The primary question presented in this appeal is whether the district court erred in affirming the decision of the Secretary of the Department of Health and Human Services denying Terrón Hayes surviving child’s benefits under the Social Security Act. For the reasons stated below, we will affirm.

I

Nia J. Imani, also known as Ramona D. Hayes, filed an “Application for Surviving Child’s Insurance Benefits” with the Department of Health and Human Services (“Department”) on November 22, 1976, on behalf of her son, Terrón Hayes. Imani claimed that Terrón was the child of Terry Williams, the deceased wage earner, who died insured on November 4, 1972. After the Department denied her claim on March 18, 1977, she filed a “Request for Reconsid*509eration,” which was denied on September 26, 1978. In response to Imani’s timely request, a hearing was held before an Administrative Law Judge (“AU”) on December 18, 1978. Imani, who was represented by counsel, appeared and testified in support of her claim. In a decision dated March 6,1979, the AU concluded that Terrón was not entitled to surviving child’s insurance benefits on the social-security record of Terry Williams.

Pursuant to a court order in an unrelated case, the Department reexamined Imani’s original application and once again denied it in a notice dated April 14, 1982. Upon Imani’s request for reconsideration, the claim was again denied on June 21, 1982. Imani then sought another hearing before an AU, which was held on February 7, 1983. Imani, once again represented by counsel, appeared and testified in support of her application for Terrón. The evidence adduced at that proceeding may be outlined as follows:

Imani, then 17 years old, attended from May or June of 1972 to August of 1972, a college preparatory course in Jefferson City, Missouri. She testified that she had no sexual relations during that time. At the conclusion of the course, she returned to her parents’ home in Columbia, Missouri. Within a week of Imani’s return, Wanda Stapleton, a cousin and friend, introduced her to the wage earner, Terry Williams, then 21 years old. After two or three weeks, the relationship between Imani and Williams “sped up,” and they would meet and engage in sexual intercourse at the residence either of Ms. Stapleton or of Dáñese Williams. The latter was Imani’s sister and unrelated to Terry Williams. Imani testifies that she did not recall how many times she had sex with Williams, but eventually suggested that the number was either five or six. Their final liaison occurred on approximately October 21, 1972. Imani and Williams had a dispute at that time, because he would not take her to a movie, and she did not see him again before he was murdered on November 4, 1972.

Imani testified that she thought she might be pregnant in late October of 1972 and that, after a preliminary examination at a clinic, she called Williams two weeks before his death to discuss the matter with him. She underwent a second examination and was informed on November 3, 1972, that she was in fact pregnant. She was unable, however, to relate that information to Williams before he was shot to death on the following day. Imani claimed, nonetheless, that Williams “knew” he was the father. She also offered hearsay evidence in an attempt to prove that Williams had acknowledged to others that he would be a father. She could not, however, show that Williams was regularly providing her with funds, although he did occasionally purchase some beer and food for their dates. Nonetheless, she claimed that he gave Wanda Stapleton $10 to give to Imani to cover the costs of a pregnancy test.

Terrón Hayes was born on June 4, 1973, in Columbia, Missouri. The pregnancy was full-term, so that conception probably occurred in late August or early September of 1972. A comparison of the blood types of Imani and Williams does not exclude paternity, but also cannot conclusively determine it, because approximately 30% of the black males in the United States could have fathered a child with Terron’s blood type. Imani offered evidence concerning the statements and actions of third parties to support her claim that Williams was the father. She also produced photographs in an attempt to demonstrate a striking resemblance between her son and Williams. The AU, however, was not persuaded by the pictures, and Imani subsequently stated that Terrón resembled both of his parents.

In an exhaustive order dated June 17, 1983, the AU found that the child was not entitled to the benefits sought in the application filed in November of 1976. In support of this conclusion, he made the following findings:

1. Terrón Hayes is not the “child” of the wage earner under Missouri State *510law as required by Section 216(h)(2)(A) of the Social Security Act.

