the GENUS of heavy bodies'
AND 'heavy bodies move naturally downwards'
confidence: medium
note: >
The classic syllogism. If read as "all the parts" (u), the substance is uu,
where GENUS isn't listed: novel.
T2:
anchor: "namely"
formula: "S5 ∵ S3 [L: S4]"
canonicalization: >
the parts of earth and water move naturally toward the center of the universe
BECAUSE the parts of earth and water move naturally downwards
subjects:
delta: false
equal: true
reason: '"the parts of earth and water" == "the parts of earth and water"'
predicates:
equal: false
reason: '"move toward the center of the universe" != "move downwards"'
form: alpha
substance: "α FF"
substance_reason: both predicates are checkable claims about motion
lever: novel
lever_statement: S4
lever_written_out: "Y (moving downwards) is IDENTICAL to X (moving toward the center of the universe)"
classification: "α FF novel"
reconstruction: >
'the parts of earth and water move naturally toward the center of the universe'
BECAUSE 'moving downwards IS moving toward the center of the universe'
AND 'the parts of earth and water move naturally downwards'
confidence: medium
note: >
The contested step: it identifies "down" with "toward the center of the
universe". A definitional lever between two factual predicates; the PTA
lists DEFINITION only under VF. Either a gap in the table or a step 2
decision presented as an argument.
T3:
anchor: "Since" (the first one)
formula: "S5 ∵ S6"
canonicalization: >
that the parts of earth and water move naturally toward the center of the
universe (q) [is acceptable (A)] BECAUSE q can be seen clearly
subjects:
delta: true
reason: '"this" = S5: the premise is about the claim as a whole'
form: delta
substance: "δ II"
substance_reason: >
the source of "can be seen clearly" is anyone who looks, including the
addressee ("who is so blind as not to see"); no listed II lever fits
lever: novel
lever_written_out: "Z (being plainly visible) is a PERCEPTUAL GUARANTEE for A"
classification: "δ II novel"
confidence: low
note: >
An appeal to obviousness. "Who is so blind" also jabs at anyone who denies
q (ad hominem, δ II H), but that lever concludes U about an opponent's
view, not A about q.
T4:
anchor: "must we not conclude"
formula: "S8 ∵ S5 [L: S7]"
canonicalization: >
the whole earth moves naturally toward the center of the universe
BECAUSE the parts of earth and water move naturally toward the center of the universe
subjects:
delta: false
equal: false
reason: '"the whole earth" != "the parts of earth and water"'
predicates:
equal: true
reason: '"moves toward the center of the universe" == "move toward the center of the universe"'
form: beta
substance: "β uu"
substance_reason: >
conclusion: the whole earth as all its parts together (u);
premise: all the parts (u)
lever: COMPOSED
lever_statement: S7
classification: "β uu Cpo"
reconstruction: >
'the whole earth moves naturally toward the center of the universe'
BECAUSE 'the whole earth is COMPOSED of the parts of earth and water,
and what holds for the parts holds for the whole'
AND 'the parts of earth and water move naturally toward the center of the universe'
confidence: high
note: >
S7 states the lever's general principle; the composition fact ("the earth
is composed of earth and water") is implicit, recorded here rather than
as a statement. Same type as the website's, on a different reading.
T5:
anchor: "assigned by"
formula: "S4 ∵ S9"
canonicalization: >
THE PROPOSITION 'downward motion is motion toward the center of the universe' (q)
[IS ACCEPTABLE (A)] BECAUSE q has been assigned by nature herself
subjects:
delta: true
reason: 'S9 is about S4 as a whole: where the claim comes from'
form: delta
substance: "δ III"
substance_reason: nature is a third party, and the source Aristotle defers to
lever: EPISTEMICALLY AUTHORITATIVE
classification: "δ III Exp"
reconstruction: >
THE PROPOSITION 'downward motion is motion toward the center of the universe'
IS ACCEPTABLE BECAUSE 'nature is EPISTEMICALLY AUTHORITATIVE about motion'
AND 'nature herself has assigned it so'
confidence: medium
note: >
Supports T2's lever: the lever recursion the PTA singles out. "Herself"
marks nature as the source. If Exp is a stretch, novel: "Z is NATURALLY
AUTHORITATIVE for A". Alternative reading: α FF Cau, nature's assigned goal
as the final cause of the motion.Labelling in INCEpTION
Only T4 has a website answer (β uu Cpo, on Galileo’s reading).