2. Terrón Hayes is not the “child” of the wage earner pursuant to Section 216(h)(2)(B) of the Social Security Act as his mother and the wage earner never went through a marriage ceremony.

3. Terrón Hayes is not the “child” of the wage earner pursuant to Section 216(h)(3)(C) of the Social Security Act as the evidence of record does not establish that the wage earner was ever decreed by a court to be his father, was ever ordered by a court to contribute to his support, or ever acknowledged him in writing. Furthermore, the evidence of record does not establish that the wage earner was his biological father or that the wage earner was either living with him or contributing to his support at the time of his death.

The order of the ALJ became the final decision of the Secretary when the Department’s Appeals Council denied the claimant’s request for review.

Imani commenced the instant action in federal district court pursuant to 42 U.S.C. § 405(g) for review of the Secretary’s decision. The case was referred to a magistrate, who stated in his extensive “report and recommended entry” that there was substantial evidence to support the findings of the Secretary, as the “totality of evidence” confirmed the administrative determination that Terrón Hayes was not the “child” of Terry Williams within the meaning of the Social Security Act. The district court adopted the magistrate’s report. This appeal followed.

II

Before turning to the substantive questions presented in this appeal, we must first articulate the applicable standard of review. Under 42 U.S.C. § 405(g), the Secretary’s findings are conclusive if they are supported by “substantial evidence.” This standard applies to the district court’s review of the Secretary’s decision as well as this court’s review of the district court’s decision. Schaefer v. Heckler, 792 F.2d 81, 84 (7th Cir. 1986). “Substantial evidence” is defined as that which “a reasonable mind might accept as adequate to support a conclusion.” Id. (quoting Richardson v. Perales, 402 U.S. 389, 401, 91 S.Ct. 1420, 1427, 28 L.Ed.2d 842 (1971)). We are not allowed to reappraise the record. Davis v. Califano, 603 F.2d 618, 625 (7th Cir. 1979). The “clearly erroneous” standard for review of a trial court’s factual findings under Fed.R.Civ.P. 52(a) does not apply, because the findings under consideration are those of the Secretary, not of the district court. Schmoll v. Harris, 636 F.2d 1146, 1150 (7th Cir. 1980). The Secretary’s conclusions of law are not entitled to such deference, however, and if the Secretary committed an error of law, reversal is required without regard to the volume of the evidence in support of the factual findings. Id.

Section 202(d)(1) of the Social Security Act (“Act”), codified as amended at 42 U.S.C. § 402(d)(1), establishes the criteria for entitlement to child’s insurance benefits. It provides that every “child,” as defined by 42 U.S.C. § 416(e), of an individual who dies fully or currently insured under the Act is entitled to these benefits if the child has applied for the benefits, is unmarried, under 18 years of age, and was dependent on the deceased individual at the time of the latter’s death.

Dependency is presumed for certain classes of children. See 42 U.S.C. § 402(d)(3). 42 U.S.C. § 416(h)(2) sets forth the rules for the determination of family status. Under § 416(h)(2)(A), benefits are available to those children who, under the substantive law of the insured decedent’s domicile, would be considered a child of the insured for the purposes of intestate succession. If the applicant fails to meet that requirement, he can under § 416(h)(2)(B) still demonstrate that he is entitled to benefits by showing that the insured participated in a marriage ceremony that would be valid but for a nonobvious defect. If the applicant cannot satisfy this requirement, he may under § 416(h)(3)(C)(i) prevail nonetheless if he shows that the *511insured had acknowledged in writing that the applicant was his child, that the insured had been decreed by a court to be the parent of the applicant, or that the insured had been ordered by a court to contribute to the support of the applicant because the applicant was the child of the insured. Finally, the applicant is entitled to benefits under § 416(h)(3)(C)(ii) if he shows “by evidence satisfactory to the Secretary” that the insured was the applicant’s parent and was either living with or contributing to the support of the applicant at the time of death.

It is undisputed that Imani and Williams never married and that Williams did not acknowledge in writing that Terrón was his child, was not found to be his father in paternity proceedings, and did not contribute to Terron’s support pursuant to a court order. Thus, Imani failed to demonstrate that her son was entitled to benefits under either § 416(h)(2)(B) or § 416(h)(3)(C)(i). Nonetheless, Imani argues that Terrón is entitled to benefits under § 416(h)(2)(A) (intestate succession) or § 416(h)(3)(C)(ii) (satisfactory evidence of paternity and proof of support from deceased).

Terry Williams was domiciled in the state of Missouri at the time of his death. Thus, under § 416(h)(2)(A), the Secretary must apply that state’s law of intestate succession to determine whether the applicant was the child of Williams. The pertinent statute is Mo.Rev.Stat. § 474.060(2) (1985),1 which provides in relevant part:

[A] person born out of wedlock is a child of the mother. That person is also a child of the father, if ...

(2) The paternity is established by an adjudication before the death of the father, or is established thereafter by clear and convincing proof____

“Clear and convincing proof” has been defined in the context of establishing illegitimacy as that which “leaves no room for doubt” and as requiring “a quantum of evidence such that no conclusion other than that of illegitimacy can be reached.” B.S.H. v. 613 S.W.2d 453, 457 (Mo. App. 1981). The burden of persuasion does not seem to be so severe when one seeks to establish paternity. Nonetheless, a recent Missouri decision suggests that the burden remains high under § 474.060(2), certainly higher than the preponderance standard. Estate of Pope v. Hook, 670 S.W.2d 943 (Mo.App. 1984); see also Greer by Greer v. Heckler, 756 F.2d 794 (10th Cir. 1985).2

Imani argues that she made out her case under Missouri law, and, therefore, that the Secretary’s decision was not supported by substantial evidence. The AU noted in his order that there was some evidence tending to support a finding that Williams was the claimant’s father. However, the AU also noted that there was evidence suggesting that Williams was not. This “negating” evidence did not directly refute paternity, but consisted of either inconclusive or inconsistent testimony. Hence, it is clear that, unless we impute an element of undeterminable, and thus unreviewable, irrationality to the administrative decision-making process, the AU must have discredited Imani’s testimony, although he did not expressly so state in his order.

*512There were inconsistencies in the record. Nonetheless, by its very nature, the relationship between Imani and Williams — even as she tells the story — was transitory, and it is obvious that neither had it in mind to establish by his conduct a record for a future paternity proceeding. Affairs of the heart are not ordinarily structured by the rules of evidence. In addition, their relationship occurred almost ten years before the second administrative hearing was held, so that many of the inconsistencies are consistent with failing memory, as well as fabrication.

However, that we might have reached a different conclusion does not mean that the AU reached the wrong one. He observed the witnesses directly, and those intangible, unarticulable elements that constitute “credibility” unfortunately leave no trace that can be discerned in this or any other transcript we must review. In a case such as this, where the physical evidence Imani offered in support of paternity was not persuasive and the traditional sources of proof were tragically foreclosed, credibility is crucial. Unless the AU’s assessment of the witnesses is patently wrong in view of the cold record before us, it must stand. After a thorough review of that record, we cannot say that the AU’s rejection of Imam’s story was incorrect. We are also not unmindful that this application for benefits has been considered and reconsidered several times and that Imani consistently failed to persuade both the Secretary and the district court. She has not argued that she was denied fair treatment in the processing of the application. In view of these considerations, we must then uphold the Secretary’s finding that Imani did not establish by clear and convincing evidence that Williams was the father of Terrón.

Imani refers us to several cases in which paternity was established. She claims that these decisions have fact patterns similar to the instant case and argues that they are controlling. That a description of the evidence presented in another case might bear a resemblance to that of the instant ease does not mean that we are bound by that decision. There are many reasons why an ostensible factual correspondence is not controlling. The dispositive factor here is that, although Imani made statements that would support the conclusion' that Williams was the father, the AU simply did not believe her. Because of that disbelief, this was a close case, and in close cases the Secretary prevails.

Imani also argues that she presented “evidence satisfactory to the Secretary” to show paternity and that she demonstrated that Williams was living with or contributing to the support of Terrón at the time of death, so that the requirements of § 416(h)(3)(C)(ii) were satisfied. Our discussion above regarding the failure of proof on the question of paternity under Missouri law should apply here also, because the AU indicated that, with reference to § 416(h)(3)(C)(ii), the record failed to show that Williams was the biological father. Thus, he apparently did not believe enough of Imani’s story to meet the less stringent burden of persuasion of § 416(h)(3)(C)(ii).3 As we noted above, we perceive no reason to disturb that credibility determination.

We do note that Imani takes issue with the requirements of § 416(h)(3)(C)(ii), and argues that they invest the Secretary with “unbridled discretion.” An objection to the *513latitude accorded an agency by statute, as opposed to regulation, is best addressed to the legislature. In any event, we need not extensively discuss the standard for determining paternity under that provision, because there is simply nothing in the record to support the second requirement of § 416(h)(3)(C)(ii), i.e., that Williams was either living with or contributing to the support of Terrón at the time of his death.

It is true that some adjustment to the manner of proving support should be made when the applicant is an illegitimate child born after his alleged father (especially one who was not regularly employed) dies. In such a case, the attention and support conferred upon the mother inures to the benefit of the fetus, and the Secretary should consider whether the alleged aid is commensurate with the needs of the unborn child at the time of the father’s demise. See Schaefer v. Heckler, 792 F.2d 81, 85-87 (7th Cir. 1986).

Nonetheless, as we noted in Schaefer, “in cases involving children born after or shortly before the wage earner’s death some tangible support is still required ...; a mere expectation of support from the insured wage earner is not enough.” Id., at 86. That conclusion is controlling here. Imani did not show that during the course of their brief relationship Williams was living with her or that he was supporting her. He apparently spent some money on beer and food when they were together, but to say that these expenditures satisfy § 416(h)(3)(C)(ii) means that courtship is tantamount to support, which, in view of the purposes of the Act, see Mathews v. Lucas, 427 U.S. 495, 507, 96 S.Ct. 2755, 2763, 49 L.Ed.2d 651 (1976), cannot be correct. Imani and Williams broke off their relationship and never saw each other again because Williams refused to take Imani out on a “regular” date and to pay for their entertainment. There was no statement in the record that he was unable on that occasion to provide the funds; the clear implication was that he simply did not want to.

Of course, that the father feels animosity or indifference towards the mother does not necessarily mean that he harbors similar feelings for the unborn child, and he could provide the mother with support that will indirectly benefit the fetus. However, according to Imani’s own testimony, Williams knew that she might be pregnant for two weeks before he died. Still, he did nothing for her, except (perhaps) provide, through a mutual friend, $10 for a pregnancy test. This ambiguous admission by conduct, especially in view of the other evidence in the record, cannot persuade us that the AU was wrong in concluding that Williams, at the time of his death, was not supporting Terrón. Thus, we affirm the finding that the support requirement of § 416(h)(3)(C)(ii) was not met.

One issue remains for our consideration. Imani argues that, because § 416(h) requires that certain illegitimate children affirmatively establish dependency while it affords other illegitimate children a presumption of dependency, the provision creates classifications that violate the equal-protection component of the Fifth Amendment’s due-process clause. This claim, however, is foreclosed by the Supreme Court’s decision in Mathews v. Lucas, 427 U.S. 495, 96 S.Ct. 2755, 49 L.Ed.2d 651 (1976), and merits no further discussion here.

Ill

For the reasons stated above, the judgment of the district court is Affirmed.